Computational techniques for nonlinear dynamics of continuous systems

A method to integrate the nonlinear partial-differential equations of motion:of a cantilever beam capable of coupled flexural-torsional vibrations is presented.The techmque uses spatial finite-.dIfference approximations to reduce the equations to a set of ordmary-differential equations (ODEs) in time. and then integrates these equations in time using a fourth-order Runge-Kutta algonthm. Tools for the quahtatlve analysis of nonlinear dynamical systems, such as Poincare sections, fixed pomts, domams of attraction, and frequency response curves are discussed for high-order discretized systems