Multiple Scales Solution for General Nonlinear ContinuousSystems in Complex Form

In this paper, the method of multiple scales is used to study free vibrations and primary resonancesof geometrically nonlinear spatial continuous systems with general quadratic and cubicnonlinear operators in a complex form. It is found that in the free vibrations of generalcontinuous systems in a complex form, both forward and backward modes are excited. Thissituation is in contrast to the primary resonances in which only forward modes are excited.This analysis is applicable to general continuous systems with gyroscopic and Coriolis effects and includes many nonlinear problems as a special case.

Keywords:

Perturbation Method , Method of multiple scales , Complex partial differential equations ,