An Extended Harmonic Balance Method based on Incremental Nonlinear Control Parameters

H Haddad Khodaparast, H Madinei, MI Friswell, S Adhikari (Swansea University), S Coggon (Airbus) & JE Cooper (University of Bristol)

Mechanical Systems and Signal Processing, Vol. 85, February 2017, pp. 716-729


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 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 sets 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 system 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 MEMS devices.

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This material has been published in the Mechanical Systems and Signal Processing, Vol. 85, February 2017, pp. 716-729, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by Elsevier.

Link to paper using doi: 10.1016/j.ymssp.2016.09.008

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