Nonlinear vibrations of dynamical systems with a general form of piecewise-linear viscous damping by incremental harmonic balance method

Incremental harmonic balance (IHB) method for computation of periodic solutions of nonlinear dynamical systems is extended here for analysis of a class of periodically excited systems with a general form of piecewise-linear viscous damping characteristics, with an explicit formulation being derived , which is in many respects distinctively advantageous over classical approaches, and especially excels in performing parametric studies as frequency response property. Numerical simulation of a specific periodically excited oscillator of the considered type is effectively carried out by the IHB scheme and the results compare very well with direct numerical integration. The formulation derived here can readily be combined with the existing IHB scheme designed for treating systems with only piecewise-linear stiffness in analyzing complex dynamical behavior as bifurcation and chaos of more general piecewise-linear systems.

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