[Kumar*, 5(3): March, 2016] ISSN: (I2OR), Publication Impact Factor: 3.785
|
|
- Brianna Campbell
- 5 years ago
- Views:
Transcription
1 [Kumar*, 5(3): March, 016] ISSN: (IOR), Publcaton Impact Factor: IJESRT INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY ANALYSIS OF VIBRATION DAMPING IN PROPELLER SHAFT USING VISCOELASTIC POLYMERS J.Suresh Kumar*, G.V. Pradeep Varma Mechancal Department, Assstant Professor n DIET College, Inda. Mechancal Department, Assocate professor n CITM College, Inda. DOI: /zenodo ABSTRACT Ths project work expresses the dfference between the structures wth and wthout dampng materal. The effect of dampng on the performance of sotropc (steel) and orthotropc (Carbon Epoxy) structures s to be analysed by usng Fnte Element Analyss. The values of dampng factor, fundamental natural frequency and the statc deflecton for Steel Shaft, Carbon Epoxy Shaft and are to be compared wth and wthout vscoelastc polymer (Rubber). A new composte dampng materal s to be studed, whch conssts of a vscoelastc matrx and hgh elastc modulus fber nclusons. Ths fber-enhanced vscoelastc-dampng polymer s ntended to be appled to lghtweght flexble structures as a surface treatment for passve vbraton control. A mcro mechancal model s to be establshed and closed form expressons for the effectve storage and loss propertes of the dampng materal are to be derved. An optmal relaton between desgn parameters, such as the length, dameter, spacng, and Young s modulus of fbers and the shear modulus of vscoelastc matrx, s to be derved for achevng maxmum dampng performance. The characterstc value for the maxmum value of Loss modulus s to be found out for the dfferent values of matrx loss factors. KEYWORDS: Vscoelastc polymers, Statc, Model, Transent Dynamc Analyss. INTRODUCTION Composte materals are those contanng more than one bonded materal, each wth dfferent materal propertes. The major advantages of composte materals are that they have a hgh rato of stffness to weght and strength to weght. A prncpal advantage of composte materals les n the ablty of the desgner to talor the materal propertes to the applcaton Vscoelastc materal A Vscoelastc materal sometmes s called materal wth memory. Ths mples that a Vscoelastc materal's behavor depends not only on the current loadng condtons, but also on the loadng hstory. They are characterzed by possessng both vscous and elastc behavor. Fgure 1. shows how varous types of materals behave n the tme doman. A purely elastc materal s one n whch all the energy stored n the sample durng loadng s returned when the load s removed. As a result, the stress and stran curves for elastc materals move completely n phase. For elastc materals, Hooke s Law apples, where the stress s proportonal to the stran, and the modulus s defned at the rato of stress to stran. http: // Internatonal Journal of Engneerng Scences & Research Technology [647]
2 [Kumar*, 5(3): March, 016] ISSN: (IOR), Publcaton Impact Factor: Fg 1. Stress Stran relatonshp of Vscoelastc Materal w.r.t Tme LITERATURE SURVEY Vscoelastc dampng materals add passve dampng to structures by dsspatng vbraton stran energy and generate heat energy. The ncorporaton of dampng materals n advanced composte materals offers the possblty of hghly damped, lght weght structural components that are vbraton resstant. Concurrng vscoelastc dampng materals n compostes has shown to be successful n greatly ncreasng the dampng of composte structures. The dampng performance, however, s often not as hgh n cocured compostes as n secondarly bonded compostes, where the dampng materal does not undergo the cure process. Substtutng composte structures for conventonal metallc structures has many advantages because of hgher specfc stffness and specfc strength of composte materals. The fber enhanced vscoelastc dampng polymer s ntended to be appled to lghtweght flexble structures as a surface treatment for passve vbraton control. A desrable packng geometry for the composte materal s proposed, whch s expected to produce maxmum shear stran n the vscoelastc dampng matrx. A general method for modelng materal dampng n dynamcal systems s presented and t s prmarly concerned wth a dsspaton model based on vscoelastc assumptons. Dfferent numercal approaches for modelng and analyzng the behavor of structures havng constraned layer dampng. Two numercal studes are presented that reveal the accuracy lmts of the dfferent fnte element modelng approaches for addtve and ntegrally damped plate type structures. Now through the use of mproved computatonal based approaches (.e. fnte element method) along wth the avalablty of relable dampng materals wth accurate thermal and dynamc property characterzatons, t s possble to ncorporate dampng treatments as part of the ntal structural desgn process, thereby vrtually elmnatng sharp resonant peaks. Cylndrcal shells wth a constraned dampng layer treatment are studed usng three theores. Constraned layer dampng n structures s a very popular method to control resonant ampltudes of vbraton. Shells of revoluton (e.g., cylndrcal and concal) fnd wde applcaton n the aerospace ndustry. An effcent method s descrbed for fnte element modelng of three-layer lamnates contanng a vscoelastc layer. Modal dampng ratos are estmated from undamped normal mode results by means of the Modal Stran Energy (MSE) method. The soluton for a radally smply supported shell has been obtaned and the procedure for determnng the dampng effectveness n terms of the system loss factor for all famles of the modes of vbraton n a multlayered shell wth elastc and vscoelastc layers s reported. Approxmately 85% of the passve dampng treatments n actual applcatons are based on vscoelastc materals. The soluton for the vbraton and dampng analyss of a general multlayered cylndrcal shell consstng of an arbtrary number of orthotropc materal elastc and vscoelastc layers wth smply supported end condtons has been reported. DESCRIPTION OF PROBLEM The torque transmsson capablty of the propeller shaft for passenger cars, small trucks, and vans should be larger than 3,500 Nm and fundamental natural bendng frequency of the propeller shaft should be hgher than 6,500 rpm to avod whrlng vbraton. The outer dameter of the propeller shaft should not exceed 100 mm due to space lmtatons. The propeller shaft of transmsson system s desgned for followng specfed desgn requrements as shown n Table Due to space lmtatons the outer dameter of the shaft s restrcted to 90.4 mm. The one-pece hollow composte drve shaft for rear wheel drve automoble should satsfy three desgn specfcatons, such as statc torque transmsson capablty, torsonal bucklng capacty and the fundamental natural bendng frequency. For http: // Internatonal Journal of Engneerng Scences & Research Technology [648]
3 [Kumar*, 5(3): March, 016] ISSN: (IOR), Publcaton Impact Factor: gven specfcaton, the dampng factor for Steel, carbon Epoxy are to be calculated and compared wth and wthout dampng materal (Rubber). Table 4. 1 Problem Specfcaton Sl. No. Parameter Notaton Unts Value 1. Torque T N-m Max Speed N RPM Length L m 1.50 Table 4. Materal Propertes. Sl. No. Propertes Unts Steel Carbon Epoxy Rubber 1 Young s Modulus E11 N / m.068e e e 6 Young s Modulus E N / m.068e 11 7 e e 6 3 Densty kg / m Posson Rato Shear Modulus G N / m - 5.8e e 11 A new composte dampng materal s to be studed, whch conssts of a vscoelastc matrx and hgh elastc modulus fber nclusons. Ths fber-enhanced vscoelastc-dampng polymer s ntended to be appled to lghtweght flexble structures as a surface treatment for passve vbraton control. A mcro mechancal model s to be establshed and closed form expressons for the effectve storage and loss propertes of the dampng materal are to be derved. An optmal relaton between desgn parameters, such as the length, dameter, spacng, and Young s modulus of fbers and the shear modulus of vscoelastc matrx, s to be derved for achevng maxmum dampng performance. STATIC ANALYSIS Statc analyss calculates the effects of steady loadng condtons on a structure, whle gnorng nerta and dampng effects, such as those caused by tme-varyng loads. A statc analyss, however, ncludes steady nerta loads (such as gravty and rotatonal velocty), and tme-varyng loads that can be approxmated as statc equvalent loads (such as the statc equvalent wnd and sesmc loads commonly defned n many buldng codes). Statc Analyss of Steel Shaft wthout vscoelastc Dampng Materal by Beam and Shell Element In ths part statc deflecton of the steel shaft s calculated and compared wth ANSYS results. The specfcaton for the shaft s gven n the Table 5.1. For calculatng the deflecton, the cantlever boundary condton s taken by consderng ts self weght. Table 5.1 Specfcaton of steel shaft Sl. No. Parameters Values 1 Outer Dameter m Thckness.1 e -3 Steel Shaft wthout Dampng Materal for Shell 99 In ths case shell element s taken to calculate the deflecton value for steel shaft. Here Shell element s taken due to specfy the number of layers to nclude the dampng polymer. Here steel shaft wthout dampng materal s consdered and specfcatons are tabulated n table 5.1. http: // Internatonal Journal of Engneerng Scences & Research Technology [649]
4 [Kumar*, 5(3): March, 016] ISSN: (IOR), Publcaton Impact Factor: Fg 5. Statc Deflecton for Steel Shaft Usng ANSYS 7.0 the deflecton value s calculated. The value s 0.116*10-3 m. The deformed shape of the shaft s shown n the Fg 5.. Steel Shaft wth Dampng Materal In ths type a dampng materal (.e.) Rubber s nserted between the two layers of shaft and the deflecton value s calculated usng ANSYS. The specfcaton of the shaft wth dampng materal s shown n the Table 5.3 Table 5. 3 Specfcatons for Steel Shaft wth Rubber Sl. No. Parameters Values 1 Outer Dameter m Thckness of each layer 1.05 e -3 m 3 Number of layers 3 4 Dampng Materal Rubber 5 Element Shell 99 Fg 5.3 Stackng Sequence for Steel Shaft wth Rubber Fg 5.4 Deflecton of Steel Shaft wth Rubber Usng ANSYS 7.0 the deflecton value s calculated. The value s 0.91 e -4 m. The deformed shape of the shaft s shown n the Fg 5.4. Carbon Epoxy Shaft wthout Dampng Materal http: // Internatonal Journal of Engneerng Scences & Research Technology [650]
5 [Kumar*, 5(3): March, 016] ISSN: (IOR), Publcaton Impact Factor: In ths case Carbon Epoxy shaft s modeled wth 13 layers by consderng the shell element. The specfcatons are shown n the Table 5.4 Table 5.4 Specfcaton for Carbon Epoxy Shaft Sl. No. Parameters Values 1 Outer Dameter m Thckness of each layer 1.5 e -4 m 3 Number of layers 13 4 Element Shell 99 Fg 5.5 Stackng Sequence for Carbon Epoxy Shaft Fg 5.6 Statc Deflecton for Carbon Epoxy Shaft Usng ANSYS 7.0 the deflecton value s calculated. The value s 0.84 e -4 m. The deformed shape of the shaft s shown n the Fg 5.6. Carbon Epoxy Shaft wth Dampng Materal In ths case Carbon Epoxy shaft s modeled wth dampng materal (Rubber) and t s ncorporated n between the layers. The specfcaton of the shaft s shown n the Table 5.5. Table 5.5 Specfcaton for Carbon Epoxy Shaft wth Rubber Sl. No. Parameters Values 1 Outer Dameter.0904 m Thckness of each layer 1.5 e -4 m 3 Number of layers 14 4 Dampng Materal Rubber 5 Element Shell 99 http: // Internatonal Journal of Engneerng Scences & Research Technology [651]
6 [Kumar*, 5(3): March, 016] ISSN: (IOR), Publcaton Impact Factor: Fg 5.7 Stackng Sequence for Carbon Epoxy Shaft Fg 5.8 Statc Deflecton for Carbon Epoxy Shaft wth Rubber The stackng sequence of the Carbon Epoxy shaft wth dampng materal (Rubber) s shown n the fg 5.7. Here the 7 th layer s the rubber. Usng ANSYS 7.0 the deflecton value s calculated. The value s 0.71 e -4 m. The deformed shape of the shaft s shown n the Fg 5.8. MODAL ANALYSIS Any physcal system can vbrate. The frequences at whch vbraton naturally occurs, and the modal shapes whch the vbratng system assumes are propertes of the system, and can be determned analytcally usng Modal Analyss. Modal analyss s the procedure of determnng a structure's dynamc characterstcs; namely, resonant frequences, dampng values, and the assocated pattern of structural deformaton called mode shapes. It also can be a startng pont for another, more detaled, dynamc analyss, such as a transent dynamc analyss, a harmonc response analyss, or a spectrum analyss. Modal analyss n the ANSYS famly of products s a lnear analyss. Any nonlneartes, such as plastcty and contact (gap) elements, are gnored even f they are defned. Modal analyss can be done through several mode extracton methods: subspace, Block Lanczos, Power Dynamcs, Reduced, Unsymmetrc and Damped. The damped method allows you to nclude dampng n the structure. Modal Analyss of Steel Shaft usng Beam Element wthout Rubber Consder the free-body dagram of an element of a beam shown n fgure. Where M(r, t) s the bendng moment, V(r, t) s the shear force and f (r, t) s the external force per unt length of the beam. Fg 6.1 Beam n Bendng Euler -Bernoull beam equatons wth external force, external moment s gven by followng equatons. http: // Internatonal Journal of Engneerng Scences & Research Technology [65]
7 [Kumar*, 5(3): March, 016] ISSN: (IOR), Publcaton Impact Factor: y(r,t) y(r,t) EI A f(r,t) (1) 4 r t Usng Assumed modes approach, by solvng the above equaton the Egen values and mode shapes can be calculated. Usng the varable separable method y(r, t) may be expressed by followng equatons. 1 y(r, t) (r) q (t) () '''' '' EI (r)q (t) A (r)q (t) Ca 1 1 Va ( r,t) r (3) EI L 0 1 '''' (r)q (t) dr A L 0 1 '' (r)q (t) dr C L a 0 Va ( r,t) r By multplyng (r) on both sdes then apply the Orthogonalty prncple. EI L 0 1 '''' (r) q (t) (r) dr '''' EI (r)- (r) 0 A 4 4 (r)- (r) 0 A L 0 1 '' (r) q (t) (r) dr C L a 0 dr (4) Va (r, t) (r) dr r. (5) (6) (7) The complementary soluton of the above equaton s gven by (r) A sn ( r) B cos ( r) C snh ( r) D cosh ( r) (8) Boundary condtons of cantlever beam, y(r,t) At the fxed end: y(0, t) 0, EI 0 r (9) 3 y (L,t) y (L,t) At the free end: EI 0, EI 0 3 r r (10) Applyng these boundary condtons the soluton of dfferental equaton transformed cosh L cos L to (r) L cosh r-cos r- snh r sn r (11) snh L sn L Shear force at free end s zero, by applyng ths boundary condton n the above equaton the above equaton converted to followng equaton. (1) 1 cos L cosh L 0 From the soluton of the equaton the value can be calculate. The natural frequency of the system s gven by substtutng can be calculated. EI (13) A http: // Internatonal Journal of Engneerng Scences & Research Technology [653]
8 [Kumar*, 5(3): March, 016] ISSN: (IOR), Publcaton Impact Factor: Table 6.1 Modal Frequences for Steel Shaft usng BEAM 3 Mode Shapes Analytcal Value Theoretcal Value Usng ANSYS 7.0 ( HZ) (HZ) Fg 6. Modal Analyss for Steel Shaft usng Beam 3 Fg 6.3 Comparson of Results The fundamental natural frequency of Steel shaft usng Beam 3 element s shown n the Fg 6.. The value of the frequency s Hz.The theoretcal and FEA values are compared and shown n the Fg 6.3. Modal Analyss of Steel Shaft usng Shell Element wthout Rubber and wth Rubber In ths case Steel shaft s modeled usng Shell 99. The specfcatons used are same as n the Statc Analyss. Fg 6.4 Modal Analyss for Steel Shaft usng Shell 99 Rubber Fg 6.5 Modal Analyss for Steel Shaft wth http: // Internatonal Journal of Engneerng Scences & Research Technology [654]
9 [Kumar*, 5(3): March, 016] ISSN: (IOR), Publcaton Impact Factor: The fundamental natural frequency of the steel shaft usng Shell 99 s shown n the Fg 6.4. The value s Hz.The fundamental natural frequency of the Steel Shaft wth Rubber s shown n the Fg 6.5. The value s Hz. Modal Analyss Of Carbon Epoxy Shaft Wthout rubber and Wth Rubber Fg 6.6 Modal Analyss for Carbon Epoxy Shaft Fg 6.7 Modal Analyss for Carbon Epoxy Shaft wth Rubber The fundamental natural frequency of the Carbon Epoxy Shaft s shown n the Fg 6.6. The value s Hz. The fundamental natural frequency of the Carbon Epoxy Shaft wth s shown n the Fg 6.7. The value s Hz TRANSIENT DYNAMIC ANALYSIS Transent dynamc analyss s a technque used to determne the dynamc response of a structure under a tmevaryng load. The tme frame for ths type of analyss s such that nerta or dampng effects of the structure are consdered to be mportant. Cases where such effects play a major role are under step or mpulse loadng condtons, for example, where there s a sharp load change n a fracton of tme. If nerta effects are neglgble for the loadng condtons beng consdered, a statc analyss may be used nstead. It should be noted that a transent analyss s more nvolved than a statc or harmonc analyss. It requres a good understandng of the dynamc behavor of a structure. Therefore, a modal analyss of the structure should be ntally performed to provde nformaton about the structure's dynamc behavor. In ANSYS, transent dynamc analyss can be carred out usng 3 methods. The Full Method: Ths s the easest method to use. All types of non-lneartes are allowed. It s however very CPU ntensve to go ths route as full system matrces are used. The Reduced Method: Ths method reduces the system matrces to only consder the Master Degrees of Freedom (MDOFs). Because of the reduced sze of the matrces, the calculatons are much qucker. However, ths method handles only lnear problems (such as our cantlever case). The Mode Superposton Method: Ths method requres a prelmnary modal analyss, as factored mode shapes are summed to calculate the structure's response. It s the quckest of the three methods, but t requres a good deal of understandng of the problem at hand. In ths project the Reduced Method s used for conductng the transent analyss. Usually one need not go further than revewng the Reduced Results. However, f stresses and forces are of nterest than, we would have to Expand the Reduced Soluton. Transent Dynamc Analyss of Steel Shaft wthout dampng materal by beam element and shell element In ths part Transent Dynamc analyss of the shaft s calculated usng the same specfcatons as gven n the statc analyss. Transent Dynamc analyss s needed because the output of ths analyss s used n calculatng the dampng factor usng Log Decrement method. http: // Internatonal Journal of Engneerng Scences & Research Technology [655]
10 [Kumar*, 5(3): March, 016] ISSN: (IOR), Publcaton Impact Factor: Transent Dynamc Analyss of Steel Shaft usng Beam Element Fg 7.1 Transent Dynamc Analyss of Steel Shaft usng Beam 3 The Transent Dynamc Analyss of Steel Shaft usng Beam 3 Element s shown n the Fg 7.1. From the above Fg 7.1 dampng factor s calculated usng Log Decrement method and the value s Transent Dynamc Analyss of Steel Shaft usng Shell Element wthout and wth Rubber In ths case Steel shaft s modeled usng Shell 99. The specfcatons used are same as n the Statc Analyss. Fg 7. Transent Analyss for Steel Shaft wthout rubber Rubber Fg 7.3 Transent Analyss for Steel Shaft usng The Transent Dynamc Analyss of Steel Shaft usng Beam 3 Element s shown n the Fg 7.. From the above Fg 7. dampng factor s calculated usng Log Decrement method and the value s The Transent Dynamc Analyss of Steel Shaft usng Shell 99 wth Rubber s shown n the Fg 7.3. From the above Fg 7.3 dampng factor s calculated usng Log Decrement method and the value s Transent Dynamc Analyss of Carbon Epoxy Shaft wthout and wth Rubber http: // Internatonal Journal of Engneerng Scences & Research Technology [656]
11 [Kumar*, 5(3): March, 016] ISSN: (IOR), Publcaton Impact Factor: Fg 7.4 Transent Analyss for Carbon Epoxy Shaft Fg 7.5 Transent Analyss for Carbon Epoxy Shaft wth Rubber The Transent Dynamc Analyss of Carbon Epoxy Shaft usng Shell 99 s shown n the Fg 7.4. From the above Fg 7.4 dampng factor s calculated usng Log Decrement method and the value s The Transent Dynamc Analyss of Carbon Epoxy Shaft usng Shell 99 wth Rubber s shown n the Fg 7.5. From the above Fg 7.5 dampng factor s calculated usng Log Decrement method and the value s Optmzaton Of Dampng Propertes It s noted that means proposed for mprovng free layer treatment, and the lghtweght of fbers wll beneft applcatons where weght s an mportant consderaton. Fber aspect rato, fber tp spacng, fber angle and a number of other parameters were vared to mprove the dampng performance of a structural composte materal. In ths chapter, a mcro mechancal model for the fber-enhanced vscoelastc-dampng polymer s establshed, and closed form expressons for the effectve complex modul are shown. Based on ths model, dampng performance of the enhanced dampng polymer s optmzed by establshng an optmal relaton between the desgn parameters, such as length. Vscoelastc Dampng Treatment Vscoelastc dampng treatment performances nclude the followng: 1. Hgh loss modulus vscoelastc dampng materals. Hgh extensonal stffness constranng layers 3. A multplcty of layers 4. Optmal secton length constranng layer segments Due to the hgh elastc modulus, usually twce and three tmes as much as that of steel and alumnum, respectvely hgh elastc modulus fbrous materals, for example Kevlar or graphte fber, are desrable canddates for constrant materals n vscoelastc dampng treatments. By embeddng fber nto a vscoelastc polymer matrx to make a sngle composte dampng product, all the features cted above can be readly acheved. The optmal segment lengths of the fbers can be controlled n fabrcatng processes, and the effectve number of dampng layers can be ncreased to a great extent wthout dffculty. Furthermore, the proposed fber enhanced vscoelastc dampng polymer can be convenently nstalled on structural surfaces as a dameter, spacng, and Young s modulus of the fbers and shear modulus of the vscoelastc matrx. Effectve Complex Module Based on the fundamental prncples of constraned vscoelastc layer treatments, a packng geometry wth staggered layers as shown n the fg. 1 s selected, as t makes effcent use of the materals. http: // Internatonal Journal of Engneerng Scences & Research Technology [657]
12 [Kumar*, 5(3): March, 016] ISSN: (IOR), Publcaton Impact Factor: In ths Fg 8.1, the rods wth square cross secton and fnte length represent fbers, whch are embedded n a vscoelastc matrx. The square fber cross secton s used n the model for convenence. The spacng between neghborng fbers s assumed to be the same and the gaps between fber ends are neglected n the present analyss. The Fg 8. also show a selected representatve volume element whose geometrcal characterstcs and stress stran relatons are the same for any of such elements, regardless of the poston n the composte materal. The average stress and stran of the representatve volume element therefore are same for any such elements and also the same as that of the entre composte materal under a unform loadng. Fg 8.1 Fg 8. Fg 8.1 Schematc representaton of the fber enhanced vscoelastc polymer under stretchng Fg 8. Schematc representaton of fnte element model for representatve volume element Dsplacement Feld Under Axal Loadng Fber enhanced Vscoelastc dampng materals appled to the surface of flexble structures, wll experence perodcally axal loadng when the base structure vbrates. In the development of the dsplacement feld wthn the composte under ths axal loadng, the followng assumptons are beng made: a. Due to the much hgher stffness of the fbers, usually orders of magntude hgher than that of the vscoelastc matrx, t s assumed that the fber sustans extensonal stress only and the vscoelastc matrx transmts shear stress only. b. Unform normal stress feld and unform shear stress feld are assumed through the cross sectons of the fbers and the vscoelastc matrx, respectvely due to ther very small dmensons. c. Lnear materal propertes are assumed for the fbers and the vscoelastc matrx, as antcpated strans are small and well wthn the lnear range. d. Posson s rato effects are neglgble, agan due to small strans. e. Fbers are elastc and dsspate very lttle energy relatve to the vscoelastc matrx. The front and backsdes of the fbers are subjected to shear stresses due to exstence of the vscoelastc matrx. Due to the symmetrc confguraton of the composte, the soluton of the dsplacement feld can be reduced to a two dmensonal problem. It s well known that the complex modulus approach s an effcent method to descrbe the dynamc behavor of homogenous vscoelastc materals. Based on the above assumptons and by applyng boundary condtons, the fnal expressons for the effectve storage modulus E, loss modulus E and loss factor the propertes of the fber enhanced vscoelastc dampng ' C polymers under unaxal loadng are gven as: '' N EC E f v f D ' N1 EC E f v f D N E N 1 '' C E () (3) (1) http: // Internatonal Journal of Engneerng Scences & Research Technology [658]
13 [Kumar*, 5(3): March, 016] ISSN: (IOR), Publcaton Impact Factor: N N (5) 1 v v v v v v 1 coth 1 cot cot cot 1 coth (6) coth cot v v D 4 4 ' (7) L f Gv 1 Where, v v v v v coth 1 cot cot 1 coth t v d f E f 4 v 1 cot coth v 1 v 1 coth 1 cot E Here, represents the characterstc value, represents the matrx loss factor, and V f represents the fbre volume fracton. It can be seen that all these effectve propertes are functons of the packng geometry of the composte, and the materal propertes of the consttuents. These propertes wll be employed n the analyss, whch follows. Table 8.1 Desgn Specfcatons Sl.No Quantty Symbol Unt Value 1. Dstance between fbers t v n Dameter of fbers d f n Half length of fbers L f / n Normal stress lb/n 1.44 e 5 5. Shear modulus of matrx G v ' lb/n Tensle modulus of fbers E f lb/n 6.4 e 7 Table 8. Calculated Values for α N1 N D v =0.75 '' E C /VfEf Table 8.3 Calculated Values for 1 1 v v coth cot 4 (4) v =1 α N1 N D '' E /VfEf C E E http: // Internatonal Journal of Engneerng Scences & Research Technology [659]
14 [Kumar*, 5(3): March, 016] ISSN: (IOR), Publcaton Impact Factor: Table 8.4 Calculated Values for α N1 N D v =1.5 '' E C /VfEf OPTIMIZATION OF DAMPING PROPERTIES The closed form expressons of the effectve materal propertes developed above allow optmzaton of the dampng propertes for the fber enhanced vscoelastc polymers. The followng dscusson consders the establshment of the approprate crteron for dampng desgn optmzaton. Intutvely, a large value of loss factor s a desred property for dampng materals. Consder the dampng mechansm n a vscoelastc materal. In order to dsspate energy, a dampng materal must store some energy frst. The more energy t can store, the more energy t wll dsspate. The ablty to store energy s measured by the storage modulus of materals. It s clear that the best quantty reflectng the dampng performance of a vscoelastc materal s the loss modulus of the materal,.e., the product of the loss factor and the storage modulus. It may not always be desrable, though, to use a very hgh storage modulus to acheve a hgh loss modulus. The reason s that a hgh storage modulus of a dampng materal could sgnfcantly change the stffness of the base structure on whch t wll be bonded. Therefore, a good desgn nvolves proper balance between loss factor and storage modulus. The proposed strategy for optmzaton of the fber-enhanced vscoelastc-dampng polymer s gven below. Examne the varaton of the composte loss factor, η E, wth the characterstc value. Based on the results of the step one, select a narrowed range of to maxmze the loss modulus, E " c After all the parameters are determned, evaluate the storage modulus, η E, and loss factor, E' c. The desgn specfcaton for the model s shown n the table The calculated values are shown sn table 8., table 8. 3 and table Loss Modulus Characterstc Value (α) v v v Fg 8.3 Effect of Characterstc value on loss modulus ( E /VfEf ) Loss Factor =1 '' C value on loss factor = E Fg 8.4 Effect of Characterstc DISCUSSIONS For dfferent values of matrx loss factors, η v, maxmum value of E " c occurs at the value of around It can be concluded that for maxmum dampng performance, the characterstc value of the composte,.e.,, should be set to To satsfy ths optmum condton, one can vary the parameters used to calculate the characterstc value v v =1 v Characterstc Value http: // Internatonal Journal of Engneerng Scences & Research Technology [660]
15 [Kumar*, 5(3): March, 016] ISSN: (IOR), Publcaton Impact Factor: (.e., E f, G v ', t v, d f and L f ). For example, f E f, G v ', d f and L f are prescrbed by a specfc desgn, satsfacton of ths condton wll yeld an optmal dstance between fbers, t v. A large value for the fber Young s modulus E f, s a desred property for the fber enhanced vscoelastc dampng polymer. CONCLUSIONS The dampng factor has been found out for Steel Shaft, Carbon Epoxy Shaft wth and wthout Vscoelastc polymer (Rubber). The Statc, Modal and Transent Dynamc Analyses have been carred out usng Fnte Element Analyss. The followng observatons were made by embeddng the Vscoelastc polymer (Rubber) nto the structure. Dampng factor ncreased by 16.3%, 9.% for Steel, Carbon Epoxy shafts respectvely. The fundamental natural frequency ncreased by 1.76%, 7.% for Steel, Carbon Epoxy shafts respectvely. The deflecton value decreased by 1.38%, 1.71% for Steel, Carbon Epoxy Shafts respectvely. The ncrease n dampng factor results n further suppresson of vbratons and hence results n ncreased structural lfe. An optmal relaton between desgn parameters such as the length, dameter, spacng, and Young s modulus of fbers and the shear modulus of vscoelastc matrx has been derved for achevng maxmum dampng performance. It has been found that for maxmum dampng performance, the characterstc value of the composte should be set to BIBLIOGRAPHY [1] Autar K. Kaw, "Mechancs of Composte Materals", CRC press, [] Ahd D. Nashf, Davd I. G. Jones and John P. Henderson, Vbraton Dampng, John Wley & Sons Publcaton, 1985, Newyork. [3] C. T. Sun and Y. P. Lu, "Vbraton Dampng of Structural Elements", Prentnce Hall PTR, New Jeresy, [4] K. L. Napoltano, W. Grppo, J. B. Kosmatka and C. D. Johnson, A comparson of two cocured damped composte torson shafts, Composte Structures, Vol. 43, 1998, pp [5] J. M. Bggerstaff and J. B. Kosmatka, Dampng Performance of Cocured Composte Lamnates wth Embedded Vscoelastc Layers, Journal of Composte Materals, Vol. 3, No.1/ [6] Jn Kook Km, Da Gl Lee, and Durk Hyun Cho, 001, Investgaton of Adhesvely Bonded Jonts for Composte Propeller shafts, Journal of Composte Materals, Vol.35, No.11, pp [7] T. E. Alberts and Houchun Xa, Desgn and Analyss of Fber Enhanced Vscoelastc Dampng Polymers, Journal of Vbraton and Acoustcs, Vol. 117, October 1995, pp [8] K. J. Buharwala and J. S. Hansen, "Dynamcs of Vscoelastc Structures", AIAA Journal, Vol. 6, February 1988, pp 0-7. [9] J. B. Kosmatka and S. L. Lguore, Revew of Methods for Analyzng Constraned Layer Damped Structures, Journal of Aerospace Engneerng, Vol.6, No.3, July 1993, pp [10] T. C. Ramesh and N. Ganesan, Vbraton and Dampng Analyss of Cylndrcal Shells wth Constraned Dampng Treatment- A Comparson of Three Theores, Journal of Vbraton and Acoustcs, Vol. 117, Aprl 1995, pp [11] Conor D. Johnson and Davd A. Kenholz, Fnte Element Predcton of Dampng n Structures wth Constraned Vscoelastc Layers, AIAA Journal, Vol. 0, No. 3, September 198, pp [1] N. T. Asnan and Nayar Alam, " Vbraton and Dampng Analyss of a Multlayered Cylndrcal Shell, Part I: Theoretcal Analyss", AIAA Journal, Vol., No. 6, June 1984, pp [13] N. T. Asnan and Nayar Alam, " Vbraton and Dampng Analyss of a Multlayered Cylndrcal Shell, Part II: Numercal Results", AIAA Journal, Vol., No. 7, July 1984, pp [14] D. A. Saravanos and J. M. Perera, Dynamc Characterstcs of Specalty Composte Structures wth Embedded Dampng Layers, Journal of Vbraton and Acoustcs, Vol. 117, January 1995, pp [15] C.D. Johnson, Desgn of Passve Dampng Systems, Transactons of the ASME, Vol. 117, June 1995, pp [16] H. V. Panossan, "Structural Dampng Enhancement Va Non- Obstructve Partcle Dampng Technque", Journal of Vbraton and Acoustcs, Vol.114, January 199, pp http: // Internatonal Journal of Engneerng Scences & Research Technology [661]
16 [Kumar*, 5(3): March, 016] ISSN: (IOR), Publcaton Impact Factor: [17] M. A. Trndade, A. Benjeddou and R. Ohayon, Modelng of Frequency- Dependent Vscoelastc Materals for Actve- Passve Vbraton Dampng, Journal of Vbraton and Acoustcs, Vol.1, Aprl 000, pp [18] John F. Baldwn and Stanley G. Hutton, " Natural Modes of Modfed Structures", AIAA Journal, Vol. 3, No. 11, November 1985, pp [19] M. L. Son and F. K. Bogner, "Fnte Element Vbraton Analyss of Damped Structures", AIAA Journal, Vol. 0, No. 5, May 198, pp [0] Y. P. Lu, B. E. Douglas and E. V. Thomas, Mechancal Impedance of Damped Three- Layered Sandwch Rngs, AIAA Journal, Vol. 11, No. 5, March 1973, pp http: // Internatonal Journal of Engneerng Scences & Research Technology [66]
DUE: WEDS FEB 21ST 2018
HOMEWORK # 1: FINITE DIFFERENCES IN ONE DIMENSION DUE: WEDS FEB 21ST 2018 1. Theory Beam bendng s a classcal engneerng analyss. The tradtonal soluton technque makes smplfyng assumptons such as a constant
More informationCOMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD
COMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD Ákos Jósef Lengyel, István Ecsed Assstant Lecturer, Professor of Mechancs, Insttute of Appled Mechancs, Unversty of Mskolc, Mskolc-Egyetemváros,
More informationLecture 8 Modal Analysis
Lecture 8 Modal Analyss 16.0 Release Introducton to ANSYS Mechancal 1 2015 ANSYS, Inc. February 27, 2015 Chapter Overvew In ths chapter free vbraton as well as pre-stressed vbraton analyses n Mechancal
More informationOFF-AXIS MECHANICAL PROPERTIES OF FRP COMPOSITES
ICAMS 204 5 th Internatonal Conference on Advanced Materals and Systems OFF-AXIS MECHANICAL PROPERTIES OF FRP COMPOSITES VLAD LUPĂŞTEANU, NICOLAE ŢĂRANU, RALUCA HOHAN, PAUL CIOBANU Gh. Asach Techncal Unversty
More informationDESIGN OPTIMIZATION OF CFRP RECTANGULAR BOX SUBJECTED TO ARBITRARY LOADINGS
Munch, Germany, 26-30 th June 2016 1 DESIGN OPTIMIZATION OF CFRP RECTANGULAR BOX SUBJECTED TO ARBITRARY LOADINGS Q.T. Guo 1*, Z.Y. L 1, T. Ohor 1 and J. Takahash 1 1 Department of Systems Innovaton, School
More informationTHE EFFECT OF TORSIONAL RIGIDITY BETWEEN ELEMENTS ON FREE VIBRATIONS OF A TELESCOPIC HYDRAULIC CYLINDER SUBJECTED TO EULER S LOAD
Journal of Appled Mathematcs and Computatonal Mechancs 7, 6(3), 7- www.amcm.pcz.pl p-issn 99-9965 DOI:.75/jamcm.7.3. e-issn 353-588 THE EFFECT OF TORSIONAL RIGIDITY BETWEEN ELEMENTS ON FREE VIBRATIONS
More informationEVALUATION OF THE VISCO-ELASTIC PROPERTIES IN ASPHALT RUBBER AND CONVENTIONAL MIXES
EVALUATION OF THE VISCO-ELASTIC PROPERTIES IN ASPHALT RUBBER AND CONVENTIONAL MIXES Manuel J. C. Mnhoto Polytechnc Insttute of Bragança, Bragança, Portugal E-mal: mnhoto@pb.pt Paulo A. A. Perera and Jorge
More informationCHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE
CHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE Analytcal soluton s usually not possble when exctaton vares arbtrarly wth tme or f the system s nonlnear. Such problems can be solved by numercal tmesteppng
More informationStatistical Energy Analysis for High Frequency Acoustic Analysis with LS-DYNA
14 th Internatonal Users Conference Sesson: ALE-FSI Statstcal Energy Analyss for Hgh Frequency Acoustc Analyss wth Zhe Cu 1, Yun Huang 1, Mhamed Soul 2, Tayeb Zeguar 3 1 Lvermore Software Technology Corporaton
More informationGEO-SLOPE International Ltd, Calgary, Alberta, Canada Vibrating Beam
GEO-SLOPE Internatonal Ltd, Calgary, Alberta, Canada www.geo-slope.com Introducton Vbratng Beam Ths example looks at the dynamc response of a cantlever beam n response to a cyclc force at the free end.
More informationSecond Order Analysis
Second Order Analyss In the prevous classes we looked at a method that determnes the load correspondng to a state of bfurcaton equlbrum of a perfect frame by egenvalye analyss The system was assumed to
More informationChapter 3. Estimation of Earthquake Load Effects
Chapter 3. Estmaton of Earthquake Load Effects 3.1 Introducton Sesmc acton on chmneys forms an addtonal source of natural loads on the chmney. Sesmc acton or the earthquake s a short and strong upheaval
More informationFUZZY FINITE ELEMENT METHOD
FUZZY FINITE ELEMENT METHOD RELIABILITY TRUCTURE ANALYI UING PROBABILITY 3.. Maxmum Normal tress Internal force s the shear force, V has a magntude equal to the load P and bendng moment, M. Bendng moments
More informationELASTIC WAVE PROPAGATION IN A CONTINUOUS MEDIUM
ELASTIC WAVE PROPAGATION IN A CONTINUOUS MEDIUM An elastc wave s a deformaton of the body that travels throughout the body n all drectons. We can examne the deformaton over a perod of tme by fxng our look
More informationEffects of Boundary Conditions on Cross-Ply Laminated Composite Beams
Internatonal Journal of Engneerng Research And Advanced Technology (IJERAT) DOI: http://dx.do.org/0.734/ijerat.344 E-ISSN : 454-635 Vol.3 (0) Oct -07 Effects of Boundary Condtons on Cross-Ply Lamnated
More informationIrregular vibrations in multi-mass discrete-continuous systems torsionally deformed
(2) 4 48 Irregular vbratons n mult-mass dscrete-contnuous systems torsonally deformed Abstract In the paper rregular vbratons of dscrete-contnuous systems consstng of an arbtrary number rgd bodes connected
More information829. An adaptive method for inertia force identification in cantilever under moving mass
89. An adaptve method for nerta force dentfcaton n cantlever under movng mass Qang Chen 1, Mnzhuo Wang, Hao Yan 3, Haonan Ye 4, Guola Yang 5 1,, 3, 4 Department of Control and System Engneerng, Nanng Unversty,
More informationGEOSYNTHETICS ENGINEERING: IN THEORY AND PRACTICE
GEOSYNTHETICS ENGINEERING: IN THEORY AND PRACTICE Prof. J. N. Mandal Department of cvl engneerng, IIT Bombay, Powa, Mumba 400076, Inda. Tel.022-25767328 emal: cejnm@cvl.tb.ac.n Module - 9 LECTURE - 48
More informationCHAPTER 9 CONCLUSIONS
78 CHAPTER 9 CONCLUSIONS uctlty and structural ntegrty are essentally requred for structures subjected to suddenly appled dynamc loads such as shock loads. Renforced Concrete (RC), the most wdely used
More informationIndeterminate pin-jointed frames (trusses)
Indetermnate pn-jonted frames (trusses) Calculaton of member forces usng force method I. Statcal determnacy. The degree of freedom of any truss can be derved as: w= k d a =, where k s the number of all
More informationSTATIC ANALYSIS OF TWO-LAYERED PIEZOELECTRIC BEAMS WITH IMPERFECT SHEAR CONNECTION
STATIC ANALYSIS OF TWO-LERED PIEZOELECTRIC BEAMS WITH IMPERFECT SHEAR CONNECTION Ákos József Lengyel István Ecsed Assstant Lecturer Emertus Professor Insttute of Appled Mechancs Unversty of Mskolc Mskolc-Egyetemváros
More informationNONLINEAR NATURAL FREQUENCIES OF A TAPERED CANTILEVER BEAM
Advanced Steel Constructon Vol. 5, No., pp. 59-7 (9) 59 NONLINEAR NATURAL FREQUENCIES OF A TAPERED CANTILEVER BEAM M. Abdel-Jaber, A.A. Al-Qasa,* and M.S. Abdel-Jaber Department of Cvl Engneerng, Faculty
More informationFinite Element Modelling of truss/cable structures
Pet Schreurs Endhoven Unversty of echnology Department of Mechancal Engneerng Materals echnology November 3, 214 Fnte Element Modellng of truss/cable structures 1 Fnte Element Analyss of prestressed structures
More informationCOMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS
Avalable onlne at http://sck.org J. Math. Comput. Sc. 3 (3), No., 6-3 ISSN: 97-537 COMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS
More informationWeek3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity
Week3, Chapter 4 Moton n Two Dmensons Lecture Quz A partcle confned to moton along the x axs moves wth constant acceleraton from x =.0 m to x = 8.0 m durng a 1-s tme nterval. The velocty of the partcle
More informationWeek 9 Chapter 10 Section 1-5
Week 9 Chapter 10 Secton 1-5 Rotaton Rgd Object A rgd object s one that s nondeformable The relatve locatons of all partcles makng up the object reman constant All real objects are deformable to some extent,
More informationOPTIMAL DESIGN OF VISCOELASTIC COMPOSITES WITH PERIODIC MICROSTRUCTURES
OPTIMAL DESIN OF VISCOELASTIC COMPOSITES WITH PERIODIC MICROSTRUCTURES eong-moo 1, Sang-Hoon Park 2, and Sung-Ke oun 2 1 Space Technology Dvson, Korea Aerospace Research Insttute, usung P.O. Box 3, Taejon,
More informationNON LINEAR ANALYSIS OF STRUCTURES ACCORDING TO NEW EUROPEAN DESIGN CODE
October 1-17, 008, Bejng, Chna NON LINEAR ANALYSIS OF SRUCURES ACCORDING O NEW EUROPEAN DESIGN CODE D. Mestrovc 1, D. Czmar and M. Pende 3 1 Professor, Dept. of Structural Engneerng, Faculty of Cvl Engneerng,
More informationIn this section is given an overview of the common elasticity models.
Secton 4.1 4.1 Elastc Solds In ths secton s gven an overvew of the common elastcty models. 4.1.1 The Lnear Elastc Sold The classcal Lnear Elastc model, or Hooean model, has the followng lnear relatonshp
More informationORIGIN 1. PTC_CE_BSD_3.2_us_mp.mcdx. Mathcad Enabled Content 2011 Knovel Corp.
Clck to Vew Mathcad Document 2011 Knovel Corp. Buldng Structural Desgn. homas P. Magner, P.E. 2011 Parametrc echnology Corp. Chapter 3: Renforced Concrete Slabs and Beams 3.2 Renforced Concrete Beams -
More informationA Mechanics-Based Approach for Determining Deflections of Stacked Multi-Storey Wood-Based Shear Walls
A Mechancs-Based Approach for Determnng Deflectons of Stacked Mult-Storey Wood-Based Shear Walls FPINNOVATIONS Acknowledgements Ths publcaton was developed by FPInnovatons and the Canadan Wood Councl based
More informationLab 2e Thermal System Response and Effective Heat Transfer Coefficient
58:080 Expermental Engneerng 1 OBJECTIVE Lab 2e Thermal System Response and Effectve Heat Transfer Coeffcent Warnng: though the experment has educatonal objectves (to learn about bolng heat transfer, etc.),
More informationPhysics 5153 Classical Mechanics. D Alembert s Principle and The Lagrangian-1
P. Guterrez Physcs 5153 Classcal Mechancs D Alembert s Prncple and The Lagrangan 1 Introducton The prncple of vrtual work provdes a method of solvng problems of statc equlbrum wthout havng to consder the
More informationInductance Calculation for Conductors of Arbitrary Shape
CRYO/02/028 Aprl 5, 2002 Inductance Calculaton for Conductors of Arbtrary Shape L. Bottura Dstrbuton: Internal Summary In ths note we descrbe a method for the numercal calculaton of nductances among conductors
More informationΔ x. u(x,t) Fig. Schematic view of elastic bar undergoing axial motions
ME67 - Handout 4 Vbratons of Contnuous Systems Axal vbratons of elastc bars The fgure shows a unform elastc bar of length and cross secton A. The bar materal propertes are ts densty ρ and elastc modulus
More informationAPPROXIMATE ANALYSIS OF RIGID PLATE LOADING ON ELASTIC MULTI-LAYERED SYSTEMS
6th ICPT, Sapporo, Japan, July 008 APPROXIMATE ANALYSIS OF RIGID PLATE LOADING ON ELASTIC MULTI-LAYERED SYSTEMS James MAINA Prncpal Researcher, Transport and Infrastructure Engneerng, CSIR Bult Envronment
More informationModeling of Dynamic Systems
Modelng of Dynamc Systems Ref: Control System Engneerng Norman Nse : Chapters & 3 Chapter objectves : Revew the Laplace transform Learn how to fnd a mathematcal model, called a transfer functon Learn how
More informationModifying the Shear Buckling Loads of Metal Shear Walls for Improving Their Energy Absorption Capacity
Modfyng the Shear Bucklng Loads of Metal Shear Walls for Improvng Ther Energy Absorpton Capacty S. Shahab, M. Mrtaher, R. Mrzaefa and H. Baha 3,* George W. Woodruff School of Mechancal Engneerng, Georga
More informationAnalytical and Numerical Analysis of Free Bulge Tube Hydroforming
Amercan Journal of Appled Scences 5 (8): 97-979, 8 ISSN 546-939 8 Scence Publcatons Analytcal and Numercal Analyss of Free Bulge Tube Hydroformng F. Djavanrood, M. Ghesary and H. Zogh-shal Department of
More informationNumerical Heat and Mass Transfer
Master degree n Mechancal Engneerng Numercal Heat and Mass Transfer 06-Fnte-Dfference Method (One-dmensonal, steady state heat conducton) Fausto Arpno f.arpno@uncas.t Introducton Why we use models and
More informationBuckling analysis of single-layered FG nanoplates on elastic substrate with uneven porosities and various boundary conditions
IOSR Journal of Mechancal and Cvl Engneerng (IOSR-JMCE) e-issn: 78-1684,p-ISSN: 30-334X, Volume 15, Issue 5 Ver. IV (Sep. - Oct. 018), PP 41-46 www.osrjournals.org Bucklng analyss of sngle-layered FG nanoplates
More informationModule 3 LOSSY IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module 3 LOSSY IMAGE COMPRESSION SYSTEMS Verson ECE IIT, Kharagpur Lesson 6 Theory of Quantzaton Verson ECE IIT, Kharagpur Instructonal Objectves At the end of ths lesson, the students should be able to:
More information( ) = ( ) + ( 0) ) ( )
EETOMAGNETI OMPATIBIITY HANDBOOK 1 hapter 9: Transent Behavor n the Tme Doman 9.1 Desgn a crcut usng reasonable values for the components that s capable of provdng a tme delay of 100 ms to a dgtal sgnal.
More informationUncertainty in measurements of power and energy on power networks
Uncertanty n measurements of power and energy on power networks E. Manov, N. Kolev Department of Measurement and Instrumentaton, Techncal Unversty Sofa, bul. Klment Ohrdsk No8, bl., 000 Sofa, Bulgara Tel./fax:
More informationComputer Based Porosity Design by Multi Phase Topology Optimization
Computer Based Porosty Desgn by Mult Phase Topology Optmzaton Andreas Burbles and Matthas Busse Fraunhofer-Insttut für Fertgungstechnk und Angewandte Materalforschung - IFAM Wener Str. 12, 28359 Bremen,
More informationA comprehensive study: Boundary conditions for representative volume elements (RVE) of composites
Insttute of Structural Mechancs A comprehensve study: Boundary condtons for representatve volume elements (RVE) of compostes Srhar Kurukur A techncal report on homogenzaton technques A comprehensve study:
More informationDifference Equations
Dfference Equatons c Jan Vrbk 1 Bascs Suppose a sequence of numbers, say a 0,a 1,a,a 3,... s defned by a certan general relatonshp between, say, three consecutve values of the sequence, e.g. a + +3a +1
More informationAPPENDIX F A DISPLACEMENT-BASED BEAM ELEMENT WITH SHEAR DEFORMATIONS. Never use a Cubic Function Approximation for a Non-Prismatic Beam
APPENDIX F A DISPACEMENT-BASED BEAM EEMENT WITH SHEAR DEFORMATIONS Never use a Cubc Functon Approxmaton for a Non-Prsmatc Beam F. INTRODUCTION { XE "Shearng Deformatons" }In ths appendx a unque development
More informationAdjoint Methods of Sensitivity Analysis for Lyapunov Equation. Boping Wang 1, Kun Yan 2. University of Technology, Dalian , P. R.
th World Congress on Structural and Multdscplnary Optmsaton 7 th - th, June 5, Sydney Australa Adjont Methods of Senstvty Analyss for Lyapunov Equaton Bopng Wang, Kun Yan Department of Mechancal and Aerospace
More informationMECHANICS OF MATERIALS
Fourth Edton CHTER MECHNICS OF MTERIS Ferdnand. Beer E. Russell Johnston, Jr. John T. DeWolf ecture Notes: J. Walt Oler Texas Tech Unversty Stress and Stran xal oadng Contents Stress & Stran: xal oadng
More informationModule 3: Element Properties Lecture 1: Natural Coordinates
Module 3: Element Propertes Lecture : Natural Coordnates Natural coordnate system s bascally a local coordnate system whch allows the specfcaton of a pont wthn the element by a set of dmensonless numbers
More informationPhysics 5153 Classical Mechanics. Principle of Virtual Work-1
P. Guterrez 1 Introducton Physcs 5153 Classcal Mechancs Prncple of Vrtual Work The frst varatonal prncple we encounter n mechancs s the prncple of vrtual work. It establshes the equlbrum condton of a mechancal
More informationPlease review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.
Please revew the followng statement: I certfy that I have not gven unauthorzed ad nor have I receved ad n the completon of ths exam. Sgnature: Instructor s Name and Secton: (Crcle Your Secton) Sectons:
More informationΔ x. u(x,t) Fig. Schematic view of elastic bar undergoing axial motions
ME67 - Handout 4 Vbratons of Contnuous Systems Axal vbratons of elastc bars The fgure shows a unform elastc bar of length and cross secton A. The bar materal propertes are ts densty ρ and elastc modulus
More informationin a horizontal wellbore in a heavy oil reservoir
498 n a horzontal wellbore n a heavy ol reservor L Mngzhong, Wang Ypng and Wang Weyang Abstract: A novel model for dynamc temperature dstrbuton n heavy ol reservors s derved from and axal dfference equatons
More informationVisco-Rubber Elastic Model for Pressure Sensitive Adhesive
Vsco-Rubber Elastc Model for Pressure Senstve Adhesve Kazuhsa Maeda, Shgenobu Okazawa, Koj Nshgch and Takash Iwamoto Abstract A materal model to descrbe large deformaton of pressure senstve adhesve (PSA
More informationModeling and Simulation of a Hexapod Machine Tool for the Dynamic Stability Analysis of Milling Processes. C. Henninger, P.
Smpack User Meetng 27 Modelng and Smulaton of a Heapod Machne Tool for the Dynamc Stablty Analyss of Mllng Processes C. Hennnger, P. Eberhard Insttute of Engneerng project funded by the DFG wthn the framework
More informationHEAT TRANSFER THROUGH ANNULAR COMPOSITE FINS
Journal of Mechancal Engneerng and Technology (JMET) Volume 4, Issue 1, Jan-June 2016, pp. 01-10, Artcle ID: JMET_04_01_001 Avalable onlne at http://www.aeme.com/jmet/ssues.asp?jtype=jmet&vtype=4&itype=1
More informationFrame element resists external loads or disturbances by developing internal axial forces, shear forces, and bending moments.
CE7 Structural Analyss II PAAR FRAE EEET y 5 x E, A, I, Each node can translate and rotate n plane. The fnal dsplaced shape has ndependent generalzed dsplacements (.e. translatons and rotatons) noled.
More informationChapter Eight. Review and Summary. Two methods in solid mechanics ---- vectorial methods and energy methods or variational methods
Chapter Eght Energy Method 8. Introducton 8. Stran energy expressons 8.3 Prncpal of statonary potental energy; several degrees of freedom ------ Castglano s frst theorem ---- Examples 8.4 Prncpal of statonary
More informationFastener Modeling for Joining Composite Parts
AM-VPD09-006 Fastener Modelng for Jonng Composte Parts Alexander Rutman, Assocate Techncal Fellow, Sprt AeroSystems Chrs Boshers, Stress ngneer, Sprt AeroSystems John Parady, Prncpal Applcaton ngneer,
More informationNovember 5, 2002 SE 180: Earthquake Engineering SE 180. Final Project
SE 8 Fnal Project Story Shear Frame u m Gven: u m L L m L L EI ω ω Solve for m Story Bendng Beam u u m L m L Gven: m L L EI ω ω Solve for m 3 3 Story Shear Frame u 3 m 3 Gven: L 3 m m L L L 3 EI ω ω ω
More informationGlobal Sensitivity. Tuesday 20 th February, 2018
Global Senstvty Tuesday 2 th February, 28 ) Local Senstvty Most senstvty analyses [] are based on local estmates of senstvty, typcally by expandng the response n a Taylor seres about some specfc values
More informationStructure and Drive Paul A. Jensen Copyright July 20, 2003
Structure and Drve Paul A. Jensen Copyrght July 20, 2003 A system s made up of several operatons wth flow passng between them. The structure of the system descrbes the flow paths from nputs to outputs.
More informationx = , so that calculated
Stat 4, secton Sngle Factor ANOVA notes by Tm Plachowsk n chapter 8 we conducted hypothess tests n whch we compared a sngle sample s mean or proporton to some hypotheszed value Chapter 9 expanded ths to
More informationFirst Law: A body at rest remains at rest, a body in motion continues to move at constant velocity, unless acted upon by an external force.
Secton 1. Dynamcs (Newton s Laws of Moton) Two approaches: 1) Gven all the forces actng on a body, predct the subsequent (changes n) moton. 2) Gven the (changes n) moton of a body, nfer what forces act
More informationMoments of Inertia. and reminds us of the analogous equation for linear momentum p= mv, which is of the form. The kinetic energy of the body is.
Moments of Inerta Suppose a body s movng on a crcular path wth constant speed Let s consder two quanttes: the body s angular momentum L about the center of the crcle, and ts knetc energy T How are these
More informationConstitutive Modelling of Superplastic AA-5083
TECHNISCHE MECHANIK, 3, -5, (01, 1-6 submtted: September 19, 011 Consttutve Modellng of Superplastc AA-5083 G. Gulano In ths study a fast procedure for determnng the constants of superplastc 5083 Al alloy
More informationNote 10. Modeling and Simulation of Dynamic Systems
Lecture Notes of ME 475: Introducton to Mechatroncs Note 0 Modelng and Smulaton of Dynamc Systems Department of Mechancal Engneerng, Unversty Of Saskatchewan, 57 Campus Drve, Saskatoon, SK S7N 5A9, Canada
More informationNUMERICAL RESULTS QUALITY IN DEPENDENCE ON ABAQUS PLANE STRESS ELEMENTS TYPE IN BIG DISPLACEMENTS COMPRESSION TEST
Appled Computer Scence, vol. 13, no. 4, pp. 56 64 do: 10.23743/acs-2017-29 Submtted: 2017-10-30 Revsed: 2017-11-15 Accepted: 2017-12-06 Abaqus Fnte Elements, Plane Stress, Orthotropc Materal Bartosz KAWECKI
More informationA Hybrid Variational Iteration Method for Blasius Equation
Avalable at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 1932-9466 Vol. 10, Issue 1 (June 2015), pp. 223-229 Applcatons and Appled Mathematcs: An Internatonal Journal (AAM) A Hybrd Varatonal Iteraton Method
More informationDETERMINATION OF COMPOSITE EFFECTIVE CHARACTERISTICS AND COMPLEX MODULES FOR SHELL STRUCTURES FROM THE SOLUTION OF INVERSE PROBLEM
DETERMINATION OF COMPOSITE EFFECTIVE CHARACTERISTICS AND COMPLEX MODULES FOR SHELL STRUCTURES FROM THE SOLUTION OF INVERSE PROBLEM V. Matveyenko, N. Yurlova, D. Grachev Insttute of Contnuous Meda mechancs
More informationStudy on Non-Linear Dynamic Characteristic of Vehicle. Suspension Rubber Component
Study on Non-Lnear Dynamc Characterstc of Vehcle Suspenson Rubber Component Zhan Wenzhang Ln Y Sh GuobaoJln Unversty of TechnologyChangchun, Chna Wang Lgong (MDI, Chna [Abstract] The dynamc characterstc
More informationPERFORMANCE OF HEAVY-DUTY PLANETARY GEARS
THE INTERNATIONAL CONFERENCE OF THE CARPATHIAN EURO-REGION SPECIALISTS IN INDUSTRIAL SYSTEMS 6 th edton PERFORMANCE OF HEAVY-DUTY PLANETARY GEARS Attla Csobán, Mhály Kozma 1, 1 Professor PhD., Eng. Budapest
More informationSupplementary Notes for Chapter 9 Mixture Thermodynamics
Supplementary Notes for Chapter 9 Mxture Thermodynamcs Key ponts Nne major topcs of Chapter 9 are revewed below: 1. Notaton and operatonal equatons for mxtures 2. PVTN EOSs for mxtures 3. General effects
More informationLecture 12: Classification
Lecture : Classfcaton g Dscrmnant functons g The optmal Bayes classfer g Quadratc classfers g Eucldean and Mahalanobs metrcs g K Nearest Neghbor Classfers Intellgent Sensor Systems Rcardo Guterrez-Osuna
More informationFINITE DIFFERENCE ANALYSIS OF CURVED DEEP BEAMS ON WINKLER FOUNDATION
VOL. 6, NO. 3, MARCH 0 ISSN 89-6608 006-0 Asan Research Publshng Network (ARPN). All rghts reserved. FINITE DIFFERENCE ANALYSIS OF CURVED DEEP BEAMS ON WINKLER FOUNDATION Adel A. Al-Azzaw and Al S. Shaker
More informationLecture Note 3. Eshelby s Inclusion II
ME340B Elastcty of Mcroscopc Structures Stanford Unversty Wnter 004 Lecture Note 3. Eshelby s Incluson II Chrs Wenberger and We Ca c All rghts reserved January 6, 004 Contents 1 Incluson energy n an nfnte
More informationPreliminary Design of Moment-Resisting Frames
Prelmnary Desgn of Moment-Resstng Frames Preprnt Aamer Haque Abstract A smple method s developed for prelmnary desgn of moment-resstng frames. Preprnt submtted to Elsever August 27, 2017 1. Introducton
More informationTransfer Functions. Convenient representation of a linear, dynamic model. A transfer function (TF) relates one input and one output: ( ) system
Transfer Functons Convenent representaton of a lnear, dynamc model. A transfer functon (TF) relates one nput and one output: x t X s y t system Y s The followng termnology s used: x y nput output forcng
More informationTHE SMOOTH INDENTATION OF A CYLINDRICAL INDENTOR AND ANGLE-PLY LAMINATES
THE SMOOTH INDENTATION OF A CYLINDRICAL INDENTOR AND ANGLE-PLY LAMINATES W. C. Lao Department of Cvl Engneerng, Feng Cha Unverst 00 Wen Hwa Rd, Tachung, Tawan SUMMARY: The ndentaton etween clndrcal ndentor
More informationSTUDY OF A THREE-AXIS PIEZORESISTIVE ACCELEROMETER WITH UNIFORM AXIAL SENSITIVITIES
STUDY OF A THREE-AXIS PIEZORESISTIVE ACCELEROMETER WITH UNIFORM AXIAL SENSITIVITIES Abdelkader Benchou, PhD Canddate Nasreddne Benmoussa, PhD Kherreddne Ghaffour, PhD Unversty of Tlemcen/Unt of Materals
More informationStructural Dynamics and Earthquake Engineering
Structural Dynamcs and Earthuake Engneerng Course 9 Sesmc-resstant desgn of structures (1) Sesmc acton Methods of elastc analyss Course notes are avalable for download at http://www.ct.upt.ro/users/aurelstratan/
More informationThe Finite Element Method
The Fnte Element Method GENERAL INTRODUCTION Read: Chapters 1 and 2 CONTENTS Engneerng and analyss Smulaton of a physcal process Examples mathematcal model development Approxmate solutons and methods of
More informationModal Strain Energy Decomposition Method for Damage Detection of an Offshore Structure Using Modal Testing Information
Thrd Chnese-German Jont Symposum on Coastal and Ocean Engneerng Natonal Cheng Kung Unversty, Tanan November 8-16, 2006 Modal Stran Energy Decomposton Method for Damage Detecton of an Offshore Structure
More informationENGN 40 Dynamics and Vibrations Homework # 7 Due: Friday, April 15
NGN 40 ynamcs and Vbratons Homework # 7 ue: Frday, Aprl 15 1. Consder a concal hostng drum used n the mnng ndustry to host a mass up/down. A cable of dameter d has the mass connected at one end and s wound/unwound
More information(Online First)A Lattice Boltzmann Scheme for Diffusion Equation in Spherical Coordinate
Internatonal Journal of Mathematcs and Systems Scence (018) Volume 1 do:10.494/jmss.v1.815 (Onlne Frst)A Lattce Boltzmann Scheme for Dffuson Equaton n Sphercal Coordnate Debabrata Datta 1 *, T K Pal 1
More informationPhysics 53. Rotational Motion 3. Sir, I have found you an argument, but I am not obliged to find you an understanding.
Physcs 53 Rotatonal Moton 3 Sr, I have found you an argument, but I am not oblged to fnd you an understandng. Samuel Johnson Angular momentum Wth respect to rotatonal moton of a body, moment of nerta plays
More informationResource Allocation with a Budget Constraint for Computing Independent Tasks in the Cloud
Resource Allocaton wth a Budget Constrant for Computng Independent Tasks n the Cloud Wemng Sh and Bo Hong School of Electrcal and Computer Engneerng Georga Insttute of Technology, USA 2nd IEEE Internatonal
More informationDYNAMIC BEHAVIOR OF PILE GROUP CONSIDERING SOIL-PILE-CAP INTERACTION
October 1-17, 8, Bejng, Chna DYNAMIC BEHAVIOR OF PILE GROUP CONSIDERING SOIL-PILE-CAP INTERACTION A. M. Halaban 1 and M. Malek 1 Professor, Faculty of Cvl Engneerng, Isfahan Unversty of Technology, Isfahan,
More informationRobert Eisberg Second edition CH 09 Multielectron atoms ground states and x-ray excitations
Quantum Physcs 量 理 Robert Esberg Second edton CH 09 Multelectron atoms ground states and x-ray exctatons 9-01 By gong through the procedure ndcated n the text, develop the tme-ndependent Schroednger equaton
More informationOptimum Design of Steel Frames Considering Uncertainty of Parameters
9 th World Congress on Structural and Multdscplnary Optmzaton June 13-17, 211, Shzuoka, Japan Optmum Desgn of Steel Frames Consderng ncertanty of Parameters Masahko Katsura 1, Makoto Ohsak 2 1 Hroshma
More informationχ x B E (c) Figure 2.1.1: (a) a material particle in a body, (b) a place in space, (c) a configuration of the body
Secton.. Moton.. The Materal Body and Moton hyscal materals n the real world are modeled usng an abstract mathematcal entty called a body. Ths body conssts of an nfnte number of materal partcles. Shown
More informationEffect of anisotropy on laminated composite plates containing circular holes
Indan Journal of ngneerng & Materals Scences Vol. 1, June 005, pp. 07-13 ffect of ansotropy on lamnated composte plates contanng crcular holes H Murat Arslan Cukurova Unversty, Cvl ngneerng Department,
More informationDynamic Analysis Based On ANSYS of Turning and Grinding Compound Machine Spindle Box Zanhui Shu and Qiushi Han
Advanced Materals Research Onlne: 2012-01-03 ISSN: 1662-8985, Vols. 433-440, pp 524-529 do:10.4028/www.scentfc.net/amr.433-440.524 2012 Trans Tech Publcatons, Swtzerland Dynamc Analyss Based On ANSYS of
More informationLecture 12: Discrete Laplacian
Lecture 12: Dscrete Laplacan Scrbe: Tanye Lu Our goal s to come up wth a dscrete verson of Laplacan operator for trangulated surfaces, so that we can use t n practce to solve related problems We are mostly
More informationChapter - 2. Distribution System Power Flow Analysis
Chapter - 2 Dstrbuton System Power Flow Analyss CHAPTER - 2 Radal Dstrbuton System Load Flow 2.1 Introducton Load flow s an mportant tool [66] for analyzng electrcal power system network performance. Load
More informationDetermination of the response distributions of cantilever beam under sinusoidal base excitation
Journal of Physcs: Conference Seres OPEN ACCESS Determnaton of the response dstrbutons of cantlever beam under snusodal base exctaton To cte ths artcle: We Sun et al 13 J. Phys.: Conf. Ser. 448 11 Vew
More informationA Timoshenko Piezoelectric Beam Finite Element with Consistent Performance Irrespective of Geometric and Material Configurations
99 A Tmoshenko Pezoelectrc Beam Fnte Element wth Consstent Performance Irrespectve of Geometrc and Materal Confguratons Abstract The conventonal Tmoshenko pezoelectrc beam fnte elements based on Frst-order
More informationAssessment of Site Amplification Effect from Input Energy Spectra of Strong Ground Motion
Assessment of Ste Amplfcaton Effect from Input Energy Spectra of Strong Ground Moton M.S. Gong & L.L Xe Key Laboratory of Earthquake Engneerng and Engneerng Vbraton,Insttute of Engneerng Mechancs, CEA,
More information