摘要
构建双边对称刚性约束的非光滑双摆模型,研究简谐激励作用下该系统的碰撞周期解及其存在条件。应用模态分析法,引入矩阵理论,构造恰当的可逆变换矩阵,在理论上计算出物理参数和碰撞恢复系数的取值范围,并给出双碰周期解的解析表达式。在理论结果的基础上,利用碰撞恢复矩阵作为衔接条件,采用理论分析和数值模拟相结合的方法,分析系统小角度运动的碰撞周期解。
A double pendulum model with bi-lateral rigid constraint is constructed under harmonic excitation.The impact periodic solution of a nonlinear dynamic system under harmonic excitation and its existence conditions are studied.Adopting the modal analysis and matrix theory,an invertible transformation is introduced to obtain the parameter conditions for the existence of the impact periodic solution of the system.On the basis of the theoretical calculation results,applying Matlab software,numerical simulation is carried out to obtain the impact periodic solution of the system with small angle motion,which verifies that the theoretical research results have certain theoretical guidance in engineering practice.
作者
郭秀英
张刚
田瑞兰
GUO Xiu-ying;ZHANG Gang;TIAN Rui-lan(School of Mathematical Sciences,Hebei Normal University,Shijiazhuang 050024,China;Department of Mathematics and Physics,Shijiazhuang Tiedao University,Shijiazhuang 050043,China;State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures,Shijiazhuang Tiedao University,Shijiazhuang 050043,China;Department of Engineering Mechanics,Shijiazhuang Tiedao University,Shijiazhuang 050043,China)
出处
《振动工程学报》
EI
CSCD
北大核心
2021年第1期185-193,共9页
Journal of Vibration Engineering
基金
国家自然科学基金资助项目(11872253,1602151)
河北省杰出青年科学基金资助项目(A2017210177)
河北省教育厅百名优秀创新人才项目(SLRC2019037)
河北省自然科学基金资助项目(A2019421005,A2019402043)
河北省“三三三人才工程”资助项目(A202005007)
河北省高等学校科学技术研究项目(ZD2019047)。
关键词
非线性振动
非光滑双摆
碰撞周期解
对称刚性约束
恢复系数
nonlinear vibration
non-smooth double pendulum
impact periodic solution
symmetric bilateral rigid constraint
coefficient of restitution
