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    Constrained Optimization Multi-dimensional Harmonic Balance Method for Quasi-periodic Motions of Nonlinear Systems

    Haitao Liao1

    CMES-Computer Modeling in Engineering & Sciences, Vol.95, No.3, pp. 207-234, 2013, DOI:10.3970/cmes.2013.095.207

    Abstract The constrained optimization multi-dimensional harmonic balance method for calculating the quasi-periodic solutions of nonlinear systems is presented. The problem of determining the worst quasi-periodic response is transformed into a nonlinear optimization problem with nonlinear equality constraints. The general nonlinear equality constraints are built using a set of nonlinear algebraic equations which is derived using the multi-dimensional harmonic balance method. The Multi- Start algorithm is adopted to solve the resulting constrained maximization problem. Finally, the validity of the proposed method is demonstrated with a Duffing oscillator and numerical case studies for problems with uncertainties are performed More >

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