Computational Techniques for Nonlinear Dynamics of Continuous Systems

Abstract

A method to integrate the nonlinear partial-differential equations of motion of a cantilever beam capable of coupled flexural-torsional vibrations is presented. The technique uses spatial finite-difference approximations to reduce the equations to a set of ordinary-differential equations (ODEs) in time, and then integrates these equations in time using a fourth-order Runge-Kutta algorithm. Tools for the qualitative analysis of nonlinear dynamical systems, such as Poincaré sections, fixed points, domains of attraction, and frequency response curves are discussed for high-order discretized systems.