No Cover Image

Journal article 212 views 5 downloads

An extended harmonic balance method based on incremental nonlinear control parameters / Hamed Haddad Khodaparast; Hadi Madinei; Michael I. Friswell; Sondipon Adhikari; Simon Coggon; Jonathan E. Cooper

Mechanical Systems and Signal Processing, Volume: 85, Pages: 716 - 729

Swansea University Author: Friswell, Michael

DOI (Published version): 10.1016/j.ymssp.2016.09.008

Abstract

A new formulation for calculating the steady-state responses of multiple-degree-of-freedom (MDOF) non-linear dynamic systems due to harmonic excitation is developed. This is aimed at solving multi-dimensional nonlinear systems using linear equations. Nonlinearity is parameterised by a set of ‘non-li...

Full description

Published in: Mechanical Systems and Signal Processing
Published: 2017
URI: https://cronfa.swan.ac.uk/Record/cronfa29777
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract: A new formulation for calculating the steady-state responses of multiple-degree-of-freedom (MDOF) non-linear dynamic systems due to harmonic excitation is developed. This is aimed at solving multi-dimensional nonlinear systems using linear equations. Nonlinearity is parameterised by a set of ‘non-linear control parameters' such that the dynamic system is effectively linear for zero values of these parameters and nonlinearity increases with increasing values of these parameters. Two sets of linear equations which are formed from a first-order truncated Taylor series expansion are developed. The first set of linear equations provides the summation of sensitivities of linear system responses with respect to non-linear control parameters and the second set are recursive equations that use the previous responses to update the sensitivities. The obtained sensitivities of steady-state responses are then used to calculate the steady state responses of non-linear dynamic systems in an iterative process. The application and verification of the method are illustrated using a non-linear Micro-Electro-Mechanical System (MEMS) subject to a base harmonic excitation. The non-linear control parameters in these examples are the DC voltages that are applied to the electrodes of the MEMS devices.
College: College of Engineering
Start Page: 716
End Page: 729