Effect of Fractional Damping in Double-Well Duffing–Vander Pol Oscillator Driven by Different Sinusoidal Forces

Autor:	V. Chinnathambi, Shanmuganathan Rajasekar, S. Athisayanathan, M. V. Sethu Meenakshi
Rok vydání:	2019
Předmět:	Physics Classical mechanics Mechanics of Materials Applied Mathematics Modeling and Simulation 0103 physical sciences Computational Mechanics General Physics and Astronomy Statistical and Nonlinear Physics 010306 general physics 010301 acoustics 01 natural sciences Engineering (miscellaneous)
Zdroj:	International Journal of Nonlinear Sciences and Numerical Simulation. 20:115-124
ISSN:	2191-0294 1565-1339
DOI:	10.1515/ijnsns-2016-0165
Popis:	The effect of nonlinear damping including fractional damping on the onset of horseshoe chaos is studied both analytically and numerically in the double-well Duffing–Vander Pol (DVP) oscillator driven by various sinusoidal forces. The sinusoidal type periodic forces of our interest are sine wave, rectified sine wave, and modulus of sine wave. Using the Melnikov analytical method, the threshold condition for the onset of horseshoe chaos is obtained for each sinusoidal force. Melnikov threshold curves are drawn in (f,\;ω) parameters space for each force. When the damping component (p) increases from a small value, the Melnikov threshold value ( f M ) $(f_{M})$ is decreased for each force. Suppression of horseshoe chaos is predicted due to the effect of weak periodic perturbation and nonlinear fractional damping. Analytical predictions are demonstrated through direct numerical simulations.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::b2a99c6d7c7c79db2ec9d0e8ae1e61e5 https://doi.org/10.1515/ijnsns-2016-0165 Zobrazit plný text záznamu