PERIODIC-RESPONSE OF MECHANICAL SYSTEMS WITH LOCAL NONLINEARITIES USING AN ENHANCED GALERKIN TECHNIQUE

A new semi-analytical framework for the study of mechanical systems wi th local non-linearities is presented. It recognizes that many practic al built-up structures consist of non-linearities, typically at joints or junctions, with a few degrees-of-freedom, coupled with many linear degrees-of-freedom of the adjoining components. Unlike linear systems , sinusoidal excitation produces a periodic response, including super and subharmonics. A Galerkin based computational method for the soluti on of the steady state periodic response of mechanical systems with lo cal non-linearities, defined in the time and/or frequency domains, is proposed. The method incorporates a form of order reduction and numeri cal continuation with distinct benefits. Order reduction enables inclu sion of the extensive and necessary, but often linear, assembled compo nent dynamics with minimal computational cost. Additionally, the propo sed form of reduction allows non-linearities explicitly defined in the frequency and the time domain to be handled simultaneously. The conti nuation scheme, based on the QR decomposition, facilities parametric s tudies for design by using the system solution for one set of paramete rs to optimally predict the steady state periodic solution for a simil ar set of parameters. Two specific examples have been chosen to illust rate the key concepts and methodology of the dual domain method. In th e first example, a rigid body connected to a simply supported elastic beam via a Iron-linear spring is considered. The hydraulic engine moun ting system is presented as the second example; a practical representa tive of the issues discussed in this article. Results of digital and a nalog computational studies verify the accuracy of the proposed method and highlight its unique capabilities. (C) 1996 Academic Press Limite d