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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Communications in Nonlinear Science and Numerical Simulation
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
