Effect of plate s parameters on vibration of isotropic tapered rectangular plate with different boundary conditions
|
|
- Abner Booker
- 5 years ago
- Views:
Transcription
1 Original Article Effect of plate s parameters on vibration of isotropic tapered rectangular plate ith different boundar conditions Journal of Lo Frequenc Noise, Vibration and Active Control 216, Vol. 35(2) ! The Author(s) 216 Reprints and permissions: sagepub.co.uk/journalspermissions.nav DOI: / lfn.sagepub.com Anupam Khanna 1 and Ashish Singhal 2 Abstract A mathematical model is presented to analse the vibration of a tapered isotropic rectangular plate under thermal condition. Tapering in the thickness of rectangular plate is considered bi-parabolic. Here, temperature variation is assumed bi-linearl, i.e. temperature varies linearl in the -direction and linearl in the -direction. First to modes of frequenc of rectangular plate are calculated for five boundar conditions such as C-C-C-C, SS-SS-SS-SS, C-SS-SS-SS, C-SS-C-SS and C-C-C-SS, here C and SS stand for clamped boundar and simpl supported boundar, respectivel. The plate is considered homogeneous and made up of a visco-elastic isotropic material. Raleigh Ritz technique is applied to get the first to modes of frequencies at different values of plate s parameters. Numeric results are presented in tabulated and graphical forms. Keords Isotropic tapered plate, clamped plate, simpl supported plate, thermal gradient, aspect ratio Introduction In recent ears, tapered plates are being increasingl used in modern engineering structures or space vehicles due to their ide technical importance. Consideration of tapered plates not onl helps to reduce the eight of structural elements but also improves the utilisation of the material. Almost ever structure or vehicle orks under the influence of elevated temperature field due to hich a heat flu is created and it directl affects the efficienc of a vehicle or structure. In the available literature, man authors have discussed the vibration of plates having one or to directional tapering ith one-dimensional thermal effect but little ork has been done in the field of to-dimensional thermal effects. Therefore, the authors of this paper discuss vibration problem of visco-elastic rectangular plate ith biparabolic thickness variation along ith bi-linear thermal condition. A surve of research papers, monographs and books published in the last si decades is given as follos. A monograph on vibration of plates ith different shapes and boundar conditions is given b Leissa. 1 Leissa 2 studied the effect of non-homogeneit on the free vibrations of rectangular plate of various combinations of clamped, simpl supported, and free boundar conditions. Jain and Soni 3 discussed the free vibrations of rectangular plate ith parabolic varing thickness using classic theor of plate. In this paper, to parallel edges of the plate are considered as simpl supported and different boundar conditions are considered for the remaining to edges. Tomar and Gupta 4 studied the effect of thermal gradient on the free vibrations of an orthotropic rectangular plate ith bi-linearl thickness variation for various boundar conditions. Leissa 5 analsed the effect of thermal 1 Department of Mathematics, D.A.V. College-Sadhaura, Yamuna Nagar, Harana, India 2 Department of Mathematics, Northern India Engineering College, Delhi, India Corresponding author: Anupam Khanna, Department of Mathematics, D.A.V. College-Sadhaura, Yamuna Nagar, Harana, India. rajieanupam@gmail.com
2 14 Journal of Lo Frequenc Noise, Vibration and Active Control 35(2) gradient on the vibration of parallelogram plate ith bi-directional thickness variation in both directions for various combinations of boundar conditions. Qiu et al. 6 presented some eperiments on the active control of circular disk vibration. Lal 7 studied transverse vibrations of an orthotropic non-uniform plate ith continuousl varing densit. To parallel edges are considered simpl supported and different combinations of boundar conditions are considered for the other to parallel edges. Li 8 has given a vibrational analsis of rectangular plate ith general elastic boundar support. Leissa 9 discussed the historical bases of Raleigh and Ritz s methods to minimise the frequenc of the vibrations of different structures of beams, bars, plates, etc. Gupta and Kumar 1 studied the thermal effect on vibrations of non-homogeneous rectangular plate ith bi-linearl varing thickness variations. Lal and Dhanpati 11 analsed the free transverse vibrations of non-homogeneous plate of varing thickness. Hota et al. 12 analsed the free vibration of perforated plates. Gupta and Kumar 13 analsed the effect of thermall induced vibration of orthotropic trapezoidal plate ith linearl varing thickness. Shooshtari and Razavi 14 orked on non-linear vibration of laminated fiber-reinforced rectangular plates. Abu Bakar et al. 15 analsed aismmetric vibration of circular plate ith attached annular piezoceramic plate. Khanna and Arora 16 analsed the effect of sinusoidal varing thickness on the vibrations of non-homogeneous parallelogram plate ith bi-linearl temperature variation. The also discussed the effect of non-homogeneit of the material. Khanna and Kaur 17 studied the effect of eponentiall varing thickness, temperature, and Poisson ratio on the free vibration of visco-elastic rectangular plate. The main endeavour of the present investigation is to stud the effects of varing plate s parameters, i.e. thermal gradient (due to temperature variation), taper constants (due to thickness variation) and aspect ratio (ratio of length and breadth of the plate) on the vibration of visco-elastic isotropic rectangular plate. Here, the first to modes of frequenc of the vibration of isotropic rectangular plate are calculated ith the help of Raleigh Ritz technique for five different boundar conditions. Results are given in the form of tables and graphs. Analsis of equation of motion The differential equation describing the motion of a visco-elastic isotropic rectangular plate ma be ritten as 2 2 þ ð1þ here and are the coordinates of the plate geometr, M and M are the bending moments, M is the tisting moment per unit length of plate, is the mass per unit volume, h is the thickness of plate and is the displacement at time t. The epressions for M,M and M are given b 2 M ¼ ~DD 2, M ¼ ~DD 2 here ~D is visco-elastic operator. Here, D 1 is the fleural rigidit of the plate s material and it is epressed as 2 and M ¼ ~DD 1 Eh 3 D 1 ¼ 12ð1 2 Þ Substituting the values of M,M and M in equation (1), one ed 4 D þ @ 3 2 þ @ 3 2 D 2 D 2 þ 2ð1 D 2 2 ¼ ð2þ ð3þ
3 Khanna and Singhal 141 Using variable separation method, deflection ma be considered as the product of to functions as 21 ð,, tþ ¼ð, Þ:TðtÞ ð4þ here (, ) is the deflection function in and and T(t) is a time function for the vibration of rectangular plate. Substituting equation (4) into equation (3), one obtains D 4 D þ @ 3 2 þ @ D 2 þ 2ð1 D 2 =h T=@t edt Equating both sides of equation (5) to a constant p 2, one þ D 2 D 2 D þ @ 3 2 þ 2ð1 D 2 p 2 ð6þ 2 2 þ p2 ~DT ¼ ð7þ Equations (6) and (7) are differential equations of motion and time function for visco-elastic rectangular plate. Since the research area of vibration of plates is too ide to discuss at once, the authors proceed ith a fe limitations. Limitation 1 Thickness of the rectangular plate is considered non-uniform, i.e. thickness of the plate varies bi-parabolic 18 as (shon in Figure 1) 2 2 h ¼ h 1 þ 1 1 þ 2 a 2 b 2 ð8þ Figure 1. Rectangular Plate ith 2-directional thickness variation.
4 142 Journal of Lo Frequenc Noise, Vibration and Active Control 35(2) here a and b are the length and breadth of rectangular plate, respectivel, 1 and 2 are the taper parameters in the -direction and -direction, respectivel, and h is the thickness of the plate at ¼ ¼. Limitations 2 The structures of high-speed space vehicles, i.e. supersonic flights, missiles, etc. are subjected to high surface temperature and large thermal gradient. These conditions can seriousl affect or damage the structure of these vehicles. Variations in the structure s characteristics as a result of thermal effect can be observed b the changes in frequenc of vibration. Therefore, the authors assumed bi-linear temperature variations as 22 ¼ 1 1 ð9þ a b here denotes the temperature ecess above the reference temperature at an point on the plate and denotes the temperature ecess above the reference temperature at ¼ ¼. The temperature dependence of the modulus of elasticit for most of the engineering materials can be epressed as follos 2 E ¼ E ð1 Þ ð1þ here E is value of the Young s modulus at reference temperature, i.e. ¼ and is slope of variation of E and. Using equation (9) in equation (1), one obtains h E ¼ E 1 1 ð11þ a b here ¼ ( <1) is the thermal gradient. Using equations (8) and (11) in equation (2), one gets E 1 1 a b h 3 1 þ 2 1 a 1 þ 2 2 D 1 ¼ 2 b 2 12ð1 2 Þ ð12þ Limitation 3 In order to fulfil the practical aspects for using in structures or vehicles, the authors discuss five different boundar conditions for the rectangular plate, i.e. C-C-C-C, SS-SS-SS-SS, C-SS-SS-SS, C-SS-C-SS and C-C-C-SS 23,24 as follos: (i) hen the boundar of plate is C-C-C-C, the boundar conditions ¼ at ¼, a and ¼ at ¼, To satisf these boundar conditions, the to-term deflection function is defined as ¼ h 1 1 A 1 þ A 2 1 (ii) hen the boundar of the plate is SS-SS-SS-SS, the boundar conditions 2 ¼ at ¼, a and ¼ at ¼,
5 Khanna and Singhal 143 To satisf these boundar conditions, the to-term deflection function is defined as h ¼ 1 h A 1 þ A 2 1 (iii) hen the boundar of the plate is C-SS-SS-SS, the boundar conditions ¼ at 2 ¼ at ¼ a and ¼ at ¼, To satisf these boundar conditions, the to-term deflection function is defined as ¼ h A 1 þ A 2 1 (iv) hen the boundar of the plate is C-SS-C-SS, the boundar conditions ¼ at ¼, a and ¼ at ¼, To satisf these boundar conditions, the to-term deflection function is defined as ¼ h 1 A 1 þ A 2 1 (v) hen the boundar of plate is C-C-C-SS, the boundar conditions ¼ at ¼, a ¼ at ¼ 2 ¼ at ¼ b To satisf these boundar conditions, the to-term deflection function is defined as ¼ h 1 1 A 1 þ A 2 1 Here, A 1 and A 2 are the arbitrar constants occurred due to the first to modes of vibration. Solution of frequenc equation Raleigh Ritz technique is applied to solve the frequenc equation. In this method, one requires that the maimum strain energ (S E ) must be equal to the maimum kinetic energ (K E ). So it is necessar for the problem under consideration that 25 ðs E K E Þ¼ ð13þ Here K E ¼ 1 2 p2 Z a Z b h 2 dd and S E ¼ 1 2 Z a Z b " þ 2ð1 2 2 #
6 144 Journal of Lo Frequenc Noise, Vibration and Active Control 35(2) Assuming the non-dimensional variables as X ¼ a, Y ¼ a, ¼ a, h ¼ h a ð14þ Using equation (14), the kinetic energ (K E ) and strain energ (S E ) become K E ¼ 1 Z 1 Z b=a 2 p2 h a 5 ð1 þ 1 X 2 a 2 Þ 1 þ 2 b 2 Y2 2 dydx ð15þ and S E ¼ E h 3 Z 1 Z b=a n a3 24ð1 2 1 ð1 XÞ 1 a oð1 Þ b Y þ 1 X 2 Þ 3 a þ 2 b 2 Y2 " þ 2ð1 ð16þ Using the modified values of kinetic and strain energ in equation (13), one gets S E l2 K E ¼ ð17þ here K E ¼ Z 1 Z b=a ð1 þ 1 X 2 a 2 Þ 1 þ 2 b 2 Y2 2 dydx and Z 1 Z b=a n S E ¼ 1 ð1 XÞ 1 a oð1 b Y þ 1 X 2 Þ 3 a þ 2 b 2 Y2 " þ 2ð1 Here, l 2 ¼ 12p2 a 2 ð1 2 Þ is the frequenc parameter. E h 2 Equation (17) consists of to unknon constants, i.e. A 1 and A 2 arising due to the substitution of corresponding to the different boundar conditions. These to constants are to be determined as follos Simplifing equation (18), one S l2 K E ¼, n ¼ 1, 2 ð18þ n bn 1 A 1 þ bn 2 A 2 ¼, n ¼ 1, 2 ð19þ here b n1 and b n2 include parametric constants, i.e. taper constants, thermal gradient, aspect ratio and frequenc parameter. For a non-trivial solution, the determinant of the coefficient must be zero. So, one gets the frequenc equation as b 11 b 12 b 21 b 22 ¼ ð2þ
7 Khanna and Singhal 145 Table 1. Frequenc versus thermal gradient at fied a/b ¼ ¼ 2 ¼. 1 ¼ 2 ¼.4 1 ¼ 2 ¼.8 B.C s Mode I Mode II Mode I Mode II Mode I Mode II C-C-C-C SS-SS-SS-SS C-SS-SS-SS C-SS-C-SS C-C-C-SS C-C-C-C SS-SS-SS-SS C-SS-SS-SS C-SS-C-SS C-C-C-SS C-C-C-C SS-SS-SS-SS C-SS-SS-SS C-SS-C-SS C-C-C-SS Table 2. Frequenc versus taper constants at fied a/b ¼ 1.5, ¼ B.C s Mode I Mode II Mode I Mode II Mode I Mode II C-C-C-C SS-SS-SS-SS C-SS-SS-SS C-SS-C-SS C-C-C-SS C-C-C-C SS-SS-SS-SS C-SS-SS-SS C-SS-C-SS C-C-C-SS C-C-C-C SS-SS-SS-SS C-SS-SS-SS C-SS-C-SS C-C-C-SS ith the help of equation (22), one can obtain a quadratic equation in l 2 from hich the to values of frequenc parameter for both the modes of vibration can be evaluated easil. Results and discussion Computations ere made for the first to modes of frequenc at different values of thermal gradient (), taper constants ( 1 and 2 ) and aspect ratio (a/b) for the five different boundar conditions. In calculations, Poisson ratio is considered as constant, i.e..345, and thickness of the plate h at X ¼ Y ¼ is taken as.1 m.
8 146 Journal of Lo Frequenc Noise, Vibration and Active Control 35(2) Table 3. Frequenc versus aspect ratio. ¼ 1 ¼ 2 ¼. ¼ 1 ¼ 2 ¼.4 ¼ 1 ¼ 2 ¼.8 a/b B.C s Mode I Mode II Mode I Mode II Mode I Mode II.5 C-C-C-C SS-SS-SS-SS C-SS-SS-SS C-SS-C-SS C-C-C-SS C-C-C-C SS-SS-SS-SS C-SS-SS-SS C-SS-C-SS C-C-C-SS C-C-C-C SS-SS-SS-SS C-SS-SS-SS C-SS-C-SS C-C-C-SS Figure 2. Frequenc (Mode 1) versus thermal gradient. Frequenc for the first to modes of vibration ere calculated for increasing values of thermal gradient at various combinations of taper parameters and fied value of aspect ratio, and the results are shon in Table 1. It is evident that the frequenc for both the modes of vibration of plate ith different boundar conditions decrease continuousl as thermal gradient () increases corresponding to each paired value of 1 and 2. It is interesting to note that the first mode of frequenc is maimum for C-C-C-SS plate but minimum for C-C-C-C plate. For second mode, frequenc is maimum for C-C-C-C plate, hile minimum for SS-SS-SS-SS. Table 2 shos the frequenc for the first to modes of vibration for various values of taper parameters at a fied aspect ratio and thermal gradient. The authors conclude that the frequenc continuousl increases as one of
9 Khanna and Singhal 147 Figure 3. Frequenc (Mode 2) versus thermal gradient. Figure 4. Frequenc (Mode 1) versus taper constant ( 1 ). the taper parameter increases for a fied value of another. It is clear from Table 2 that the frequenc increases faster hen 2 increases from. to.8 as compared to increasing 1. Frequenc for the first to modes of vibration at different values of aspect ratio for the fied values of plate s parameters are calculated and presented in Table 3. It is noted that the frequencies for both the modes of vibration increase rapidl as the aspect ratio (a/b) increases from.5 to 1.5 for the five different boundar conditions at each paired value of a, 1 and 2. For better understanding of the results in terms of boundar conditions, the results in Tables 1 to 3 are presented in a graphical form. It is clear from Figures 2 and 3 that the frequenc for both the modes of vibration decreases continuousl at fied values of taper constant and the aspect ratio for different boundar conditions.
10 148 Journal of Lo Frequenc Noise, Vibration and Active Control 35(2) Figure 5. Frequenc (Mode 2) versus taper constant ( 1 ). Figure 6. Frequenc (Mode 1) versus taper constant ( 2 ). One can clearl observe from Figures 4 to 7 that the frequenc increases continuousl for the first to modes of vibrations as the taper constants ( 1 and 2 ) increase for the fied values of the thermal gradient and aspect ratio. The authors conclude from the graphs in Figures 8 and 9 that the frequenc for both the modes of vibration increases ver fast as the aspect ratio (a/b) increases from.5 to 1.5 for all the five combinations of boundar conditions. Comparison and conclusions Table 4 shos a comparison of the results of frequenc for both the modes of vibration for C-C-C-C boundar condition onl ith Khanna and Singhal 22 at the corresponding values of the plate s parameters. Here, the authors
11 Khanna and Singhal 149 Figure 7. Frequenc (Mode 2) versus taper constant ( 2 ). Figure 8. Frequenc (Mode 1) versus aspect ratio (a/b). found that the frequenc for the both modes of vibration is less than that in the present paper (shon in italic) than 22 (shon in bold) at the corresponding values of the plate s parameters. It shos that the frequenc of the rectangular plate changes ith the change in tapering of the plate. The results, in light of the comparison, can thus be summarised in the folloing points: 1. Frequenc can be controlled b appropriate tapering, i.e. b assuming suitable values of taper parameters. Desired values of frequenc can be obtained b choosing appropriate taper parameters.
12 15 Journal of Lo Frequenc Noise, Vibration and Active Control 35(2) Figure 9. Frequenc (Mode 2) versus aspect ratio (a/b). Table 4. Frequenc of present paper versus 15 at a/b ¼ ¼ 2 ¼.4 1 ¼ 2 ¼.8 Mode 1 Mode 2 Mode 1 Mode Boundar conditions directl affect the vibrational characteristics of the rectangular plate. 3. First mode of frequenc is maimum at C-C-C-SS boundar condition but minimum at C-C-C-C boundar condition. But second mode is maimum at C-C-C-C boundar condition and minimum at SS-SS-SS-SS boundar condition. 4. ith increasing values of thermal gradient, frequenc decreases for both the modes of vibration of plate. It implies that temperature variations also directl affect the vibration of plate. 5. Vibration can be controlled effectivel b bi-parabolic thickness variation (present paper) as compared to the bi-linear thickness variation. 22 Therefore, scientists and design engineers ho are orking in designing space vehicles or structures are advised to analse the findings of the present stud in a practical manner to make more efficient and authentic mechanical structures and safe designs of vehicles. Declaration of conflicting interests The author(s) declared no potential conflicts of interest ith respect to the research, authorship, and/or publication of this article. Funding The author(s) received no financial support for the research, authorship, and/or publication of this article. References 1. Leissa A. Vibration of plates, NASA SP-16 (1969), Scientific and Technical Information Division, National Aeronautics and Space Administration (NASA).
13 Khanna and Singhal Leissa A. The free vibration of rectangular plates. J Sound Vibr 1973; 31: Jain RK and Soni SR. Free vibrations of rectangular plates of parabolicall varing thickness. Indian J Pure Appl Math 1973; 4: Tomar JS and Gupta AK. Effect of thermal gradient on frequencies of an orthotropic rectangular plate hose thickness varies in to directions. J Sound Vibr 1985; 98: Leissa A. Recent studies in plate vibration part II: complicating effects. Shock Vibr 1987; 19: Qiu J, Huang X, ang D, et al. Eperiments on the active control of circular disk vibration. J Lo Freq Noise V A Control 21; 2: Lal R. Transverse vibrations of orthotropic non-uniform rectangular plates ith continuousl varing densit. Indian J Pure Appl Math 23; 34: Li L. Vibration analsis of rectangular plate ith general elastic boundar support. J Sound Vibr 24; 273: Leissa A. The historical bases of the Raleigh and Ritz Methods. J Sound Vibr 24; 287: Gupta AK and Kumar L. Thermal effects on vibration of non-homogeneous visco-elastic rectangular plate of linearl varing thickness in to directions. Meccanica 28; 43: Lal R and Dhanpati. Effect of non-homogeneit on the vibration of orthotropic rectangular plates of varing thickness resting on a Pasternak foundation. J Vib Acoust 29; 131: Hota SS, Padhi P and Rout M. Free vibration of perforated plates. Noise Vibr orldide 29; 4: Gupta AK and Kumar S. Thermall induced vibration of orthotropic trapezoidal plate of linearl varing thickness. J Vib Control 211; 17: Shooshtari A and Razavi S. Non-linear vibration response of laminated fibre-reinforced rectangular plates. Int J Veh Noise Vib 212; 8: Abu Bakar S, Mostafa M, Faris F, et al. Aismmetric vibration analsis of isotropic circular plate ith attached annular piezoceramic plate. Int J Veh Noise Vib 212; 8: Khanna A and Arora P. Effect of sinusoidal thickness variation on vibrations of non-homogeneous parallelogram plate ith bi-linearl temperature variations. Indian J Sci Technol 213; 6: Khanna A and Kaur N. Effect of non-homogeneit on free vibration of visco-elastic rectangular plate ith varing structural parameters. J Vibroeng 213; 15: Gupta AK and Khanna A. Vibration of clamped visco-elastic rectangular plate ith parabolic thickness variations. Shock Vibr 28; 15: Khanna A and Kaur N. Vibration of non-homogeneous plate subject to thermal gradient. J Lo Freq Noise V A Control 214; 31: Gupta AK and Khanna A. Vibration of visco-elastic rectangular plate ith linearl thickness variations in both directions. J Sound Vibr 27; 31: Gupta AK, Panar V and Vats RP. Vibrations of non-homogeneous rectangular plate of variable thickness in both directions ith thermal gradient effect. Int J Appl Math Mech 21; 6: Khanna A and Singhal A. An analtical approach on thermall induced vibrations of non-homogeneous tapered plate. J Math 213; 6 pages. 23. Chandrashekhara K. Theor of plates. Hdrabad, India: Orient Blacksan, Universities Press. 24. Chakravert S. Vibration of plates. Boca Raton, Fla, USA: CRC Press, Talor and Francis Group, Khanna A and Bhatia M. Thermal effect of vibration of non-homogeneous square plate having linearl varing thickness. Int J Appl Eng Res 211; 6:
1123. Effect of non-homogeneity on free vibration of visco-elastic rectangular plate with varying structural parameters
1123. Effect of non-homogeneity on free vibration of visco-elastic rectangular plate with varying structural parameters Anupam Khanna 1, Narinder Kaur 2 Department of Mathematics, Maharishi Markandeshwar
More informationEFFECT OF DAMPING AND THERMAL GRADIENT ON VIBRATIONS OF ORTHOTROPIC RECTANGULAR PLATE OF VARIABLE THICKNESS
Available at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 193-9466 Vol. 1, Issue 1 (June 17), pp. 1-16 Applications and Applied Mathematics: An International Journal (AAM) EFFECT OF DAMPING AND THERMAL
More informationThermally Induced Vibration of Non-Homogeneous Visco-Elastic Rectangular Plate of Variable Thickness
Thermally Induced Vibration of Non-Homogeneous Visco-Elastic Rectangular Plate of Variable Thickness 1 A.K. Gupta, 2 Sudhanshu Aggarwal 1 Associate Professor, Department of Mathematics M. S. College, Saharanpur-247001,
More informationVibration Analysis of Non-Homogeneous Tapered Parallelogram Plate with Two Dimensional Thickness and Temperature Variation
International Journal of Applied Science-Research and Review (IJAS) www.ijas.org.uk Original Article Vibration Analysis of Non-Homogeneous Tapered Parallelogram Plate with Two Dimensional Thickness and
More informationVibration of clamped visco-elastic rectangular plate with parabolic thickness variations
Shock and Vibration 15 (28) 713 723 713 IOS Press Vibration of clamped visco-elastic rectangular plate with parabolic thickness variations A.K. Gupta a, and Anupam Khanna b a Department of Mathematics,
More informationNote on Mathematical Development of Plate Theories
Advanced Studies in Theoretical Phsics Vol. 9, 015, no. 1, 47-55 HIKARI Ltd,.m-hikari.com http://d.doi.org/10.1988/astp.015.411150 Note on athematical Development of Plate Theories Patiphan Chantaraichit
More informationINTERNATIONAL JOURNAL OF APPLIED ENGINEERING RESEARCH, DINDIGUL Volume 2, No 2, 2011
Volume, No, 11 Copyright 1 All rights reserved Integrated Pulishing Association REVIEW ARTICLE ISSN 976 459 Analysis of free virations of VISCO elastic square plate of variale thickness with temperature
More informationInternational Journal of Technical Research and Applications Tushar Choudhary, Ashwini Kumar Abstract
International Journal of Technical Research and Applications e-issn: 30-8163 www.ijtra.com Volume 3 Issue 1 (Jan-Feb 015) PP. 135-140 VIBRATION ANALYSIS OF STIFF PLATE WITH CUTOUT Tushar Choudhar Ashwini
More informationVibration Analysis of Isotropic and Orthotropic Plates with Mixed Boundary Conditions
Tamkang Journal of Science and Engineering, Vol. 6, No. 4, pp. 7-6 (003) 7 Vibration Analsis of Isotropic and Orthotropic Plates with Mied Boundar Conditions Ming-Hung Hsu epartment of Electronic Engineering
More informationVibration of Plate on Foundation with Four Edges Free by Finite Cosine Integral Transform Method
854 Vibration of Plate on Foundation with Four Edges Free b Finite Cosine Integral Transform Method Abstract The analtical solutions for the natural frequencies and mode shapes of the rectangular plate
More information1.1 The Equations of Motion
1.1 The Equations of Motion In Book I, balance of forces and moments acting on an component was enforced in order to ensure that the component was in equilibrium. Here, allowance is made for stresses which
More informationME 7502 Lecture 2 Effective Properties of Particulate and Unidirectional Composites
ME 75 Lecture Effective Properties of Particulate and Unidirectional Composites Concepts from Elasticit Theor Statistical Homogeneit, Representative Volume Element, Composite Material Effective Stress-
More informationBending Analysis of Isotropic Rectangular Plate with All Edges Clamped: Variational Symbolic Solution
Journal of Emerging Trends in Engineering and pplied Sciences (JETES) (5): 86-85 Scholarlink Research Institute Journals, 0 (ISSN: -706) jeteas.scholarlinkresearch.org Journal of Emerging Trends in Engineering
More informationVibration Analysis of Plate with One Free Edge Using Energy Method (CCCF Plate)
International Journal of Engineering and Technology Volume 4 No. 1, January, 2014 Vibration Analysis of Plate with One Free Edge Using Energy Method (CCCF Plate) Ezeh, J. C, Ibearugbulem, Owus M., Ebirim,
More informationFree vibration of a microbeam resting on Pasternak s foundation via the Green Naghdi thermoelasticity theory without energy dissipation
Original Article Free vibration of a microbeam resting on Pasternak s foundation via the Green Naghdi thermoelasticity theory without energy dissipation Journal of Low Frequency Noise, Vibration and Active
More informationAvailable online at ScienceDirect. Procedia Engineering 90 (2014 )
Available online at.sciencedirect.com ScienceDirect Procedia Engineering 9 (14 383 388 1th International Conference on Mechanical Engineering, ICME 13 Effects of volumetric heat source and temperature
More informationBOUNDARY EFFECTS IN STEEL MOMENT CONNECTIONS
BOUNDARY EFFECTS IN STEEL MOMENT CONNECTIONS Koung-Heog LEE 1, Subhash C GOEL 2 And Bozidar STOJADINOVIC 3 SUMMARY Full restrained beam-to-column connections in steel moment resisting frames have been
More informationCalculus of the Elastic Properties of a Beam Cross-Section
Presented at the COMSOL Conference 2009 Milan Calculus of the Elastic Properties of a Beam Cross-Section Dipartimento di Modellistica per l Ingegneria Università degli Studi della Calabria (Ital) COMSOL
More informationA HIGHER-ORDER BEAM THEORY FOR COMPOSITE BOX BEAMS
A HIGHER-ORDER BEAM THEORY FOR COMPOSITE BOX BEAMS A. Kroker, W. Becker TU Darmstadt, Department of Mechanical Engineering, Chair of Structural Mechanics Hochschulstr. 1, D-64289 Darmstadt, Germany kroker@mechanik.tu-darmstadt.de,
More informationy R T However, the calculations are easier, when carried out using the polar set of co-ordinates ϕ,r. The relations between the co-ordinates are:
Curved beams. Introduction Curved beams also called arches were invented about ears ago. he purpose was to form such a structure that would transfer loads, mainl the dead weight, to the ground b the elements
More informationBending of Shear Deformable Plates Resting on Winkler Foundations According to Trigonometric Plate Theory
J. Appl. Comput. ech., 4(3) (018) 187-01 DOI: 10.055/JAC.017.3057.1148 ISSN: 383-4536 jacm.scu.ac.ir Bending of Shear Deformable Plates Resting on Winkler Foundations According to Trigonometric Plate Theor
More informationMECHANICS OF MATERIALS REVIEW
MCHANICS OF MATRIALS RVIW Notation: - normal stress (psi or Pa) - shear stress (psi or Pa) - normal strain (in/in or m/m) - shearing strain (in/in or m/m) I - area moment of inertia (in 4 or m 4 ) J -
More informationPassive Damping Characteristics of Carbon Epoxy Composite Plates
Journal of Materials Science and Engineering A 6 (-) 35-4 doi:.765/6-63/6.-.5 D DAVID PUBLISHING Passive Damping Characteristics of Carbon Epoxy Composite Plates Dileep Kumar K * and V V Subba Rao Faculty
More informationModal analysis of an elliptical plate clamped along its boundary
Modal analysis of an elliptical plate clamped along its boundary T.Lakshmi Reddy 1, P.V. Pavan Kumar 2, Akshay Prajapati 3 1 PG Scholar, Mechanical, Maulana Azad National Institute of Technology, Bhopal,
More informationAircraft Structures Structural & Loading Discontinuities
Universit of Liège Aerospace & Mechanical Engineering Aircraft Structures Structural & Loading Discontinuities Ludovic Noels Computational & Multiscale Mechanics of Materials CM3 http://www.ltas-cm3.ulg.ac.be/
More informationFree Vibration Analysis of Rectangular Plates Using a New Triangular Shear Flexible Finite Element
International Journal of Emerging Engineering Research and echnolog Volume Issue August PP - ISSN - (Print) & ISSN - (Online) Free Vibration Analsis of Rectangular Plates Using a New riangular Shear Fleible
More informationDeflection of Beams. Equation of the Elastic Curve. Boundary Conditions
Deflection of Beams Equation of the Elastic Curve The governing second order differential equation for the elastic curve of a beam deflection is EI d d = where EI is the fleural rigidit, is the bending
More informationChapter 18 KINETICS OF RIGID BODIES IN THREE DIMENSIONS. The two fundamental equations for the motion of a system of particles .
hapter 18 KINETIS F RIID DIES IN THREE DIMENSINS The to fundamental equations for the motion of a sstem of particles ΣF = ma ΣM = H H provide the foundation for three dimensional analsis, just as the do
More informationResearch Article Equivalent Elastic Modulus of Asymmetrical Honeycomb
International Scholarl Research Network ISRN Mechanical Engineering Volume, Article ID 57, pages doi:.5//57 Research Article Equivalent Elastic Modulus of Asmmetrical Honecomb Dai-Heng Chen and Kenichi
More informationConstants of Metal Rubber Material
Constants of Metal Rubber Material Modern Applied Science; Vol. 8, No. 5; 014 ISSN 1913-1844 E-ISSN 1913-185 Published b Canadian Center of Science and Education Aleander Mikhailovich Ulanov 1 1 Samara
More informationFlexural Analysis of Deep Aluminum Beam
Journal of Soft Computing in Civil Engineering -1 (018) 71-84 journal homepage: http://www.jsoftcivil.com/ Fleural Analysis of Deep Aluminum Beam P. Kapdis 1, U. Kalwane 1, U. Salunkhe 1 and A. Dahake
More informationVIBRATION OF VISCO ELASTIC ORTHOTROPIC PARALLELOGRAM PLATE WITH PARABOLICALLY THICKNESS VARIATION
1. Arun Kumar GUPTA, 2. Amit KUMAR, 3. Dhram Veer GUPTA VIBRATION OF VISCO ELASTIC ORTHOTROPIC PARALLELOGRAM PLATE WITH PARABOLICALLY THICKNESS VARIATION 1 2. DEPARTMENT OF MATHEMATICS, M. S. COLLEGE,
More informationSurvey of Wave Types and Characteristics
Seminar: Vibrations and Structure-Borne Sound in Civil Engineering Theor and Applications Surve of Wave Tpes and Characteristics Xiuu Gao April 1 st, 2006 Abstract Mechanical waves are waves which propagate
More informationA two variable refined plate theory for orthotropic plate analysis
A two variable refined plate theory for orthotropic plate analysis R.P. Shimpi *, H.G. Patel Department of Aerospace Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, Maharashtra,
More informationARTICLE IN PRESS. Thin-Walled Structures
RTICLE I PRESS Thin-Walled Structures 47 () 4 4 Contents lists availale at ScienceDirect Thin-Walled Structures journal homepage: www.elsevier.com/locate/tws Buckling analsis of plates using the two variale
More informationFree Transverse Vibration Analysis of thin rectangular plates having arbitrarily varying non-homogeneity along two concurrent edge Avinash Kumar
Free Transverse Vibration Analysis of thin rectangular plates having arbitrarily varying non-homogeneity along two concurrent edge Avinash Kumar MECHANICAL ENGINEERING National Institute of Technology,
More informationTHE GENERAL ELASTICITY PROBLEM IN SOLIDS
Chapter 10 TH GNRAL LASTICITY PROBLM IN SOLIDS In Chapters 3-5 and 8-9, we have developed equilibrium, kinematic and constitutive equations for a general three-dimensional elastic deformable solid bod.
More informationInfluence of Chebyshev Collocation Points on the Convergence of Results in the Analysis of Annular Plate Vibrations
Tamkang Journal of Science and Engineering, Vol. 8, No 1, pp. 57 62 (2005) 57 Influence of Chebyshev Collocation Points on the Convergence of Results in the Analysis of Annular Plate Vibrations R. P. Singh
More informationAnalytical study of sandwich structures using Euler Bernoulli beam equation
Analtical stud of sandwich structures using Euler Bernoulli beam equation Hui Xue and H. Khawaja Citation: AIP Conference Proceedings 1798, 020076 (2017); doi: 10.1063/1.4972668 View online: http://dx.doi.org/10.1063/1.4972668
More informationThis is a problem of calculus of variations with an equality constraint. This problem is similar to the problem of minimizing a function
3-7 ISOPERIMETRIC PROBLEMS Isoperimetric implies constant perimeter. This is a problem of calculus of variations ith an equalit constraint in the integral form. ( V ) d ; W G( ) d This problem is similar
More informationChapter 6 2D Elements Plate Elements
Institute of Structural Engineering Page 1 Chapter 6 2D Elements Plate Elements Method of Finite Elements I Institute of Structural Engineering Page 2 Continuum Elements Plane Stress Plane Strain Toda
More informationLATERAL BUCKLING ANALYSIS OF ANGLED FRAMES WITH THIN-WALLED I-BEAMS
Journal of arine Science and J.-D. Technolog, Yau: ateral Vol. Buckling 17, No. Analsis 1, pp. 9-33 of Angled (009) Frames with Thin-Walled I-Beams 9 ATERA BUCKING ANAYSIS OF ANGED FRAES WITH THIN-WAED
More informationInternational Journal of Advanced Engineering Technology E-ISSN
Research Article INTEGRATED FORCE METHOD FOR FIBER REINFORCED COMPOSITE PLATE BENDING PROBLEMS Doiphode G. S., Patodi S. C.* Address for Correspondence Assistant Professor, Applied Mechanics Department,
More informationLaminated Composite Plates and Shells
Jianqiao Ye Laminated Composite Plates and Shells 3D Modelling With 62 Figures Springer Table of Contents 1. Introduction to Composite Materials 1 1.1 Introduction 1 1.2 Classification of Composite Materials
More informationStrain Transformation and Rosette Gage Theory
Strain Transformation and Rosette Gage Theor It is often desired to measure the full state of strain on the surface of a part, that is to measure not onl the two etensional strains, and, but also the shear
More informationShear and torsion correction factors of Timoshenko beam model for generic cross sections
Shear and torsion correction factors of Timoshenko beam model for generic cross sections Jouni Freund*, Alp Karakoç Online Publication Date: 15 Oct 2015 URL: http://www.jresm.org/archive/resm2015.19me0827.html
More informationtorsion equations for lateral BucKling ns trahair research report r964 July 2016 issn school of civil engineering
TORSION EQUATIONS FOR ATERA BUCKING NS TRAHAIR RESEARCH REPORT R96 Jul 6 ISSN 8-78 SCHOO OF CIVI ENGINEERING SCHOO OF CIVI ENGINEERING TORSION EQUATIONS FOR ATERA BUCKING RESEARCH REPORT R96 NS TRAHAIR
More informationThe Plane Stress Problem
. 4 The Plane Stress Problem 4 Chapter 4: THE PLANE STRESS PROBLEM 4 TABLE OF CONTENTS Page 4.. INTRODUCTION 4 3 4... Plate in Plane Stress............... 4 3 4... Mathematical Model.............. 4 4
More informationPLATE AND PANEL STRUCTURES OF ISOTROPIC, COMPOSITE AND PIEZOELECTRIC MATERIALS, INCLUDING SANDWICH CONSTRUCTION
PLATE AND PANEL STRUCTURES OF ISOTROPIC, COMPOSITE AND PIEZOELECTRIC MATERIALS, INCLUDING SANDWICH CONSTRUCTION SOLID MECHANICS AND ITS APPLICATIONS Volume 10 Series Editor: G.M.L. GLADWELL Department
More informationPolynomial and Rational Functions
Polnomial and Rational Functions Figure -mm film, once the standard for capturing photographic images, has been made largel obsolete b digital photograph. (credit film : modification of ork b Horia Varlan;
More informationThe Rotating Inhomogeneous Elastic Cylinders of. Variable-Thickness and Density
Applied Mathematics & Information Sciences 23 2008, 237 257 An International Journal c 2008 Dixie W Publishing Corporation, U. S. A. The Rotating Inhomogeneous Elastic Cylinders of Variable-Thickness and
More informationTRANSVERSE VIBRATION OF A GEAR WHEEL
ISSN 14-364 TRANSVERSE VIBRATION OF A GEAR WHEEL Stanislaw Noga, Rzeszow University of Technology, ul. W. Pola, 35 959 Rzeszow, Poland. Abstract: In the paper, transversal vibration of the annular plate
More informationTheory of Elasticity Formulation of the Mindlin Plate Equations
Theor of lasticit Formulation of the indlin Plate quations Nwoji, C.U. #1, Onah H.N. #, ama B.O. #3, Ike, C.C. * 4 #1, #, #3 Dept of Civil ngineering, Universit of Nigeria, Nsukka, nugu State, Nigeria.
More informationChapter 5 Equilibrium of a Rigid Body Objectives
Chapter 5 Equilibrium of a Rigid Bod Objectives Develop the equations of equilibrium for a rigid bod Concept of the free-bod diagram for a rigid bod Solve rigid-bod equilibrium problems using the equations
More informationA refined shear deformation theory for bending analysis of isotropic and orthotropic plates under various loading conditions
JOURNAL OF MATERIALS AND ENGINRING STRUCTURES (015) 3 15 3 Research Paper A refined shear deformation theor for bending analsis of isotropic and orthotropic plates under various loading conditions Bharti
More informationModeling of the Bending Stiffness of a Bimaterial Beam by the Approximation of One-Dimensional of Laminated Theory
. Flores-Domínguez Int. Journal of Engineering Research and Applications RESEARCH ARTICLE OPEN ACCESS odeling of the Bending Stiffness of a Bimaterial Beam by the Approimation of One-Dimensional of Laminated
More informationMAE 323: Chapter 4. Plane Stress and Plane Strain. The Stress Equilibrium Equation
The Stress Equilibrium Equation As we mentioned in Chapter 2, using the Galerkin formulation and a choice of shape functions, we can derive a discretized form of most differential equations. In Structural
More informationFATIGUE ANALYSIS: THE SUPER-NEUBER TECHNIQUE FOR CORRECTION OF LINEAR ELASTIC FE RESULTS
6 TH INTERNATIONAL CONGRESS OF THE AERONAUTICAL SCIENCES FATIGUE ANALYSIS: THE SUPER-NEUBER TECHNIQUE FOR CORRECTION OF LINEAR ELASTIC FE RESULTS L. Samuelsson * * Volvo Aero Corporation, Sweden Kewords:
More informationEffect of Specimen Dimensions on Flexural Modulus in a 3-Point Bending Test
Effect of Specimen Dimensions on Flexural Modulus in a 3-Point Bending Test M. Praveen Kumar 1 and V. Balakrishna Murthy 2* 1 Mechanical Engineering Department, P.V.P. Siddhartha Institute of Technology,
More informationVIBRATION AND DAMPING ANALYSIS OF FIBER REINFORCED COMPOSITE MATERIAL CONICAL SHELLS
VIBRATION AND DAMPING ANALYSIS OF FIBER REINFORCED COMPOSITE MATERIAL CONICAL SHELLS Mechanical Engineering Department, Indian Institute of Technology, New Delhi 110 016, India (Received 22 January 1992,
More informationA PROTOCOL FOR DETERMINATION OF THE ADHESIVE FRACTURE TOUGHNESS OF FLEXIBLE LAMINATES BY PEEL TESTING: FIXED ARM AND T-PEEL METHODS
1 A PROTOCOL FOR DETERMINATION OF THE ADHESIVE FRACTURE TOUGHNESS OF FLEXIBLE LAMINATES BY PEEL TESTING: FIXED ARM AND T-PEEL METHODS An ESIS Protocol Revised June 2007, Nov 2010 D R Moore, J G Williams
More informationDynamics and control of mechanical systems
JU 18/HL Dnamics and control of mechanical sstems Date Da 1 (3/5) 5/5 Da (7/5) Da 3 (9/5) Da 4 (11/5) Da 5 (14/5) Da 6 (16/5) Content Revie of the basics of mechanics. Kinematics of rigid bodies coordinate
More informationAircraft Structures Beams Torsion & Section Idealization
Universit of Liège Aerospace & Mechanical Engineering Aircraft Structures Beams Torsion & Section Idealiation Ludovic Noels omputational & Multiscale Mechanics of Materials M3 http://www.ltas-cm3.ulg.ac.be/
More informationVibrational Power Flow Considerations Arising From Multi-Dimensional Isolators. Abstract
Vibrational Power Flow Considerations Arising From Multi-Dimensional Isolators Rajendra Singh and Seungbo Kim The Ohio State Universit Columbus, OH 4321-117, USA Abstract Much of the vibration isolation
More informationFinite elements for plates and shells. Advanced Design for Mechanical System LEC 2008/11/04
Finite elements for plates and shells Sstem LEC 008/11/04 1 Plates and shells A Midplane The mid-surface of a plate is plane, a curved geometr make it a shell The thickness is constant. Ma be isotropic,
More informationBending of Simply Supported Isotropic and Composite Laminate Plates
Bending of Simply Supported Isotropic and Composite Laminate Plates Ernesto Gutierrez-Miravete 1 Isotropic Plates Consider simply a supported rectangular plate of isotropic material (length a, width b,
More informationAnalysis of Thick Cantilever Beam Using New Hyperbolic Shear Deformation Theory
International Journal of Research in Advent Technology, Vol.4, No.5, May 16 E-ISSN: 1-967 Analysis of Thick Cantilever Beam Using New Hyperbolic Shear Deformation Theory Mr. Mithun. K. Sawant 1, Dr. Ajay.
More information1 Differential Equations for Solid Mechanics
1 Differential Eqations for Solid Mechanics Simple problems involving homogeneos stress states have been considered so far, wherein the stress is the same throghot the component nder std. An eception to
More informationEigenvalue analysis of Timoshenko beams and axisymmetric Mindlin plates by the pseudospectral method
Journal of Sound and Vibration 269 (2004) 609 621 JOURNAL OF SOUND AND VIBRATION www.elsevier.com/locate/jsvi Eigenvalue analysis of Timoshenko beams and axisymmetric Mindlin plates by the pseudospectral
More informationSimulation of Geometrical Cross-Section for Practical Purposes
Simulation of Geometrical Cross-Section for Practical Purposes Bhasker R.S. 1, Prasad R. K. 2, Kumar V. 3, Prasad P. 4 123 Department of Mechanical Engineering, R.D. Engineering College, Ghaziabad, UP,
More informationThree-dimensional free vibration analysis of functionally graded rectangular plates using the B-spline Ritz method
The 01 World Congress on Advances in Civil, Environmental, and Materials Research (ACEM 1) Seoul, Korea, August 6-30, 01 Three-dimensional free viration analsis of functionall graded rectangular plates
More informationComparison of Estimators in Case of Low Correlation in Adaptive Cluster Sampling. Muhammad Shahzad Chaudhry 1 and Muhammad Hanif 2
ISSN 684-8403 Journal of Statistics Volume 3, 06. pp. 4-57 Comparison of Estimators in Case of Lo Correlation in Muhammad Shahad Chaudhr and Muhammad Hanif Abstract In this paper, to Regression-Cum-Eponential
More informationFinite Element Analysis of Piezoelectric Cantilever
Finite Element Analysis of Piezoelectric Cantilever Nitin N More Department of Mechanical Engineering K.L.E S College of Engineering and Technology, Belgaum, Karnataka, India. Abstract- Energy (or power)
More informationPolynomial and Rational Functions
Polnomial and Rational Functions Figure -mm film, once the standard for capturing photographic images, has been made largel obsolete b digital photograph. (credit film : modification of ork b Horia Varlan;
More informationx y plane is the plane in which the stresses act, yy xy xy Figure 3.5.1: non-zero stress components acting in the x y plane
3.5 Plane Stress This section is concerned with a special two-dimensional state of stress called plane stress. It is important for two reasons: () it arises in real components (particularl in thin components
More informationVariational formulation of the B.V.P. in terms of displacements is. This principle is particularly useful in analyzing large deflection
4-8 CATIGLIANO' THEOREM OF LEAT WORK. Principle of stationar potential energ: Variational formulation of the B.V.P. in terms of displacements is achieved b the principle. This principle is particularl
More informationHeat and Mass Transfer on Unsteady M.H.D Oscillatory Flow of Non-Newtonian Fluid through Porous Medium in Parallel Plate Channel
Heat and Mass Transfer on Unstead M.H.D Oscillator Flow of Non-Newtonian Fluid through Porous Medium in Parallel Plate Channel Dr. G. Kathaani, Dr. P. Sambasivudu, D. M. Praveen Babu Assistant Professor,
More informationRegression-Based Neural Network Simulation for Vibration Frequencies of the Rotating Blade
Regression-Based Neural Network Simulation for Vibration Frequencies of the Rotating Blade Atma Sahu and S. Chakravarty Abstract The aim of this paper is to demonstrate the use of regression-based neural
More informationPHYSICS PART II SECTION- I. Straight objective Type
PHYSICS PAT II SECTION- I Straight objective Tpe This section contains 9 multiple choice questions numbered to 1. Each question has choices,, (C) and, out of which ONLY ONE is correct.. A parallel plate
More informationAn example of Lagrangian for a non-holonomic system
Uniersit of North Georgia Nighthaks Open Institutional Repositor Facult Publications Department of Mathematics 9-9-05 An eample of Lagrangian for a non-holonomic sstem Piotr W. Hebda Uniersit of North
More informationREVIEW FOR EXAM II. Dr. Ibrahim A. Assakkaf SPRING 2002
REVIEW FOR EXM II. J. Clark School of Engineering Department of Civil and Environmental Engineering b Dr. Ibrahim. ssakkaf SPRING 00 ENES 0 Mechanics of Materials Department of Civil and Environmental
More informationTRANSVERSE VIBRATION ON A BEAM AN ANALYTICAL MODEL
TRANVERE VIBRATION ON A BEAM AN ANALYTICAL MODEL Derivation of the wave equation Geoffre Kolbe Consider a short section of a beam, length L and having cross-sectional area. Due to a turning moment applied
More informationINTERFACE CRACK IN ORTHOTROPIC KIRCHHOFF PLATES
Gépészet Budapest 4-5.Ma. G--Section-o ITERFACE CRACK I ORTHOTROPIC KIRCHHOFF PLATES András Szekrénes Budapest Universit of Technolog and Economics Department of Applied Mechanics Budapest Műegetem rkp.
More informationLECTURE 13 Strength of a Bar in Pure Bending
V. DEMENKO MECHNCS OF MTERLS 015 1 LECTURE 13 Strength of a Bar in Pure Bending Bending is a tpe of loading under which bending moments and also shear forces occur at cross sections of a rod. f the bending
More informationColloquium in honour of Geneviève Comte-Bellot. Similarities and Differences Rainer Friedrich, TU MünchenM
Colloquium in honour of Geneviève Comte-Bellot Compressible Turbulent Channel & Pipe Flo: Similarities and Differences Rainer Friedrich, TU MünchenM Compressible turbulent flos Motivation Compressible
More informationPassive Damping Characteristics of Carbon Epoxy Composite Plates
Journal of aterials Science and Engineering A 6 (1-2) (2016) 35-42 doi: 10.17265/2161-6213/2016.1-2.005 D DAVID PUBLISHIG Passive Damping Characteristics of Carbon Epoxy Composite Plates Dileep Kumar K
More informationFree Vibration Analysis of Kirchoff Plates with Damaged Boundaries by the Chebyshev Collocation Method. Eric A. Butcher and Ma en Sari
Free Vibration Analysis of Kirchoff Plates with Damaged Boundaries by the Chebyshev Collocation Method Eric A. Butcher and Ma en Sari Department of Mechanical and Aerospace Engineering, New Mexico State
More informationDynamic Analysis of Laminated Composite Plate Structure with Square Cut-Out under Hygrothermal Load
Dynamic Analysis of Laminated Composite Plate Structure with Square Cut-Out under Hygrothermal Load Arun Mukherjee 1, Dr. Sreyashi Das (nee Pal) 2 and Dr. A. Guha Niyogi 3 1 PG student, 2 Asst. Professor,
More informationL intensité de structure
L intensité de structure Jean-Claude Pascal LAUM, ENSIM Plan Epression de l intensité dans les poutres Formulation approchée La mesure Epression de l intensité de structure Epression de l intensité de
More informationUsing MATLAB and. Abaqus. Finite Element Analysis. Introduction to. Amar Khennane. Taylor & Francis Croup. Taylor & Francis Croup,
Introduction to Finite Element Analysis Using MATLAB and Abaqus Amar Khennane Taylor & Francis Croup Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Croup, an informa business
More informationConceptual question Conceptual question 12.2
Conceptual question 12.1 rigid cap of weight W t g r A thin-walled tank (having an inner radius of r and wall thickness t) constructed of a ductile material contains a gas with a pressure of p. A rigid
More informationNATURAL FREQUENCIES OF A HONEYCOMB SANDWICH PLATE Revision F. A diagram of a honeycomb plate cross-section is shown in Figure 1.
NATURAL FREQUENCIES OF A HONEYCOMB SANDWICH PLATE Revision F By Tom Irvine Email: tomirvine@aol.com August 5, 008 Bending Stiffness of a Honeycomb Sandwich Plate A diagram of a honeycomb plate cross-section
More informationVibro-acoustic response of FGM plates considering the thermal effects Tieliang Yang1, a, Qibai Huang1, *
3rd International Conference on Materials Engineering, Manufacturing Technology and Control (ICMEMTC 2016) Vibro-acoustic response of FGM plates considering the thermal effects Tieliang Yang1, a, Qibai
More informationElectromagnetics I Exam No. 3 December 1, 2003 Solution
Electroagnetics Ea No. 3 Deceber 1, 2003 Solution Please read the ea carefull. Solve the folloing 4 probles. Each proble is 1/4 of the grade. To receive full credit, ou ust sho all ork. f cannot understand
More informationFlexure of Thick Cantilever Beam using Third Order Shear Deformation Theory
International Journal of Engineering Research and Development e-issn: 78-67X, p-issn: 78-8X, www.ijerd.com Volume 6, Issue 1 (April 13), PP. 9-14 Fleure of Thick Cantilever Beam using Third Order Shear
More informationScienceDirect. The Stability of a Precessing and Nutating Viscoelastic Beam with a Tip Mass
Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 144 (2016 ) 68 76 12th International Conference on Vibration Problems, ICOVP 2015 The Stability of a Precessing and Nutating
More informationA SIMPLE ANALYTICAL MODEL OF LASER BENDING
5 th International & 6 th All India Manufacturing Technolog Design and Research Conference (AIMTDR 04) December th 4 th 04 IIT Guwahati Assam India A SIMPLE ANALYTICAL MODEL OF LASER BENDING A. Eideh U.S.
More informationOn the Missing Modes When Using the Exact Frequency Relationship between Kirchhoff and Mindlin Plates
On the Missing Modes When Using the Eact Frequenc Relationship between Kirchhoff and Mindlin Plates C.W. Lim 1,*, Z.R. Li 1, Y. Xiang, G.W. Wei 3 and C.M. Wang 4 1 Department of Building and Construction,
More informationTHERMALLY DRIVEN GAS FLOWS IN CAVITIES FAR FROM LOCAL EQUILIBRIUM
8 th GRACM International Congress on Computational Mechanics Volos, 1 Jul 15 Jul 15 TERMALLY DRIVEN GAS FLOWS IN CAVITIES FAR FROM LOCAL EQUILIBRIUM Giorgos Tatsios 1, Dimitris Valougeorgis 1 and Stefan
More informationSTUDY OF THE EFFECT OF COMPOSITE CONSTRAINED LAYERS IN VIBRATION DAMPING OF PLATES
Int. J. of Applied Mechanics and Engineering, 214, vol.19, No.1, pp.23-29 DOI: 1.2478/ijame-214-15 Brief note STUDY OF THE EFFECT OF COMPOSITE CONSTRAINED LAYERS IN VIBRATION DAMPING OF PLATES K.S.K. SASIKUMAR
More information