A new modified Lindstedt–Poincare method for nonlinear damped forced oscillations

Abstract

Nonlinear damped forced oscillators are very importance in the fields of mechanical, electrical and other dynamical systems. Small oscillations are being investigated by classical perturbations. Earlier Cheung et al. presented a modified Lindstedt–Poincare method for large amplitude of oscillation; but its mathematical manipulation is tremendously difficult. Moreover, it fails to determine the solutions when linear restoring force vanishes. In this article, a modification of the same method is made which greatly reduces mathematical calculations. On the other hand, it provides more accurate results and is used whether linear restoring force is present or not.

Keywords

• Modified Lindstedt–Poincare method
• Nonlinear damped forced oscillators
• Approximate solutions
• Frequency amplitude relation