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

被引：3
|
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.
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页数：15
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