This content is not included in
your SAE MOBILUS subscription, or you are not logged in.
Modeling the Vibrations of and Energy Distributions in Car Body Structures
Technical Paper
2011-01-1573
ISSN: 0148-7191, e-ISSN: 2688-3627
Annotation ability available
Sector:
Language:
English
Abstract
A general numerical method, the so-called Fourier Spectral Element Method (FSEM), is described for the dynamic analysis of complex systems such as car body structures. In this method, a complex dynamic system is viewed as an assembly of a number of fundamental structural components such as beams, plates, and shells. Over each structural component, the basic solution variables (typically, the displacements) are sought as a continuous function in the form of an improved Fourier series expansion which is mathematically guaranteed to converge absolutely and uniformly over the solution domain of interest. Accordingly, the Fourier coefficients are considered as the generalized coordinates and determined using the powerful Rayleigh-Ritz method. Since this method does not involve any assumption or an introduction of any artificial model parameters, it is broadly applicable to the whole frequency range which is usually divided into low, mid, and high frequency regions. Further, because the current model is mesh-less and grid-free, it is particularly suited for sensitivity and statistical analyses and facilitates a smooth transition between the different frequency regions by switching on/off any statistical processing or spatial- and frequency-averaging features. As an example, this method is used to study the vibration characteristics of a car body structure (body-in-white). It is shown that the spatial- and frequency-averaging processes may not be desired for the mid-frequency analysis because the important dynamic characteristic of a system tends to be completely wiped out by them.
Recommended Content
Technical Paper | A Study on the Development Process of a Body with High Stiffness |
Technical Paper | Denting Simulation and Verification |
Technical Paper | Influence of Low-Frequency Powertrain-Vibrations on Driveability-Assessments |
Authors
Citation
Li, W., "Modeling the Vibrations of and Energy Distributions in Car Body Structures," SAE Technical Paper 2011-01-1573, 2011, https://doi.org/10.4271/2011-01-1573.Also In
References
- Hambric, S. A. Power flow and mechanical intensity calculations in structural finite element analysis Journal of Vibration and Acoustics 112 542 549 1990
- Gavric, L. Pavic, G. A finite element method for computation of structural intensity by the normal mode approach Journal of Sound and Vibration 164 29 43 1993
- Szwerc, R. P. Burroughs, C. B. Hambric, S. A. McDevitt, T. E. Power flow in coupled bending and longitudinal waves in beams Journal of the Acoustical Society of America 107 3186 3195 2000
- Mace, B. R. Shorter, P. Energy flow models from finite element analysis Journal of Sound and Vibration 233 369 389 2000
- Rabbiolo, G. Bernhard, R. J. Milner, F. A. Definition of a high-frequency threshold for plates and acoustical spaces Journal of Sound and Vibration 277 647 667 2004
- Lyon, R. H. DeJong, R. G. Theory and Application of Statistical Energy Analysis 2nd Butterworth-Heinemann Boston 1995
- Mace, B. R. Rosenberg, J. The SEA of two coupled plates: an investigation into the effects of system irregularity Journal of Sound and Vibration 212 395 415 1999
- Wester, E. C. N. Mace, B. R. Statistical energy analysis of two edge-coupled rectangular plates: ensemble averages Journal of Sound and Vibration 193 793 822 1996
- Yap, F. F. Woodhouse, J. Investigation of damping effects on statistical energy analysis of coupled structures Journal of Sound and Vibration 197 351 371 1996
- Craik, R. J. M. Steel, J. A. Evans, D. I. Statistical energy analysis of structure-borne sound transmission at low frequencies Journal of Sound and Vibration 144 95 107 1991
- Fahy, F. J. Statistical energy analysis: an overview Keane, A. J. Price, W. G. Statistical Energy Analysis: A Critical Overview, with Applications in Structural Dynamics Cambridge University Press Cambridge 1 18 1997
- Fahy, F. J. Mohamed, A. D. A study of uncertainty in application of SEA to coupled beam and plate systems, Part I: computational experiments Journal of Sound and Vibration 158 45 67 1992
- Bercin, A. N. Langley, R. S. Application of the dynamic stiffness technique to the inplane vibrations of plate structures Computers and Structures 59 869 875 1996
- Langley, R. S. Analysis of power flow in beams and frameworks using the direct-dynamic stiffness method Journal of Sound and Vibration 136 439 452 1990
- Park, D. H. Hong, S. Y. Kil, F. G. Jeon, J. J. Power flow models and analysis of in-plane waves in finite coupled think plates Journal of Sound and Vibration 244 651 668 2001
- Doyle, J. F. Wave Propagation in Structures Springer Berlin 1989
- Ahmida, K. M. Arruda, J. R. F. Spectral element-based prediction of active power flow in Timoshenko beams International Journal of Solids and Structures 38 1669 1679 2001
- Igawa, H. Komatru, K. Yamaguchi, I. Kasai, T. Wave propagation analysis of frame structures using the spectral element method Journal of Sound and Vibration 277 1071 1081 2004
- Keane, A. J. Price, W. G. A note on the power flowing between two conservatively coupled multi-modal sub-system Journal of Sound and Vibration 144 185 196 1991
- Keane, J. Energy flows between arbitrary configurations of conservatively coupled multi-modal elastic subsystems Proceedings of the Royal Society of London A 436 537 568 1992
- Beshara, M. Keane, A. J. Vibrational power flows in beam networks with compliant and dissipative joints Journal of Sound and Vibration 203 321 339 1997
- Shankar, K. Keane, A. J. Power flow predictions in a structure of rigidly joined beams using receptance theory Journal of Sound and Vibration 180 867 890 1995
- Farag, N. H. Pan, J. Dynamic response and power flow in three-dimensional coupled beam structures. I. Analytical modeling Journal of the Acoustical Society of America 102 315 325 1997
- Li, W. L. Xu, H. A. An exact Fourier series method for the vibration analysis of multi-span beam systems Computational and Nonlinear Dynamics 4 2009
- Li, W. L. Bonilha, M. W. Xiao, J. Vibrations and power flows in a coupled beam system ASME Journal of Vibration and Acoustics 129 616 622 2007
- Li, W.L. Zhang, X.F. Du, J.T. Liu, Z.G. An exact series solution for the transverse vibration of rectangular plates with general elastic boundary supports Journal of Sound and Vibration 321 254 269 2009
- Zhang, X.F. Li, W.L. Vibrations of rectangular plates with arbitrary non-uniform elastic edge restraints Journal of Sound and Vibration 326 221 234 2009
- Xu, H. A. Du, J. T. Li, W. L. Vibrations of rectangular plates reinforced by any number of beams of arbitrary lengths and placement angles Journal of Sound and Vibration 329 3759 3779 2010
- Xu, H. A. Du, J. T. Li, W. L. Vibration and power flow analysis of periodically reinforced plates Science China
- Li, W.L. An alternative form of Fourier series expansion
- Li, W. L. Xu, H. A. Vibration and Power Flow Analyses of Built-up Structures in a Broad Frequency Range IMAC XXVII Orlando, Florida 2009