Dynamics of a multi-DOF beam system with discontinuous support

Abstract

This paper deals with the long term behaviour of periodically excited mechanical systems consisting of linear components and local nonlinearities. The particular system investigated is a 2D pinned-pinned beam, which halfway its length is supported by a one-sided spring and excited by a periodic transversal force. The linear part of this system is modelled by means of the finite element method and subse1uently reduced using a Component Mode Synthesis method. Periodic solutions are computed by solving a two-point boundary value problem using finite differences or, alternatively, by using the shooting method. Branches of periodic solutions are followed at a changing design variable by applying a path following technique. Floquet multipliers are calculated to determine the local stability of these solutions and to identify local bifurcation points. Also stable and unstable manifolds are calculated. The long term behaviour is also investigated by means of standard numerical time integration, in particular for determining chaotic motions. In addition, the Cell Mapping technique is applied to identify periodic and chaotic solutions and their basins of attraction. An extension of the existing cell mapping methods enables to investigate systems with many degress of freedom. By means of the above methods very rich complex dynamic behaviour is demonstrated for the beam system with one-sided spring support. This behaviour is confirmed by experimental results.