Title: Internal Resonances in 3-D Nonlinear Dynamical System
Authors: Mousa A. ALshawish and Ahmed N. Alshembari
Volume: 3
Issue: 9
Pages: 35-63
Publication Date: 2019/09/28//
Abstract:
This paper is concerned with the three dimensional motion of a nonlinear dynamical system. The motion is described by nonlinear partial differential equation, which is converted by Galerkin method to three-dimensional ordinary differential equations. The three dimensional free vibration of the beam, are solved analytically and numerically by the multiple time scales perturbation technique and the Runge-Kutta fourth order method. Phase plane technique and frequency response equations are used to investigate he stability of the system and the effects of the parameters of the system, respectively.