Asymptotic Solutions of Fifth Order Over-Damped Nonlinear Systems with Cubic Nonlinearity

Abstract

Many engineering problems and physical systems of fifth degrees of freedom are governed by the fifth order nonlinear differential equations which are over-damped. In this article a fifth order nonlinear differential equation modeling an over-damped symmetrical system is considered. A perturbation technique based on the KBM method and the work of Akbar et al. is developed for obtaining the transient response when the eigenvalues are in integral multiple. The results obtained by the presented technique agree with those results obtained by the numerical method nicely. An example is solved to illustrated method.