Asymptotic perturbation analysis for nonlinear oscillations in viscoelastic systems with hardening exponent. (English) Zbl 1359.74052

Summary: The response of many living and engineering structural systems to dynamic loads is often translated in differential equations including some parameters which may change with time. This change may affect in a dramatic way the qualitative behavior of the dynamic response of these systems. It is then suitable to investigate the asymptotic behavior of these systems when some dynamic parameters tend to their critical value. The problem, given a structural model which depends on a strain hardening exponent, is to verify if a small perturbation in this parameter produces a small qualitative change in the dynamic response of the system. To this end, asymptotic perturbation and numerical analyses are performed. The study showed that a small change in the strain hardening exponent does not produce a significant change in the qualitative behavior of the dynamic response of the structural model. The current research work has permitted from a theoretical point of view to note the accuracy of the theory of averaging and the stability of the system. Thus, from a practical point of view, the current model may serve as an alternative to other models for an easy numerical simulation of the dynamics of some mechanical systems experiencing a weak viscoelastic response in view of prediction and operation performance.


74D10 Nonlinear constitutive equations for materials with memory
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
70K20 Stability for nonlinear problems in mechanics
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