On the Poincar’e-Lindstedt perturbation method for a Non-Linear Rayleigh Oscillator with periodic damping coefficient

Abstract

In this paper the Poincar’e-Lindstedt perturbation method will be applied to analyse an oscillator with Rayleigh type with Periodic Damping Coefficient. The mathematical model of the oscillator describes flow-induced vibrations in a uniform wind field. The horizontal cylinder supported by springs as a model can be designed vibrate in vertical direction. It will be studied a solution approximation of the oscillator by using Poincar’e-Lindstedt perturbation method. The basic idea of the Poincar’e-Lindstedt perturbation is that from the simple harmonic oscillator, the period of oscillation depends on the amplitude of the motion. The Lindstedt perturbation expansion allows the frequency to adapt to the nonlinearity by defining the “stretched time variable” The periodic solution of Limit cycle will be studied in this paper.