THEAPPROXIMATE ANALYTIC SOLUTIONS FOR FREE VIBRATIONS OF A MASS GROUNDED BY LINEAR AND NONLINEAR SPRINGS IN SERIES

摘要

In many technical applications, spring-like flexible elements or real springs connected in series are used. The applicable range of these components determines whether or not the system behavior has a linear or nonlinear characteristic. This study is concerned to a system that consists of a mass grounded two springs which one of those springs is linear and the other is nonlinear. Two methods are studied to analyze the dynamic system behavior. One method makes use of a set of Energy Balance Method (EBM) and the other is Homotopy Perturbation Method (HPM). The results indicate that the present analysis is accurate, and provides us a unified and systematic procedure which is simple and more straightforward than the other modal analysis. The main objective of present study is to obtain highly accurate analytical solutions for free vibrations of a conservative oscillator with inertia and static type cubic nonlinearities.