In this paper, an analytical technique has been developed based on a modified harmonic balance method to determine higher-order approximate periodic solutions for a nonlinear oscillator with discontinuity for which the elastic force term, is an anti-symmetric and quadratic term. Usually, a set of nonlinear algebraic equations is solved with this method. However, analytical solutions of these al...

The method of harmonic balance (HB) is a spectrally accurate used to obtain periodic steady state solutions dynamical systems subjected perturbations. We adapt HB solve for the stress response Giesekus model under large amplitude oscillatory shear (LAOS) deformation. transforms system differential equations set nonlinear algebraic in Fourier coefficients. Convergence studies find that differenc...

This article assesses two Harmonic Balance Method-based numerical Lagrangian strategies for the characterization of periodic response a mechanical system subject to unilateral contact constraints. The model used evaluation is an academic rod facing obstacle that firstly considered as equivalent stiffness (flexible) and then rigid obstacle. Nonlinear frequency curves are obtained through arc-len...