DESIGN OF TLCD UNDER RANDOM LOADS: A NEW FORMULATION
|
|
- Clarissa Charles
- 5 years ago
- Views:
Transcription
1 Meccanica dei Materiali e delle Strutture Vol. 3 (0), no.3, pp. -8 ISSN: X Dipartimento di Ingegneria Civile Ambientale e dei Materiali - DICAM DESIGN OF TLCD UNDER RANDOM LOADS: A NEW FORMULATION Alberto Di Matteo *, Francesco Lo Iacono, Giacomo Navarra, Antonina Pirrotta * * Dipartimento di Ingegneria Civile, Ambientale e dei Materiali (DICAM) Università degli Studi di Palermo, Viale delle Scienze, 908 Palermo, Italy antonina.pirrotta@unipa.it Facoltà di Ingegneria ed Architettura Università degli Studi di Enna Kore, Cittadella Universitaria, 9400 Enna, Italy giacomo.navarra@unikore.it; francesco.loiacono@unikore.it (Ricevuto 0 Giugno 0, Accettato 0 Ottobre 0) Key words: passive control, tuned liquid column damper, stochastic linearization. Abstract. Several types of passive control devices have been proposed in recent years in order to reduce the dynamic responses of different kind of structural systems. Among them, the Tuned Liquid Column Damper (TLCD) proved to be very effective in reducing vibration of structures. This paper aims at developing a pre-design simplified formulation, by means of a stochastic linearization technique, able to predict the effectiveness of TLCD when subjected to random agencies. The numerical result are then validated through an experimental campaign on a small scale SDOF shear-type model built in the Experimental Dynamic Laboratory of University of Palermo and equipped with a TLCD excited at the base with random noises through a shaking table. INTRODUCTION Tuned Liquid Column Damper (TLCD) systems can be considered as a particular type of passive mass dampers and represent an effective alternative to Tuned Mass Damper (TMD) systems [] to control the vibration level of structures. TLCDs dissipate vibration energy by a combined action of the movement of the liquid in a U-shaped container, the restoring force on the liquid due to the gravity and the damping effect due to the passage of the liquid through the orifice with inherent head loss characteristics. The TLCD is generally modelled as a single degree of freedom (SDOF) oscillator which is rigidly attached to a vibrating structure [] and, like TMDs, the effectiveness of a TLCD depends on proper tuning and damping value. However, unlike traditional TMDs, the TLCD response is non-linear and the optimal parameters cannot be established a-priori and Meccanica dei Materiali e delle Strutture 3 (0), 3, PP. -8
2 numerical optimization methods are needed [3]-[5]. Several investigations on TLCDs controlled structures under stochastic loads have been recently conducted by many authors and some useful design formulas for TLCD have been derived [6]. Recently, the authors of this paper presented a modified mathematical formulation of the TLCD equation of motion which has been proved to be very effective in the prediction of the experimental system vibrations when the input is deterministic and periodic [7]-[8]. Due to the randomness of environmental forces a deeper investigation of the behaviour of TLCD controlled systems is needed. In this paper the stochastic linearization technique is used in order to develop a pre-design simplified formula for the optimal TLCD parameters on lightly damped single-degree-of-freedom structures loaded by random agencies. The ready-touse and straightforward proposed formulation has been verified by comparison with the numerical Monte Carlo simulation based on the non-linear complete system and, finally, the theoretical and numerical results are proved to be in very good agreement with the results obtained by an experimental campaign on a small scale SDOF shear-type model built in the Experimental Dynamic Laboratory of University of Palermo and equipped with a TLCD excited at the base with random noises through a shaking table. PROBLEM FORMULATION Let it be assumed that a main structure (Figure -a), characterized by a light-damped sheartype single-degree-of-freedom (SDOF) system, is subjected to base excitation and is mitigated by using a tuned liquid column damper (Figure -b). x (t) 5 mm b d 500 mm y (t) h x (t) 50 mm upper plate a) b) Figure. a) SDOF shear-type model; b) SDOF system with TLCD. While the equation of motion of the uncontrolled system may be expressed as in equation (), the classical formulation of the equations of motion, widely used in literature [], for the TLCD controlled system can be represented as reported in (). ( ) + ( ) + ( ) = ( ) Mx ɺɺ t Cxɺ t Kx t Mx ɺɺ t () In equations () and (), M, C and K are the mass, damping and stiffness parameters of the SDOF system, respectively, xɺɺ represents the ground acceleration, x and y are the g g Meccanica dei Materiali e delle Strutture 3 (0), 3, PP. -8
3 displacement of the SDOF with reference to the ground, and the displacement of the liquid in vertical columns, respectively, mtlcd = ρ AL is the total liquid mass of the TLCD, mh = ρ Ab equals to the liquid mass of the only horizontal portion, being ρ the liquid mass density, A the cross sectional area, and L the total liquid length inside the tube (L=b+h). The head loss coefficient and the gravitational constant are denoted by ξ and g, respectively. The upper dots mean time derivatives. ( M m ) ɺɺ x ( t) mɺɺ y ( t) Cxɺ ( t) Kx( t) ( M m ) ɺɺ x ( t) + TLCD + h + + = + TLCD g mɺɺ hx t m ɺɺ TLCDy t A yɺ t yɺ t Agy t mɺɺ hxg t ( ) + ( ) + ρ ξ ( ) ( ) + ρ ( ) = ( ) In order to reduce the number of the parameters involved, let us express the equations of motion in a more convenient dimensionless form. This can be achieved by dividing the equations () by M and by m, respectively: TLCD ( µ ) ɺɺ x( t) αµ ɺɺ y ( t) ζ ω xɺ ( t) ω x( t) ( µ ) ɺɺ xg ( t) αɺɺ x( t) + ɺɺ y ( t) + c yɺ ( t) yɺ ( t) + ω y ( t) = αɺɺ x ( t) = + g where µ = mtlcd M, α = mh mtlcd, ω = K M, ω = g L, ζ = C Mω ; c = ξ L. Since the damping term in the second of equations (3) is nonlinear, even supposing that the uncontrolled structure behaves linearly, the whole damper-structure system has inherent nonlinear properties. It follows that simple design techniques as Response Spectra (RS) method may not be pursued. In order to overcome this difficulty, this paper aims at defining an equivalent system in which a linear viscous damping coefficient is chosen through a simplified procedure by using the Statistical Linearization Technique (SLT) [9]. () (3) 3 STOCHASTIC LINEARIZATION OF TLCD Let us consider that the structure-damper system depicted in Figure -b is excited by random forces at base that can be modelled as zero mean Gaussian processes. It follows that the displacements and their derivatives are stochastic processes too and, as customary, are denoted with capital letter. Due to the presence of the nonlinear damping term, the response processes are non-gaussian. According to the SLT, the original nonlinear system (3) is replaced by a linear equivalent one as follows: ( µ ) Xɺɺ ( t) αµ Yɺɺ ( t) ζ ω Xɺ ( t) ω X ( t) ( µ ) Xɺɺ g ( t) α Xɺɺ ( t) + Yɺɺ ( t) + ζ ω Yɺ ( t) + ω Y ( t) = α Xɺɺ ( t) = + g where ζ is the equivalent damping ratio that is to be chosen in order to minimize the mean square error made in passing from (3) to (4). Omitting for clarity s sake the dependence from the time, we have: ( c Y Y ζ ωy ) = ζ E min ɺ ɺ ɺ (5) where E[ ] means ensemble average. Once the minimum is performed and the responses Meccanica dei Materiali e delle Strutture 3 (0), 3, PP (4)
4 processes have been considered as Gaussian ones, the equivalent damping is obtained as: c ζ = σ Y ω π (6) ɺ where σy ɺ is the standard deviation of the velocity of the fluid. The use of equation (6) for design purposes is not straightforward since σy ɺ is still unknown and it implicitly depends on ζ, then, as usually an iterative procedure is necessary [9]. Since the main goal of the present paper is to readily find the equivalent damping ratio of TLCDs in a design framework, the iterative procedure cannot be pursued. Equation (6) provides a relationship between the equivalent damping ratio ζ and the standard deviation of the fluid velocity σy ɺ. In order to find a direct, even simplified, relationship between the input characterization GXɺɺ g ( ω) and the estimated value for ζ, a closed-form solution in terms of steady state response statistic σy ɺ is needed. In order to do so, let us suppose that the input can be modelled as a zero-mean stationary Gaussian white noise process. In this framework, for the linear system (4) the Lyapunov equation of the evolution of the covariance matrix can be used and the steady state response statistics could be easily evaluated. After some algebra the exact solution for the steady state variance of the fluid velocity can be expressed as: π S σɺ = (7) 0 y zω in which the factor z, has a very cumbersome expression which cannot be used for practical design purposes. In order to obtain a design formula we have to introduce the following approximations. We can assume that ω is practically coincident with ω, since the damper has to be tuned with the main system; moreover, if the main system is lightly damped, the higher powers of ζ can be neglected. Introducing these assumptions the following expression of z is obtained: ( ) z = µ ζ + γζ (8) where the dimensionless parameter γ = µ + µ α depends only on the geometry of the TLCD. In such a way the variance of the fluid velocity σy ɺ can be directly related with the white noise strength S 0 and by eliminating σy ɺ, a direct expression that provides the equivalent damping ratio ζ as a function of the white noise strength S 0 is obtained: S c ζ ζ + γζ = (9) 0 ( ) 3 µω The nonlinear algebraic equation (9) can be easily numerically solved in order to obtain a good estimate of ζ to be used for design purposes. In the following sections the proposed procedure will be validated through numerical and experimental tests. 4 NUMERICAL VALIDATION In the present section the simplified formulation is validated by means of numerical simulations. In order to define a realistic analytical system on which numerical integration of Meccanica dei Materiali e delle Strutture 3 (0), 3, PP. -8 4
5 motion equations can be performed, we will now refer to the analytical model of TLCD () whose parameters, as reported in Table, have been computed by identifying the dynamical properties of the experimental model that will be presented in the next section. The steady state response statistics of the TLCD-controlled system are obtained through a 000 samples Monte Carlo simulation directly integrating the equations of motion by means of a 4 th -order Runge-Kutta scheme. The response statistics of the uncontrolled system () and of the equivalent linear system (4) may be evaluated either by a Monte Carlo simulation, or by means of a stochastic analysis, since these are linear systems. In a similar way the steady state Power Spectral Density (PSD) functions have been computed. Obviously, in the definition of the equivalent linear system (4) the value for ζ is determined by means of the simplified proposed procedure (9). E[X ] [m ] 5x0-3 4x0-3 3x0-3 x x0 0 uncontrolled nonlinear equivalent linear S 0 [(m/s ) /(rad/s)] E[Y ] [m ] x0-3 x0-3 8x0-4 4x0-4 0x0 0 nonlinear equivalent linear S 0 [(m/s ) /(rad/s)] Figure. Variance of displacements versus input strength: a) uncontrolled system (green line), main displacement of non linear system (red line) and equivalent linear system (orange dashed line); b) fluid displacement of non linear system (blue line) and equivalent linear system (blue dashed line) Figure shows the variances of the main system displacement E X ( t) and of the fluid displacement E Y ( t) for different values of the input strength S 0, respectively. These variances are computed for the uncontrolled system and compared with those obtained for the TLCD-controlled system by using both nonlinear equations (3), and equivalent linear equations (4). It is evident that the control system is effective and that the equivalent linear system fits the nonlinear one even for large values of the input strength. G(f) [m /(rad/s)] Output PSD G xx,unc G xx,nl G xx_lin G yy,nl G yy_lin a) b) f [Hz] f [Hz] Figure 3. Steady state PSD functions: a) for a low value of input strength; b) for an high value of input strength; uncontrolled system displacement (green solid line), main system TLCD-controlled displacement (red lines), fluid displacement (blue lines); solid lines for nonlinear system, dashed lines for equivalent linear system. Figure 3-a reports steady state PSD functions for a low value of the input strength 4 S 0 = 0 (m/s ) /(rad/s). From this picture is clearly visible the effect of the TLCD that generates two peaks in the controlled system (solid red line) instead of the higher single peak G(f) [m /(rad/s)] Meccanica dei Materiali e delle Strutture 3 (0), 3, PP. -8 5
6 of the uncontrolled system (green solid line). Furthermore, it is possible to note that dashed lines (equivalent linear system) cannot be distinguished by the solid lines (nonlinear system) for this level of input strength. In Figure 3-b steady state PSD functions for an high value of the input strength S 0 = 0 (m/s ) /(rad/s) are reported. From this picture it is evident the higher value of damping associated to the current value of input strength. Moreover, now it is possible to distinguish PSDs obtained by the equivalent linear system (dashed lines) from those computed by from nonlinear system (solid lines), which also exhibit a superharmonic frequency at 4.35 Hz due to the nonlinearity. 5 EXPERIMENTAL VALIDATION In the present section the numerical results obtained by using the proposed formulation for the equivalent linear damping estimation are validated by means of an experimental campaign. In order to do so, a small-scale shear-type SDOF model equipped with a TLCD has been built in the Laboratory of Experimental Dynamic at University of Palermo. Figure 4-a reports a picture of the uncontrolled model over a shake table, while in Figure 4-b the picture of the TLCD-controlled system is reported. The main uncontrolled system is a small scale single degree of freedom (SDOF) shear-type frame composed by two steel columns (length 500 mm, width 50 mm and thickness mm) and two nylon rigid plates (length 50 mm, width 50 mm and thickness 5 mm) as base and floor respectively. The total mass model is kg, of which kg takes into account the dead weight of the tube mass of TLCD. a) b) Figure 4. Experimental one storey shear-type model setup; a) uncontrolled system; b) TLCD-controlled system. The TLCD device, is a U shaped cylinder tube, with constant cross section 3 A =.9 0 m, rigidly connected to the upper plate of the main system, to create a simple TLCD-controlled system. The centerlines of the vertical branches are at a distance of 05 mm 3 each other. The tube has been filled with water ( ρ = 000 kg/m ), up to a level of 40 mm from the centerline of the base tube in order to be tuned with the uncontrolled system. The water that has been poured has a total liquid mass m TLCD = kg. and total liquid length of L = 85 mm, which corresponds to a mass ratio µ = m M TLCD = 0.098, close to 0%. The acceleration responses, at the base and at the storey of both uncontrolled and Meccanica dei Materiali e delle Strutture 3 (0), 3, PP. -8 6
7 controlled systems, have been acquired using miniaturized piezoelectric accelerometers and then processed using a self-developed signal processing software in LabView and MATLAB environment. Both uncontrolled and controlled models have been excited at the base through a shaking table that provides the displacement controlled ground motion. Table. Parameters for the definition of a structure-tlcd system - eq. () and eq. (3). parameter value parameter value M kg µ unitless m TLCD 0.48 kg α unitless m h kg ω 0.07 rad/s C 0.53 Ns/m ω rad/s K N/m ζ unitless ρ 000 kg/m 3 c m - A m ξ unitless As a first stage, the dynamic parameters of the uncontrolled system and of the TLCDcontrolled system were identified by exciting the structure with broadband noises in the range Hz. The dynamic parameters were identified by using some well-known parameter extraction techniques [0] such as Rational Fractional Polynomial method, genetic algorithm and particle-swarm optimization method that provide similar estimations of the parameters that are reported in Table uncontrolled exp. uncontrolled num. nonlinear exp. nonlinear num. equivalent linear num Figure 5: Experimental validation in term of variances. Variances of uncontrolled system (green) and TLCDcontrolled systems (red). Solid lines indicates numerical results (eq. () for uncontrolled system, eq. (3) for TLCD-controlled system), dashed line stands for equivalent linear system (eq. (4)), dots stand for experimental results. The effectiveness of the control has been validated by computing the response statistics in terms of variances from 50 samples of ground acceleration for several levels of input strength and then comparing them with the variances obtained by solving numerically the equation (3) and (4). This comparison is reported in Figure 5 showing that the experimental results are in a good agreement with the numerical ones and the effectiveness of the control in reducing structural responses is clearly visible. Moreover, the equivalent linear system follows very closely the trends of both experimental statistics and numerical results by using the nonlinear equation, thus proving the reliability of the proposed formulation in predicting structural responses, even in experimental field. Meccanica dei Materiali e delle Strutture 3 (0), 3, PP. -8 7
8 CONCLUSIONS In the present paper the effectiveness of a simplified pre-design formulation for TLCD passive control system subjected to random loads has been investigated. The proposed formulation has been validated through some numerical simulations and an experimental campaign on a small scale SDOF shear-type model in the Laboratory of Experimental Dynamic at University of Palermo. Results showed that stochastic linearization technique works very well both in frequency and in time domain. Moreover, the response statistics obtained by classical nonlinear formulation, by the equivalent linear system obtained by using the proposed formulation and by the experimental results are very close to each others, thus proving the reliability of the proposed approach. The design formulation outlined in the paper can easily be applied also to random processes which have Response Spectra coherent with building codes. REFERENCE [] Warburton G.B., 98, Optimum Absorber Parameters for Various Combinations of Response and Excitation Parameters, Earthquake Engineering and Structural Dynamics, 0, [] Sakai F., Takeda S., Tamaki, T., 989, Tuned liquid column damper- new type device for suppression of building vibrations, Proceedings of the international conference on highrise buildings, [3] Hochrainer M.J., 005, Tuned liquid column damper for structural control, Acta Mechanica, 75, [4] Farshidianfar A., Oliazadeh P., 009, Closed form optimal solution of a tuned liquid column damper responding to earthquake, World Academy of Science, Engineering and Technology, 59, [5] Yalla S.K., Kareem A., 000, Optimum absorber parameters for Tuned Liquid Column Dampers, Journal of Structural Engineering, 6(8), [6] Chang C.C., 999, Mass dampers and their optimal designs for building vibration control, Engineering Structures,, [7] Di Matteo A., Lo Iacono F., Navarra G., Pirrotta A., 0, The control performance of TLCD and TMD: experimental investigation, 5th European Conference on Structural Control, 8 0 June, Genoa, Italy. [8] Di Matteo A., Lo Iacono F., Navarra G., Pirrotta A., 0, The TLCD Passive Control: Numerical Investigations Vs Experimental Results, Proceedings of the ASME 0 - International Mechanical Engineering Congress & Exposition IMECE0, 9 5 November, 0, Houston, Texas, USA. [9] Roberts J.B., Spanos P.D., 990, Random Vibration and Statistical Linearization, Wiley, New York, USA. [0] Ewins D. J., 984, Modal Testing: Theory and Practice. Research Studies Press, Taunton, Somerset, England. Meccanica dei Materiali e delle Strutture 3 (0), 3, PP. -8 8
Earthquake Excited Base-Isolated Structures Protected by Tuned Liquid Column Dampers: Design Approach and Experimental Verification
Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 199 017 1574 1579 X International Conference on Structural Dynamics, EURODYN 017 Earthquake Excited Base-Isolated Structures
More informationReal-Time Hybrid Simulation of Single and Multiple Tuned Liquid Column Dampers for Controlling Seismic-Induced Response
6 th International Conference on Advances in Experimental Structural Engineering 11 th International Workshop on Advanced Smart Materials and Smart Structures Technology August 1-2, 215, University of
More informationStochastic Dynamics of SDOF Systems (cont.).
Outline of Stochastic Dynamics of SDOF Systems (cont.). Weakly Stationary Response Processes. Equivalent White Noise Approximations. Gaussian Response Processes as Conditional Normal Distributions. Stochastic
More informationWire rope springs for passive vibration control of a light steel structure
Wire rope springs for passive vibration control of a light steel structure STEFANO PAGANO, SALVATORE STRANO Dipartimento di Ingegneria Industriale Università degli Studi di Napoli Federico II Via Claudio
More informationMATHEMATICAL MODEL OF DYNAMIC VIBRATION ABSORBER-RESPONSE PREDICTION AND REDUCTION
ANNALS of Faculty Engineering Hunedoara International Journal of Engineering Tome XIV [2016] Fascicule 1 [February] ISSN: 1584-2665 [print; online] ISSN: 1584-2673 [CD-Rom; online] a free-access multidisciplinary
More informationIntroduction to Vibration. Mike Brennan UNESP, Ilha Solteira São Paulo Brazil
Introduction to Vibration Mike Brennan UNESP, Ilha Solteira São Paulo Brazil Vibration Most vibrations are undesirable, but there are many instances where vibrations are useful Ultrasonic (very high
More informationDYNAMIC RESPONSE OF EARTHQUAKE EXCITED INELASTIC PRIMARY- SECONDARY SYSTEMS
DYNAMIC RESPONSE OF EARTHQUAKE EXCITED INELASTIC PRIMARY- SECONDARY SYSTEMS Christoph ADAM 1 And Peter A FOTIU 2 SUMMARY The objective of the paper is to investigate numerically the effect of ductile material
More informationOptimal design of nonlinear energy sinks for SDOF structures subjected to white noise base excitations
Loughborough University Institutional Repository Optimal design of nonlinear energy sinks for SDOF structures subjected to white noise base excitations This item was submitted to Loughborough University's
More informationEngineering Structures
Engineering Structures 31 (2009) 715 728 Contents lists available at ScienceDirect Engineering Structures journal homepage: www.elsevier.com/locate/engstruct Particle swarm optimization of tuned mass dampers
More informationCROSS-POWER SPECTRAL DENSITY AND CROSS-CORRELATION REPRESENTATION BY USING FRACTIONAL SPECTRAL MOMENTS
Meccanica dei materiali e delle Strutture Vol. 3 (1, no., pp. 9-16 ISSN: 35-679X Dipartimento di Ingegneria Civile, Ambientale, Aerospaziale, dei Materiali - DICAM CROSS-POWER SPECTRAL DENSITY AND CROSS-CORRELATION
More informationDesign and Analysis of a Simple Nonlinear Vibration Absorber
IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE) e-issn: 78-1684,p-ISSN: 30-334X, Volume 11, Issue Ver. VI (Mar- Apr. 014), PP 84-90 Design and Analysis of a Simple Nonlinear Vibration Absorber
More informationChapter 23: Principles of Passive Vibration Control: Design of absorber
Chapter 23: Principles of Passive Vibration Control: Design of absorber INTRODUCTION The term 'vibration absorber' is used for passive devices attached to the vibrating structure. Such devices are made
More informationGiacomo Boffi. Dipartimento di Ingegneria Civile Ambientale e Territoriale Politecnico di Milano
http://intranet.dica.polimi.it/people/boffi-giacomo Dipartimento di Ingegneria Civile Ambientale e Territoriale Politecnico di Milano April 21, 2017 Outline of Structural Members Elastic-plastic Idealization
More informationRESPONSE SURFACE METHODS FOR STOCHASTIC STRUCTURAL OPTIMIZATION
Meccanica dei Materiali e delle Strutture Vol. VI (2016), no.1, pp. 99-106 ISSN: 2035-679X Dipartimento di Ingegneria Civile, Ambientale, Aerospaziale, Dei Materiali DICAM RESPONSE SURFACE METHODS FOR
More informationNonlinear rocking of rigid blocks on flexible foundation: analysis and experiments
Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 199 (017) 84 89 X International Conference on Structural Dynamics, EURODYN 017 Nonlinear rocking of rigid blocks on flexible
More informationStochastic Structural Dynamics Prof. Dr. C. S. Manohar Department of Civil Engineering Indian Institute of Science, Bangalore
Stochastic Structural Dynamics Prof. Dr. C. S. Manohar Department of Civil Engineering Indian Institute of Science, Bangalore Lecture No. # 32 Probabilistic Methods in Earthquake Engineering-1 (Refer Slide
More informationASEISMIC DESIGN OF TALL STRUCTURES USING VARIABLE FREQUENCY PENDULUM OSCILLATOR
ASEISMIC DESIGN OF TALL STRUCTURES USING VARIABLE FREQUENCY PENDULUM OSCILLATOR M PRANESH And Ravi SINHA SUMMARY Tuned Mass Dampers (TMD) provide an effective technique for viration control of flexile
More informationPreliminary Examination in Dynamics
Fall Semester 2017 Problem 1 The simple structure shown below weighs 1,000 kips and has a period of 1.25 sec. It has no viscous damping. It is subjected to the impulsive load shown in the figure. If the
More informationA STRATEGY FOR IDENTIFICATION OF BUILDING STRUCTURES UNDER BASE EXCITATIONS
A STRATEGY FOR IDENTIFICATION OF BUILDING STRUCTURES UNDER BASE EXCITATIONS G. Amato and L. Cavaleri PhD Student, Dipartimento di Ingegneria Strutturale e Geotecnica,University of Palermo, Italy. Professor,
More informationDesign of coupled tuned liquid column gas dampers for multi-mode reduction in vibrating structures
Acta Mech 229, 911 928 (2018) https://doi.org/10.1007/s00707-017-2007-0 ORIGINAL PAPER M. J. Hochrainer P. A. Fotiu Design of coupled tuned liquid column gas dampers for multi-mode reduction in vibrating
More informationPreliminary Examination - Dynamics
Name: University of California, Berkeley Fall Semester, 2018 Problem 1 (30% weight) Preliminary Examination - Dynamics An undamped SDOF system with mass m and stiffness k is initially at rest and is then
More informationThe Behaviour of Simple Non-Linear Tuned Mass Dampers
ctbuh.org/papers Title: Authors: Subject: Keyword: The Behaviour of Simple Non-Linear Tuned Mass Dampers Barry J. Vickery, University of Western Ontario Jon K. Galsworthy, RWDI Rafik Gerges, HSA & Associates
More informationVibration Reduction of Wind Turbines Using Tuned Liquid Column Damper Using Stochastic Analysis
Journal of Physics: Conference Series PAPER OPEN ACCESS Vibration Reduction of Wind Turbines Using Tuned Liquid Column Damper Using Stochastic Analysis To cite this article: M H Alkmim et al 216 J. Phys.:
More informationChapter 6 Vibration Design
Chapter 6 Viration Design Acceptale viration levels (ISO) Viration isolation Viration asorers Effects of damping in asorers Optimization Viscoelastic damping treatments Critical Speeds Design for viration
More informationTuning TMDs to Fix Floors in MDOF Shear Buildings
Tuning TMDs to Fix Floors in MDOF Shear Buildings This is a paper I wrote in my first year of graduate school at Duke University. It applied the TMD tuning methodology I developed in my undergraduate research
More informationLaboratory notes. Torsional Vibration Absorber
Titurus, Marsico & Wagg Torsional Vibration Absorber UoB/1-11, v1. Laboratory notes Torsional Vibration Absorber Contents 1 Objectives... Apparatus... 3 Theory... 3 3.1 Background information... 3 3. Undamped
More informationSIMULATION AND TESTING OF A 6-STORY STRUCTURE INCORPORATING A COUPLED TWO MASS NONLINEAR ENERGY SINK. Sean Hubbard Dept. of Aerospace Engineering
Proceedings of the ASME 1 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 1 August 1-15, 1, Chicago, IL, USA DETC1-7144 SIMULATION
More informationA novel tuned liquid wall damper for multi-hazard mitigation
Civil, Construction and Environmental Engineering Civil, Construction and Environmental Engineering Conference Presentations and Proceedings 4-11-2017 A novel tuned liquid wall damper for multi-hazard
More informationClosed form optimal solution of a tuned liquid column damper responding to earthquake
World Academy of Science, Engineering and Technology 59 9 Closed form optimal solution of a tuned liquid column damper responding to earthquake A. Farshidianfar, P. Oliazadeh Abstract In this paper the
More informationExperimental Calibration and Head Loss Prediction of Tuned Liquid Column Damper
Tamkang Journal of Science and Engineering, Vol. 8, No 4, pp. 319-35 (005) 319 Experimental Calibration and Head Loss Prediction of Tuned Liquid Column Damper Jong-Cheng Wu Department of Civil Engineering,
More informationSTRUCTURAL CONTROL USING MODIFIED TUNED LIQUID DAMPERS
STRUCTURAL CONTROL USING MODIFIED TUNED LIQUID DAMPERS A. Samanta 1 and P. Banerji 2 1 Research Scholar, Department of Civil Engineering, Indian Institute of Technology Bombay, Mumbai, India, 2 Professor,
More informationVibration Control Effects of Tuned Cradle Damped Mass Damper
Journal of Applied Mechanics Vol. Vol.13, (August pp.587-594 2010) (August 2010) JSCE JSCE Vibration Control Effects of Tuned Cradle Damped Mass Damper Hiromitsu TAKEI* and Yoji SHIMAZAKI** * MS Dept.
More informationRESPONSE SPECTRUM METHOD FOR ESTIMATION OF PEAK FLOOR ACCELERATION DEMAND
RESPONSE SPECTRUM METHOD FOR ESTIMATION OF PEAK FLOOR ACCELERATION DEMAND Shahram Taghavi 1 and Eduardo Miranda 2 1 Senior catastrophe risk modeler, Risk Management Solutions, CA, USA 2 Associate Professor,
More informationTuned mass dampers on damped structures
Downloaded from orbit.dtu.dk on: Jul 15, 2018 Tuned mass dampers on damped structures Krenk, Steen; Høgsberg, Jan Becker Published in: 7th European Conference on Structural Dynamics Publication date: 2008
More informationResponse Variability of a Tuned Liquid Column Damper Applied to a Wind Turbine. Brasilia, , Brazil)
EngOpt 016-5 th International Conference on Engineering Optimization Iguassu Falls, Brazil, 19-3 June 016. Response Variability of a Tuned Liquid Column Damper Applied to a Wind Turbine M H Alkmim 1, M
More informationVibration Analysis of a Horizontal Washing Machine, Part IV: Optimal Damped Vibration Absorber
RESEARCH ARTICLE Vibration Analysis of a Horizontal Washing Machine, Part IV: Optimal Damped Vibration Absorber Galal Ali Hassaan Department of Mechanical Design & Production, Faculty of Engineering, Cairo
More informationDEVELOPMENT OF A REAL-TIME HYBRID EXPERIMENTAL SYSTEM USING A SHAKING TABLE
DEVELOPMENT OF A REAL-TIME HYBRID EXPERIMENTAL SYSTEM USING A SHAKING TABLE Toshihiko HORIUCHI, Masahiko INOUE And Takao KONNO 3 SUMMARY A hybrid experimental method, in which an actuator-excited vibration
More informationSuppression of the primary resonance vibrations of a forced nonlinear system using a dynamic vibration absorber
Suppression of the primary resonance vibrations of a forced nonlinear system using a dynamic vibration absorber J.C. Ji, N. Zhang Faculty of Engineering, University of Technology, Sydney PO Box, Broadway,
More informationStability for Bridge Cable and Cable-Deck Interaction. Dr. Maria Rosaria Marsico D.J. Wagg
Stability for Bridge Cable and Cable-Deck Interaction Dr. Maria Rosaria Marsico D.J. Wagg S.A. Neild Introduction The interaction between cables and structure can lead to complex vibration response Cables
More informationAseismic design of structure equipment systems using variable frequency pendulum isolator
Aseismic design of structure equipment systems using variable frequency pendulum isolator Pranesh Murnal a, Ravi Sinha b, a Department of Applied Mechanics, Government College of Engineering, Karad 415124,
More informationIDENTIFICATION OF FRICTION ENERGY DISSIPATION USING FREE VIBRATION VELOCITY: MEASUREMENT AND MODELING
IDENTIFICATION OF FRICTION ENERGY DISSIPATION USING FREE VIBRATION VELOCITY: MEASUREMENT AND MODELING Christoph A. Kossack, Tony L. Schmitz, and John C. Ziegert Department of Mechanical Engineering and
More informationStructural Dynamics Lecture 7. Outline of Lecture 7. Multi-Degree-of-Freedom Systems (cont.) System Reduction. Vibration due to Movable Supports.
Outline of Multi-Degree-of-Freedom Systems (cont.) System Reduction. Truncated Modal Expansion with Quasi-Static Correction. Guyan Reduction. Vibration due to Movable Supports. Earthquake Excitations.
More informationINVESTIGATION OF JACOBSEN'S EQUIVALENT VISCOUS DAMPING APPROACH AS APPLIED TO DISPLACEMENT-BASED SEISMIC DESIGN
13 th World Conference on Earthquake Engineering Vancouver, B.C., Canada August 1-6, 2004 Paper No. 228 INVESTIGATION OF JACOBSEN'S EQUIVALENT VISCOUS DAMPING APPROACH AS APPLIED TO DISPLACEMENT-BASED
More informationExperimental Investigation of the Performances of a WRS-BTU Seismic Isolator
, July 3-5, 2013, London, U.K. Experimental Investigation of the Performances of a WRS-BTU Seismic Isolator R. Brancati, G. Di Massa, S. Pagano, E. Rocca and S. Strano Abstract This paper describes an
More informationThe student will experimentally determine the parameters to represent the behavior of a damped oscillatory system of one degree of freedom.
Practice 3 NAME STUDENT ID LAB GROUP PROFESSOR INSTRUCTOR Vibrations of systems of one degree of freedom with damping QUIZ 10% PARTICIPATION & PRESENTATION 5% INVESTIGATION 10% DESIGN PROBLEM 15% CALCULATIONS
More informationInclusion of a Sacrificial Fuse to Limit Peak Base-Shear Forces During Extreme Seismic Events in Structures with Viscous Damping
Inclusion of a Sacrificial Fuse to Limit Peak Base-Shear Forces During Extreme Seismic Events in Structures with Viscous Damping V. Simon, C. Labise, G.W. Rodgers, J.G. Chase & G.A. MacRae Dept. of Civil
More informationDr.Vinod Hosur, Professor, Civil Engg.Dept., Gogte Institute of Technology, Belgaum
STRUCTURAL DYNAMICS Dr.Vinod Hosur, Professor, Civil Engg.Dept., Gogte Institute of Technology, Belgaum Overview of Structural Dynamics Structure Members, joints, strength, stiffness, ductility Structure
More informationUniversity of California at Berkeley Structural Engineering Mechanics & Materials Department of Civil & Environmental Engineering Spring 2012 Student name : Doctoral Preliminary Examination in Dynamics
More informationOutline of parts 1 and 2
to Harmonic Loading http://intranet.dica.polimi.it/people/boffi-giacomo Dipartimento di Ingegneria Civile Ambientale e Territoriale Politecnico di Milano March, 6 Outline of parts and of an Oscillator
More informationCONTROL OF PEDESTRIAN-INDUCED VIBRATIONS OF FOOTBRIDGES USING TUNED LIQUID COLUMN DAMPERS
CONTROL OF PEDESTRIN-INDUCED VIBRTIONS OF FOOTBRIDGES USING TUNED LIQUID COLUMN DMPERS Michael REITERER & Franz ZIEGLER Institute of Rational Mechanics, Vienna University of Technology, ustria Keywords:
More informationDynamics of Structures
Dynamics of Structures Elements of structural dynamics Roberto Tomasi 11.05.2017 Roberto Tomasi Dynamics of Structures 11.05.2017 1 / 22 Overview 1 SDOF system SDOF system Equation of motion Response spectrum
More informationSemiactive Tuned Liquid Column Dampers: Experimental Study
Semiactive Tuned Liquid Column Dampers: Experimental Study Swaroop K. Yalla, S.M.ASCE, 1 and Ahsan Kareem, M.ASCE Abstract: A tuned liquid column damper TLCD is a special type of auxiliary damping device
More informationInternational Journal of Advance Engineering and Research Development
Scientific Journal of Impact Factor (SJIF): 4.72 International Journal of Advance Engineering and Research Development Volume 4, Issue 11, November -2017 e-issn (O): 2348-4470 p-issn (P): 2348-6406 Study
More informationChapter 5 Design. D. J. Inman 1/51 Mechanical Engineering at Virginia Tech
Chapter 5 Design Acceptable vibration levels (ISO) Vibration isolation Vibration absorbers Effects of damping in absorbers Optimization Viscoelastic damping treatments Critical Speeds Design for vibration
More informationDynamics of structures
Dynamics of structures 2.Vibrations: single degree of freedom system Arnaud Deraemaeker (aderaema@ulb.ac.be) 1 Outline of the chapter *One degree of freedom systems in real life Hypothesis Examples *Response
More informationOPTIMUM DESIGN OF TUNED MASS DAMPERS BY DISPLACEMENT AND ENERGY APPROACH
Meccanica dei Materiali e delle trutture Vol. 3 (1), no.1, pp. 41-48 IN: 35-679X Dipartimento di Ingegneria Civile, Ambientale, Aerospaziale, Dei Materiali DICAM OPIMUM DEIGN OF UNED MA DAMPER BY DIPLACEMEN
More informationReliability-based Design Optimization of Nonlinear Energy Sinks
th World Congress on Structural and Multidisciplinary Optimization 7 th - th, June, Sydney Australia Reliability-based Design Optimization of Nonlinear Energy Sinks Ethan Boroson and Samy Missoum University
More informationVIBRATION ANALYSIS OF E-GLASS FIBRE RESIN MONO LEAF SPRING USED IN LMV
VIBRATION ANALYSIS OF E-GLASS FIBRE RESIN MONO LEAF SPRING USED IN LMV Mohansing R. Pardeshi 1, Dr. (Prof.) P. K. Sharma 2, Prof. Amit Singh 1 M.tech Research Scholar, 2 Guide & Head, 3 Co-guide & Assistant
More informationComparison between the visco-elastic dampers And Magnetorheological dampers and study the Effect of temperature on the damping properties
Comparison between the visco-elastic dampers And Magnetorheological dampers and study the Effect of temperature on the damping properties A.Q. Bhatti National University of Sciences and Technology (NUST),
More informationIf you want to find the secrets of the universe, think in terms of energy, frequency and vibration. Nikola Tesla
If you want to find the secrets of the universe, think in terms of energy, frequency and vibration. Nikola Tesla It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If
More informationNONLINEAR CHARACTERISTICS OF THE PILE-SOIL SYSTEM UNDER VERTICAL VIBRATION
IGC 2009, Guntur, INDIA NONLINEAR CHARACTERISTICS OF THE PILE-SOIL SYSTEM UNDER VERTICAL VIBRATION B. Manna Lecturer, Civil Engineering Department, National Institute of Technology, Rourkela 769008, India.
More informationStudy on Tire-attached Energy Harvester for Lowspeed Actual Vehicle Driving
Journal of Physics: Conference Series PAPER OPEN ACCESS Study on Tire-attached Energy Harvester for Lowspeed Actual Vehicle Driving To cite this article: Y Zhang et al 15 J. Phys.: Conf. Ser. 66 116 Recent
More informationSPACECRAFT EQUIPMENT VIBRATION QUALIFICATION TESTING APPLICABILITY AND ADVANTAGES OF NOTCHING
SPACECRAFT EQUIPMENT VIBRATION QUALIFICATION TESTING APPLICABILITY AND ADVANTAGES OF NOTCHING Andrea Ceresetti Alenia Spazio S.p.A. - Technical Directorate Strada Antica di Collegno 53, 46 TORINO, Italy
More informationPassive Control of the Vibration of Flooring Systems using a Gravity Compensated Non-Linear Energy Sink
The 3 th International Workshop on Advanced Smart Materials and Smart Structures Technology July -3, 7, The University of Tokyo, Japan Passive Control of the Vibration of Flooring Systems using a Gravity
More informationDynamic System Identification using HDMR-Bayesian Technique
Dynamic System Identification using HDMR-Bayesian Technique *Shereena O A 1) and Dr. B N Rao 2) 1), 2) Department of Civil Engineering, IIT Madras, Chennai 600036, Tamil Nadu, India 1) ce14d020@smail.iitm.ac.in
More informationAn Improved Computational Strategy for Vibration- Proof Structures Equipped with Nano-Enhanced Viscoelastic Devices
An Improved Computational Strategy for Vibration- Proof Structures Equipped with Nano-Enhanced Viscoelastic Devices E. Ntotsios & A. Palmeri Loughborough University, United Kingdom SUMMARY: Viscoelastic
More informationChapter 2 SDOF Vibration Control 2.1 Transfer Function
Chapter SDOF Vibration Control.1 Transfer Function mx ɺɺ( t) + cxɺ ( t) + kx( t) = F( t) Defines the transfer function as output over input X ( s) 1 = G( s) = (1.39) F( s) ms + cs + k s is a complex number:
More informationSeismic analysis of structural systems with uncertain damping
Seismic analysis of structural systems with uncertain damping N. Impollonia, G. Muscolino, G. Ricciardi Dipartirnento di Costruzioni e Tecnologie Avanzate, Universita di Messina Contrada Sperone, 31 -
More informationmidas Civil Dynamic Analysis
Edgar De Los Santos Midas IT August 23 rd 2017 Contents: Introduction Eigen Value Analysis Response Spectrum Analysis Pushover Analysis Time History Analysis Seismic Analysis Seismic Analysis The seismic
More informationVortex-induced vibration of a slender single-span cylinder
Vortex-induced vibration of a slender single-span cylinder N. Oikou Delft University of Technology, the Netherlands The goal of this paper is to study the vortex-induced vibration of slender cylindrical
More informationA Bidirectional Tuned Liquid Column Damper for Reducing the Seismic Response of Buildings
Paper N 199 A Bidirectional Tuned Liquid Column Damper for Reducing the Seismic Response of Buildings L. Rozas T. (1), R. Boroschek K. (), A. Tamburrino T. (3), M. Rojas L. (4) (1) Earthquake engineer
More informationSTATIC AND DYNAMIC ANALYSIS OF A BISTABLE PLATE FOR APPLICATION IN MORPHING STRUCTURES
STATIC AND DYNAMIC ANALYSIS OF A BISTABLE PLATE FOR APPLICATION IN MORPHING STRUCTURES A. Carrella 1, F. Mattioni 1, A.A. Diaz 1, M.I. Friswell 1, D.J. Wagg 1 and P.M. Weaver 1 1 Department of Aerospace
More informationPLEASURE VESSEL VIBRATION AND NOISE FINITE ELEMENT ANALYSIS
PLEASURE VESSEL VIBRATION AND NOISE FINITE ELEMENT ANALYSIS 1 Macchiavello, Sergio *, 2 Tonelli, Angelo 1 D Appolonia S.p.A., Italy, 2 Rina Services S.p.A., Italy KEYWORDS pleasure vessel, vibration analysis,
More informationMOOC QP Set 2 Principles of Vibration Control
Section I Section II Section III MOOC QP Set 2 Principles of Vibration Control (TOTAL = 100 marks) : 20 questions x 1 mark/question = 20 marks : 20 questions x 2 marks/question = 40 marks : 8 questions
More informationEnergy balance in self-powered MR damper-based vibration reduction system
BULLETIN OF THE POLISH ACADEMY OF SCIENCES TECHNICAL SCIENCES, Vol. 59, No. 1, 2011 DOI: 10.2478/v10175-011-0011-4 Varia Energy balance in self-powered MR damper-based vibration reduction system J. SNAMINA
More informationThe tuned mass-damper-inerter (TMDI) for passive vibration control of multi-storey building structures subject to earthquake and wind excitations
Academic excellence for business and the professions The tuned mass-damper-inerter (TMDI) for passive vibration control of multi-storey building structures subject to earthquake and wind excitations Dr
More informationResearch Article Experimental Study on Variation Rules of Damping with Influential Factors of Tuned Liquid Column Damper
Hindawi Shock and Vibration Volume 217, Article ID 62925, 17 pages https://doi.org/1.1155/217/62925 Research Article Experimental Study on Variation Rules of Damping with Influential Factors of Tuned Liquid
More informationFrequency response analysis of soil-structure interaction for concrete gravity dams
Frequency response analysis of soil-structure interaction for concrete gravity dams Anna De Falco 1, Matteo Mori 2 and Giacomo Sevieri 3 1 Dept. of Energy, Systems, Territory and Construction Engineering,
More information3 Mathematical modeling of the torsional dynamics of a drill string
3 Mathematical modeling of the torsional dynamics of a drill string 3.1 Introduction Many works about torsional vibrations on drilling systems [1, 12, 18, 24, 41] have been published using different numerical
More informationMAE106 Laboratory Exercises Lab # 6 - Vibrating systems
MAE106 Laboratory Exercises Lab # 6 - Vibrating systems Goals Understand how the oscillations in a mechanical system affect its behavior. Parts & equipment Qty Part/Equipment 1 Seeeduino board 1 Motor
More informationDepartment of Civil Engineering, Noorul Islam University, Thucklay, India 2
Journal of Chemical and Pharmaceutical Sciences ISSN: 974-5 Control of structure with tuned liquid column damper Salsala Abubaker, S.Nagan, and T.Nasar 3 Department of Civil Engineering, Noorul Islam University,
More informationSystem Identification procedures for nonlinear response of Buckling Restraint Braces J. Martínez 1, R. Boroschek 1, J. Bilbao 1 (1)University of Chile
System Identification procedures for nonlinear response of Buckling Restraint Braces J. Martínez, R. Boroschek, J. Bilbao ()University of Chile. Abstract Buckling Restrained Braces (BRB) are hysteretic
More informationInput-Output Peak Picking Modal Identification & Output only Modal Identification and Damage Detection of Structures using
Input-Output Peak Picking Modal Identification & Output only Modal Identification and Damage Detection of Structures using Time Frequency and Wavelet Techniquesc Satish Nagarajaiah Professor of Civil and
More informationSeismic Base Isolation Analysis for the Control of Structural Nonlinear Vibration
Seismic Base Isolation Analysis for the Control of Structural Nonlinear Vibration L. Y. Li & J. P. Ou Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian, 11624, China SUMMARY:
More informationSEISMIC RESPONSE OF SINGLE DEGREE OF FREEDOM STRUCTURAL FUSE SYSTEMS
3 th World Conference on Earthquake Engineering Vancouver, B.C., Canada August -6, 4 Paper No. 377 SEISMIC RESPONSE OF SINGLE DEGREE OF FREEDOM STRUCTURAL FUSE SYSTEMS Ramiro VARGAS and Michel BRUNEAU
More informationGROUND MOTION DOMINANT FREQUENCY EFFECT ON THE DESIGN OF MULTIPLE TUNED MASS DAMPERS
Journal of Earthquake Engineering, Vol. 8, No. 1 (2004) 89 105 c Imperial College Press GROUND MOTION DOMINANT FREQUENCY EFFECT ON THE DESIGN OF MULTIPLE TUNED MASS DAMPERS CHUNXIANG LI School of Civil
More informationSeismic Analysis of Structures Prof. T.K. Datta Department of Civil Engineering Indian Institute of Technology, Delhi
Seismic Analysis of Structures Prof. T.K. Datta Department of Civil Engineering Indian Institute of Technology, Delhi Lecture - 20 Response Spectrum Method of Analysis In the last few lecture, we discussed
More informationIntroduction to structural dynamics
Introduction to structural dynamics p n m n u n p n-1 p 3... m n-1 m 3... u n-1 u 3 k 1 c 1 u 1 u 2 k 2 m p 1 1 c 2 m2 p 2 k n c n m n u n p n m 2 p 2 u 2 m 1 p 1 u 1 Static vs dynamic analysis Static
More informationANNEX A: ANALYSIS METHODOLOGIES
ANNEX A: ANALYSIS METHODOLOGIES A.1 Introduction Before discussing supplemental damping devices, this annex provides a brief review of the seismic analysis methods used in the optimization algorithms considered
More informationVIBRATION AMPLIFICATION IN OSCILLATING SYSTEMS WITH DEGRADING CHARACTERISTICS *
VIBRATION AMPIFICATION IN OSCIATING SYSTEMS WITH DEGRADING CHARACTERISTICS * Tudor SIRETEANU 1, Nicolae STOIA 1 The paper is an analysis of the dynamic response of an oscillating system, considering the
More informationModeling and Experimentation: Mass-Spring-Damper System Dynamics
Modeling and Experimentation: Mass-Spring-Damper System Dynamics Prof. R.G. Longoria Department of Mechanical Engineering The University of Texas at Austin July 20, 2014 Overview 1 This lab is meant to
More informationStructural changes detection with use of operational spatial filter
Structural changes detection with use of operational spatial filter Jeremi Wojcicki 1, Krzysztof Mendrok 1 1 AGH University of Science and Technology Al. Mickiewicza 30, 30-059 Krakow, Poland Abstract
More informationCE 6701 Structural Dynamics and Earthquake Engineering Dr. P. Venkateswara Rao
CE 6701 Structural Dynamics and Earthquake Engineering Dr. P. Venkateswara Rao Associate Professor Dept. of Civil Engineering SVCE, Sriperumbudur Difference between static loading and dynamic loading Degree
More informationOn the force drop off phenomenon in shaker testing in experimental modal analysis
Shock and Vibration 9 (2002) 165 175 165 IOS Press On the force drop off phenomenon in shaker testing in experimental modal analysis Paulo Sergio Varoto and Leopoldo Pisanelli Rodrigues de Oliveira Dynamics
More informationSEISMIC RELIABILITY ANALYSIS OF BASE-ISOLATED BUILDINGS
International Symposium on Engineering under Uncertainty: Safety Assessment and Management January 4 to 6, 2012 Paper No.: CNP 070 SEISMIC RELIABILITY ANALYSIS OF BASE-ISOLATED BUILDINGS M.C. Jacob 1,
More informationEXPERIMENTAL EVALUATION OF THE MODAL DAMPING OF AUTOMOTIVE COMPONENTS WITH DIFFERENT BOUNDARY CONDITIONS
ICSV14 Cairns Australia 9-12 July, 2007 EXPERIMENTAL EVALUATION OF THE MODAL DAMPING OF AUTOMOTIVE COMPONENTS WITH DIFFERENT BOUNDARY CONDITIONS Giorgio Dalpiaz 1, Emiliano Mucchi 1 and Stefano Mischiari
More informatione jωt = cos(ωt) + jsin(ωt),
This chapter introduces you to the most useful mechanical oscillator model, a mass-spring system with a single degree of freedom. Basic understanding of this system is the gateway to the understanding
More informationAnalysis Of Seismic Performance Of Fps Base Isolated Structures Subjected To Near Fault Events
Analysis Of Seismic Performance Of Fps Base Isolated Structures Subjected To Near Fault Events Luigi Petti, Fabrizio Polichetti, Bruno Palazzo Dipartimento di Ingegneria Civile dell Università degli Studi
More informationRandom Eigenvalue Problems in Structural Dynamics: An Experimental Investigation
Random Eigenvalue Problems in Structural Dynamics: An Experimental Investigation S. Adhikari, A. Srikantha Phani and D. A. Pape School of Engineering, Swansea University, Swansea, UK Email: S.Adhikari@swansea.ac.uk
More informationEstimation of Rotational FRFs via Cancellation Methods
Estimation of Rotational FRFs via Cancellation Methods Nomenclature ij ( l, k ) ij M. Reza shory, Semnan university, Iran Email: mashoori@semnan.ac.ir exact ccelerance measured accelerance when two mechanical
More information