Tj. Royston et R. Singh, PERIODIC-RESPONSE OF MECHANICAL SYSTEMS WITH LOCAL NONLINEARITIES USING AN ENHANCED GALERKIN TECHNIQUE, Journal of sound and vibration, 194(2), 1996, pp. 243-263
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