An Application of the Melnikov Method to a Piecewise Oscillator
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Published:2023-04-21
Issue:
Volume:
Page:249-269
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ISSN:2705-1056
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Container-title:Contemporary Mathematics
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language:
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Short-container-title:Contemp. Math.
Author:
Gjata Oltiana,
Zanolin FabioORCID
Abstract
In this paper we present a new application of the Melnikov method to a class of periodically perturbed Duffing equations where the nonlinearity is non-smooth as otherwise required in the classical applications. Extensions of the Melnikov method to these situations is a topic with growing interests from the researchers in the past decade. Our model, motivated by the study of mechanical vibrations for systems with ''stops'', considers a case of a nonlinear equation with piecewise linear components. This allows us to provide a precise analytical representation of the homoclinic orbit for the associated autonomous planar system and thus obtain simply computable conditions for the zeros of the associated Melnikov function.
Publisher
Universal Wiser Publisher Pte. Ltd