横纵向位移激励下变长度梁的动力学分析  

Dynamics of Time-Varying Beams Under Transverse and LongitudinalDisplacement Excitations

作　　者：刘冠男 胡振东[1] LIU Guan-nan;HU Zhen-dong(Schol of Aerospace Engineering and Applied Mechanics,Tongji University,Shanghai 200092,China)

机构地区：[1]同济大学航空航天与力学学院,上海200092

出　　处：《机械设计与制造》2023年第7期12-16,21,共6页Machinery Design & Manufacture

摘　　要：关于变长度梁的研究,主要集中在横向自由振动及稳定性分析,有关水平及竖直两个输入方向的抗震研究却不够充分,常用的抗震设计方法没有充分考虑结构时变性对振动产生的影响。以实际工程中的变长度操作杆为算例,运用广义Hamilton原理建立横纵向地震激励下变长度梁的动力学方程,运用假设模态法与修正后的Galerkin法进行空间离散求解,通过数值仿真方法求解不同轴向运动下变长度梁在简谐波与地震波作用下的振动响应。根据计算结果,讨论了不同轴向运动所引发的梁长变化对变长度梁的振动影响规律。对比相同长度范围内变长度梁与固定梁在地震激励下的末端最大位移,前者在收缩时的结果大于后者。说明了在对变长度梁等时变结构进行抗震分析时,考虑结构时变性影响的必要性。该建模计算方法可为类似结构的抗震分析与设计提供参考。The transverse free vibrations and stabilities of time-varying beams have been analysed in several studies,whereas seismic design studies focusing on time-varying beams under horizontal and vertical excitations are scarce.Furthermore,conventional seismic design approaches do not sufficiently consider the effects of structural time variances on structural vibrations.Based on real translating rods,the generalised Hamilton's principle was used to formulate the dynamic equations for an axially translating beam that is excited by longitudinal and transverse seismic vibrations.The assumed modes method and modified Galerkin's method were used to discretise the spatial domain,while numerical simulations were used to solve for the vibrational responses of the time-varying beams with different axial motions in response to excitation by simple harmonic waves and seismic waves.Based on the simulation results,we investigated the vibrations of a time-varying beam caused by beam-length variations from different axial motions.The maximum seismically induced tip deflections of time-varying and fixed beams of similar lengths were compared,and it was determined that the former exhibited greater tip deflections than the latter during retraction operations.Therefore,the effects of time variance on time-varying structures such as time-varying beams must be considered during seismic analyses.The modelling and algorithmic methods established in this study can thus serve as useful tools for the seismic analyses and designsof similartime-varying structures.

关 键 词：变长度梁 HAMILTON原理 假设模态法 位移激励 地震响应 轴向运动 

分 类 号：TH16[机械工程—机械制造及自动化] TH212TH213.3