Nonlinear transient structural response analysis

Abstract

This work presents various aspects of the analysis of nonlinear dynamical single-degree-of-freedom (SDOF) systems possessing two example polynomial-type restoring forces. The first is a lesser known purely nonlinear, single-term expression containing both the signum function and absolute-value function, thus possessing the property of becoming non-Lipschizian at specific system equilibrium points if the real but positive polynomial exponent is set to values smaller than one.  The second restoring force corresponds to the well-known Duffing-type.  For both automous conservative systems extreme values of the response and oscillation frequency are obtained in terms of exact analytical expressions.  Solutions for the phenomena of multiple harmonic frequency component are given, and nonlinear shock response spectra readily applicable to accurate response prediction in practice are presented.

Time-varying exact closed-form solutions for both autonomous systems, either single or multiple term, are derived.  Employing the concept of differential transformation (DT) a set of algebraic equations is obtained that models the generalised dissipative nonautonomous time domain response behaviour.  The results obtained from both analytical approximate methods, single/multiple term solutions and DT, are compared to direct numerical integration Runge-Kutta routines.  It is shown that excellent agreement exists for both sets of results and that the newly derived methods are capable of even exceeding accuracy and computational performance of various commonly used Runge-Kutta algorithms.  Solution expressions for the transient nonconservative SDOF systems are readily applicable to multi-degree-of-freedom (MDOF) systems. A  rigorous uniqueness and stability analysis carried out for the oscillatory models considered in this work ensures that all of the obtained solutions are valid and feasible within their respective domain of definition.

More information

Identifiers

Catalogue record

Export record

ASCII CitationAtomBibTeXData Cite XMLDublin CoreDublin CoreEP3 XMLEndNoteHTML CitationHTML CitationHTML ListJSONMETSMODSMPEG-21 DIDLOpenURL ContextObjectOpenURL ContextObject in SpanRDF+N-TriplesRDF+N3RDF+XMLRIOXX2 XMLReferReference ManagerSimple Metadata