On a problem of modified Lindstedt–Poincare for certain strongly non-linear oscillators

Abstract

In the present paper concerns the modified Lindstedt–Poincare method is presented for extending the rang of the validity of perturbation expansion to strongly non-linear oscillation. It is an effective method for dealing with strongly non-linear vibration of single degree-of-freedom system which cannot be treated by the standard L–P method. Therefore a strongly non-linear system with large parameter μ is transformed into a small parameter system with respect to α. This method is suitable for the system with even non-linearities as well as with odd non-linearities. All numerical results computed are in pretty good and displayed graphysically. This method is suitable for the system with even non-linearities as well as with odd non-linearities. All numerical results computed are in pretty good and displayed graphysically.