Abstract
The study deals with the existence and uniqueness conditions of harmonic solutions of a class of piecewise linear oscillators with a general periodic excitation. Based on the relationship between natural frequency and driving frequency, we divide the discussion of the harmonic solutions into resonant case and non-resonant case. For resonant case, the existence conditions dependent on periodic excitation and clearance of harmonic solutions are given based on the Poincaré-Bohl fixed point theorem. Moreover, we give a necessary and sufficient condition of bounded solutions, where harmonic solutions, n-subharmonic solutions, and quasi-periodic solutions can occur simultaneously. For non-resonant case, the existence of harmonic solutions are analyzed based on contract mapping. The uniqueness of harmonic solutions for resonant and non-resonant cases are proven by variational method and reduction to absurdity. Numerical examples are presented to illustrate the theoretical results.
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