Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30076
Nonlinear and Chaotic Motions for a Shock Absorbing Structure Supported by Nonlinear Springs with Hysteresis Using Fast FEA

Authors: T. Yamaguchi, Y. Kurosawa, S. Maruyama, K. Tobita, Y. Hirano, K. Yokouchi, K. Kihara, T. Sunaga

Abstract:

This paper describes dynamic analysis using proposed fast finite element method for a shock absorbing structure including a sponge. The structure is supported by nonlinear concentrated springs. The restoring force of the spring has cubic nonlinearity and linear hysteresis damping. To calculate damping properties for the structures including elastic body and porous body, displacement vectors as common unknown variable are solved under coupled condition. Under small amplitude, we apply asymptotic method to complex eigenvalue problem of this system to obtain modal parameters. And then expressions of modal loss factor are derived approximately. This approach was proposed by one of the authors previously. We call this method as Modal Strain and Kinetic Energy Method (MSKE method). Further, using the modal loss factors, the discretized equations in physical coordinate are transformed into the nonlinear ordinary coupled equations using normal coordinate corresponding to linear natural modes. This transformation yields computation efficiency. As a numerical example of a shock absorbing structures, we adopt double skins with a sponge. The double skins are supported by nonlinear concentrated springs. We clarify influences of amplitude of the input force on nonlinear and chaotic responses.

Keywords: Dynamic response, Nonlinear and chaotic motions, Finite Element analysis, Numerical analysis.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1087320

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1608

References:


[1] T. Yamaguchi,Y. Kurosawa and S. Matsumura, “FEA for damping of structures having elastic bodies, viscoelastic bodies, porous media and gas”, Mechanical Systems and Signal Processing, Vol.21, pp.535-552, 2007.
[2] T. Yamaguchi, Y. Kurosawa and H. Enomoto, “Damped vibration analysis using finite elementmethod with approximated modal damping for automotive double walls with a porous material”, Journal of Sound and Vibration, Vol.325, pp.436-450, 2009.
[3] T. Yamaguchi, Y. Fujii, K. Nagai andS. Maruyama, “FEA forvibrated structures with non-linear concentrated spring havinghysteresis,” Mechanical Systems and Signal Processing, vol.20, pp.1905–1922, Nov. 2006.
[4] T.Yamaguchi, Y.Fujii, T.Fukushima, T.Kanai, K. NagaiandS. Maruyama, “Dynamic responses for viscoelastic shock absorbers to protect a finger under impact force,”Applied Mechanics and Materials, vol.36, pp.287-292,Oct.2010.
[5] T. Kondo,T. SasakiandT. Ayabe, “Forced vibrationanalysis of a straight-line beam structure with nonlinear support elements”, Transactions of the Japan Society of Mechanical Engineers, Vol.67, No.656C, pp.914-921, 2001.
[6] E. Pesheck,N.Boivin,C. Pierre and S. W. Shaw, “Non-linear modal analysis of structural systems using multi-mode invariant manifolds”, Nonlinear Dynamics, Vol.25, pp.183-205, 2001.
[7] A. Craggs, “A finite element model for rigid porous absorbing materials”, Journal of Sound andVibration, Vol. 61-1, pp.101-111, 1978.
[8] Y. Kagawa,T.Yamabuchi and A. Mori, “Finite element simulation of an axisymmetric acoustictransmissionsystem with a sound absorbing wall”, Journal of Sound and Vibration, Vol.53-3, pp.357-374, 1977.
[9] H. Utsuno,T. W. Wu, A. F. Seybert and T. Tanaka, “Prediction of sound fields in cavities with sound absorbing materials”, AIAA Journal,Vol.28-11, pp.1870-1875, 1990.
[10] Y. J. Kang and S. Bolton, “Finite element modeling of isotropic elastic porous materials coupled with acoustical finite elements”, Journal of the Acoustical Society of America, Vol.98- 1, pp.635-643, 1995.
[11] N. Attala, R. Panneton and P. A. Debergue, “A mixed pressure-displacement formulation for poroelastic materials”, Journal of the Acoustical Society of America, Vol.104-3, pp.1444-1452, 1998.
[12] M. A. Biot, “Theory of propagation of elastic waves in a fluid-saturated porous solid”, Journal of the Acoustical Society of America, Vol.28-2, pp.168-178, 1955.
[13] C. D. Johnson and D. A. Kienholz, “Finite element prediction of damping structures with constrained viscoelastic layers”, AIAA Journal, Vol.20-9, pp.1284-1290, 1982.
[14] B. A. Ma and J. F. He,“A finite element analysis of viscoelastically damped sandwich plates”, Journal of Sound and Vibration,Vol.152-1, pp.107-123, 1992.
[15] O. C. Zienkiewicz and Y. K. Cheung,The finite element method in structural and continuum mechanics,MacGraw-Hill, 1967.
[16] E. L. Wilson,R. L. Taylor,W. P. Doherty and J. Ghaboussi, Incompatible displacement methods, in numerical and computer methods in structural mechanics,Academic Press, 1973.
[17] T. YamaguchiandK. Nagai, “Chaotic vibration of a cylindrical shell-panel with an in-plane elastic support at boundary”,Nonlinear Dynamics, Vol.13, pp.259-277, 1997.
[18] A. Wolf,J. B. Swift, H. L. Swinny and J. A. Vastano, “Determining Lyapunov exponents from a timeseries”, Physica16D, pp.285–317, 1985.