Harmonic solutions of a dry friction system

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• 作者：Tao Li^a ; Xingwu Chen^a ; ^{xingwu.chen@hotmail.com} ; Jianrong Zhao^b
• 关键词：Degree theory ; Differential inclusion ; Dry friction ; Harmonic solution
• 刊名：Nonlinear Analysis: Real World Applications
• 出版年：2017
• 出版时间：June 2017
• 年：2017
• 卷：35
• 期：Complete
• 页码：30-44
• 全文大小：650 K
• 卷排序：35

文摘

In this paper we study harmonic solutions of the second order differential inclusion ẍ+g(x,ẋ)+u(x)Sgnẋ∋ϕ(t), which models a mechanical system with dry friction, viscous damping and TT-periodic external force. Under a weaker assumption than published works, we give sufficient conditions for the existence of harmonic solutions not only by the Degree Theory when g(x,ẋ) depends on ẋ but also by the Schauder’s Fixed Point Theorem when g(x,ẋ) is independent of ẋ. After obtaining the necessary and sufficient condition for the existence of constant solutions, we find the number of harmonic solutions based on the number of constant solutions when u(x)u(x) is a positive constant.