Nonlinear Computation Featuring Non-Smooth Effects Using the Harmonic Balance Method
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The study of nonlinear mechanical phenomena has become a major research field in engineering system design, as it gives rise to complex behaviors such as multistability. In many practical applications, physical models involving contact or friction exhibit hysteretic effects, as featured in Bouc-Wen, LuGre or Duhem models. These effects introduce asymmetrical dynamic responses and non-smooth behavior through the internal variables. For periodic responses, commonly encountered in vibratory dynamics, frequency-domain methods have gained significant attention due to their computational efficiency. The Harmonic Balance Method (HBM) approximates periodic solutions using truncated Fourier series within a Galerkin framework. However, when applied to non-smooth systems, HBM faces major difficulties, including the complex evaluation of Fourier integrals of non-smooth terms and slow convergence when high accuracy is required.
