Time and frequency response of structures with frequency dependent, non-proportional linear damping

作者: L. Zoghaib , P.-O. Mattei

DOI: 10.1016/J.JSV.2013.09.044

关键词: Nonlinear systemComputationControl theoryMathematical analysisInverse Laplace transformEigenvalues and eigenvectorsFinite element methodFrequency responseComplex planeSound powerEngineering

摘要: Abstract A method to compute the non-stationary time and frequency response of structures with a frequency-dependent non-proportional linear damping, called resonance modes method, is presented in this paper. It consists two main steps. The first step aims at spotting structure modes, which are solutions matrix nonlinear eigenvalue problem obtained using finite element complex plane. This requires eigensolver an iterative scheme, perturbation technique or combination both. second uses computed analytical expression inverse Laplace transform deduce general excitations. aluminum plate damped elastomer treatment point-force excitation, classical modal approach, direct solution shows its precision efficiency. An acoustic power computation finally validates implementation fast variant, based on technique, for vibroacoustic applications.

参考文章(23)
Klaus-Jürgen Bathe, Finite Element Procedures ,(1995)
A.L. Araújo, C.M. Mota Soares, C.A. Mota Soares, J. Herskovits, Optimal design and parameter estimation of frequency dependent viscoelastic laminated sandwich composite plates Composite Structures. ,vol. 92, pp. 2321- 2327 ,(2010) , 10.1016/J.COMPSTRUCT.2009.07.006
P.J.T. FILIPPI, D. HABAULT, P.-O. MATTEI, C. MAURY, The role of the resonance modes in the response of a fluid-loaded structure Journal of Sound and Vibration. ,vol. 239, pp. 639- 663 ,(2001) , 10.1006/JSVI.2000.3217
G. LESIEUTRE, E. BIANCHINI, Time-domain modeling of linear viscoelasticity using augmenting thermodynamic fields Collection of Technical Papers - AIAA/ASME Structures, Structural Dynamics and Materials Conference. pp. 2101- 2109 ,(1993) , 10.2514/6.1993-1550
Ioana C Finegan, Ronald F Gibson, Analytical modeling of damping at micromechanical level in polymer composites reinforced with coated fibers Composites Science and Technology. ,vol. 60, pp. 1077- 1084 ,(2000) , 10.1016/S0266-3538(00)00003-8
F.S. Barbosa, M.C.R. Farage, A finite element model for sandwich viscoelastic beams: Experimental and numerical assessment Journal of Sound and Vibration. ,vol. 317, pp. 91- 111 ,(2008) , 10.1016/J.JSV.2008.03.013
Fernando Cortés, María Jesús Elejabarrieta, Forced response of a viscoelastically damped rod using the superposition of modal contribution functions Journal of Sound and Vibration. ,vol. 315, pp. 58- 64 ,(2008) , 10.1016/J.JSV.2008.01.027
D. F. Golla, P. C. Hughes, Dynamics of Viscoelastic Structures—A Time-Domain, Finite Element Formulation Journal of Applied Mechanics. ,vol. 52, pp. 897- 906 ,(1985) , 10.1115/1.3169166