Harmonic solutions for a class of non-autonomous piecewise linear oscillators

被引：5

作者：

Zhou, Biliu ^{[1
]}

Chen, Hebai ^{[2
]}

Xu, Huidong ^{[3
]}

Zhang, Jianwen ^{[4
]}

机构：

[1] Beijing Inst Technol, Dept Mech, Beijing 100081, Peoples R China

[2] Cent South Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China

[3] Taiyuan Univ Technol, Coll Mech & Vehicle Engn, Taiyuan 030024, Shanxi, Peoples R China

[4] Taiyuan Univ Technol, Coll Math, Taiyuan 030024, Shanxi, Peoples R China

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2021年 / 102卷

基金：

中国国家自然科学基金;

关键词：

Harmonic solution; Resonant; non-resonant case; Piecewise linear oscillator; Non-autonomous system; SYSTEM; VIBRATION;

D O I：

10.1016/j.cnsns.2021.105912

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The study deals with the existence and uniqueness conditions of harmonic solutions of a class of piecewise linear oscillators with a general periodic excitation. Based on the relationship between natural frequency and driving frequency, we divide the discussion of the harmonic solutions into resonant case and non-resonant case. For resonant case, the existence conditions dependent on periodic excitation and clearance of harmonic solutions are given based on the Poincare-Bohl fixed point theorem. Moreover, we give a necessary and sufficient condition of bounded solutions, where harmonic solutions, n-subharmonic solutions, and quasi-periodic solutions can occur simultaneously. For non-resonant case, the existence of harmonic solutions are analyzed based on contract mapping. The uniqueness of harmonic solutions for resonant and non-resonant cases are proven by variational method and reduction to absurdity. Numerical examples are presented to illustrate the theoretical results. (c) 2021 Elsevier B.V. All rights reserved.

引用

页数：15

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