Low-frequency perturbations of rigid body motions of a viscoelastic inhomogeneous bar
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This paper deals with a low-frequency analysis of a viscoelastic inhomogeneous bar subject to end loads. The spatial variation of the problem parameters is taken into consideration. Explicit asymptotic corrections to the conventional equations of rigid body motion are derived in the form of integro-differential operators acting on longitudinal force or bending moment. The refined equations incorporate the effect of an internal viscoelastic microstructure on the overall dynamic response. Comparison with the exact time-harmonic solutions for extension and bending of a bar demonstrates the advantages of the developed approach. This research is inspired by modeling of railcar dynamics.
KeywordsViscoelastic Microstructure Perturbation Rigid body Low-frequency
J. Kaplunov and A. Shestakova gratefully acknowledge support from the industrial project with AMSTED Rail, USA. J. Kaplunov’s research in the area of mechanics of inhomogeneous solids was supported by National University of Science and Technology “MISiS”, Russia by grant K3-2014-052. The authors also grateful to Dr. D. Prikazchikov for a number of valuable comments.
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