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Dynamics of a harmonic oscillator perturbed by a non-smooth velocity-dependent damping force | ||
| Journal of Mahani Mathematical Research | ||
| دوره 10، شماره 2، دی 2021، صفحه 145-162 اصل مقاله (581.84 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmrc.2021.17474.1140 | ||
| نویسندگان | ||
| Zahra Monfared1؛ Zohreh Dadi* 2؛ ALi Darijani3؛ Yousef Qasemi Nezhad Raeini4 | ||
| 1Department of Mathematics & Informatics and Cluster of Excellence STRUCTURES, Heidelberg University, Heidelberg, Germany and Department of Applied Mathematics, Ferdowsi University of Mashhad (FUM), Mashhad, Iran | ||
| 2Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, Bojnord, Iran | ||
| 3Department of Mathematics, Higher Education Complex of Bam, Bam, Iran | ||
| 4Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Velocity-dependent damping؛ Non-smooth dynamical systems؛ Generalized Hopf bifurcation؛ Vibrations؛ Nonlinear oscillator | ||
| مراجع | ||
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