Dynamics of a harmonic oscillator perturbed by a non-smooth velocity-dependent damping force
Publish place: Journal of Mahani Mathematical Research، Vol: 10، Issue: 2
Publish Year: 1400
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_KJMMRC-10-2_011
تاریخ نمایه سازی: 1 آبان 1400
Abstract:
This paper studies the dynamics of a non-smooth vibrating system of the Filippov type. The main focus is on investigating the stability and bifurcation of a simple harmonic oscillator subjected to a non-smooth velocity-dependent damping force. In this way, we can analyze the effects of damping on the system's vibrations. For this purpose, we will find a parametric region for the existence of generalized Hopf bifurcation, in order to compute a branch of periodic orbits for the system. The tool for our purpose is the theoretical results about generalized Hopf bifurcation for planar Filippov systems. Some numerical simulations as examples are given to illustrate our theoretical results. Our theoretical and numerical findings indicate that the harmonic oscillator can experience different kinds of vibrations, in the presence of a non-smooth damping.
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Authors
Zahra Monfared
Department of Mathematics & Informatics and Cluster of Excellence STRUCTURES, Heidelberg University, Heidelberg, Germany and Department of Applied Mathematics, Ferdowsi University of Mashhad (FUM), Mashhad, Iran
Zohreh Dadi
Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, Bojnord, Iran
ALi Darijani
Department of Mathematics, Higher Education Complex of Bam, Bam, Iran
Yousef Qasemi Nezhad Raeini
Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran