摘要
建立了端部非线性单元耦合弹性梁系统物理模型,从能量角度,根据广义哈密顿原理和变分法建立弹性梁系统的振动控制方程.首先,运用伽辽金法展开弹性梁系统的横向振动位移并建立其残差方程,运用龙格库塔算法求解数值结果.然后,在保证计算数值结果正确性的基础上,深入研究端部耦合非线性单元对弹性梁系统频率响应的影响规律,探索端部耦合非线性单元在单频激励下对弹性梁系统振动响应的影响规律并掲示弹性梁系统非线性动力学行为的生成机理.最后,研究了弹性梁系统在复杂非线性振动响应下的振动能量传递特性.研究结果表明,合理利用端部非线性单元,能够表现出主动梁振动能量传递给从动梁的现象,降低主动梁振动,从动梁类似于吸振器.在复杂非线性振动状态下,弹性梁系统出现靶向能量传递现象,准周期振动状态是出现该现象的标志.靶向振动能量传递现象的出现为从时域角度单向控制弹性梁系统的振动水平提供可能.
In this paper,a physical model of elastic beam system with end nonlinear elements coupling is established.From the energy perspective,the vibration-governing equations of the elastic beam system are established based on the generalized Hamilton principle and variational procedure.Firstly,the Galerkin method is employed to expand the transverse vibration displacements of the elastic beam system and establish its residual equation,and the Runge-Kutta algorithm is used to solve the numerical results.Then,on the basis of ensuring the correctness of the calculated numerical results,the influence of the end-coupled nonlinear element on the frequency response of the elastic beam system is investigated in depth,and the influence of the end-coupled nonlinear element on the vibration response of the elastic beam system under the single-frequency excitation is explored,and the generating mechanism of the nonlinear dynamics of the elastic beam system is revealed.Finally,the vibration energy transfer characteristics of the elastic beam system under complex nonlinear vibration response are investigated.The results show that the reasonable utilization of end nonlinear element can exhibit the phenomenon of vibration energy transfer from the active beam to the passive beam,reducing the active beam vibration,and the passive beam is similar to an absorber.Under the complex nonlinear vibration state,the elastic beam system appears the phenomenon of targeted energy transfer,and the quasi-periodic vibration state is the sign of the phenomenon.The emergence of the targeted vibration energy transfer phenomenon provides a possibility to unidirectionally control the vibration level of the elastic beam system from the time domain perspective.
作者
李政
赵雨皓
崔海健
陈明飞
Li Zheng;Zhao Yuhao;Cui Haijian;Chen Mingfei(Key Laboratory of Advanced Manufacturing Technology of Ministry of Education,Guizhou University,Guiyang 550025,China;Wuhan Second Ship Design and Research Institute,Wuhan 430205,China;College of Mechanical Engineering,Guizhou University,Guiyang 550025,China)
出处
《力学学报》
EI
CAS
CSCD
北大核心
2024年第10期3023-3038,共16页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金(52401364和52205091)
贵州省教育厅高等学校自然科学研究项目(青年科技人才成长项目,黔教技[2024]30号)
贵州省科技计划项目2024年基础研究计划(自然科学)青年引导项目(黔科合基础-[2024]青年168)资助.
关键词
双梁系统
端部耦合非线性
伽辽金法
非线性响应
double-beam system
end-coupled nonlinearity
Galerkin method
nonlinear response
