基于能量变分原理的梁-圆柱壳耦合系统振动特性分析  

Vibration characteristics of beam-cylindrical shell coupled system based on energy variational principle

作　　者：聂睿 李天匀[1,2,3] 朱翔 陈旭[1,3] NIE Rui;LI Tianyun;ZHU Xiang;CHEN Xu(School of Naval Architecture and Ocean Engineering,Huazhong University of Science&Technology,Wuhan 430074,China;Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration,Shanghai 200240,China;Hubei Key Laboratory of Naval Architecture&Ocean Engineering Hydrodynamics,Wuhan 430074,China)

机构地区：[1]华中科技大学船舶与海洋工程学院,武汉430074 [2]高新船舶与深海开发装备协同创新中心,上海200240 [3]船舶与海洋水动力湖北省重点实验室,武汉430074

出　　处：《振动与冲击》2022年第7期1-10,共10页Journal of Vibration and Shock

基　　金：中国国家自然科学基金(51839005,51879113);中央高校基金科研业务费资助项目(2019kfyMBZ048)。

摘　　要：采用能量变分原理研究了梁-圆柱壳耦合系统振动特性。整个耦合结构可分为梁子结构和壳子结构两个部分。首先,分别采用改进傅里叶级数描述梁结构和圆柱壳结构振动位移,求取两者结构动能与结构势能;随后,利用弹簧模拟边界的方式,将边界对结构的约束转化为对应边界势能;同时,利用空间分布弹簧组来连接梁结构与壳结构,使两者耦合效应表现为对应耦合弹簧势能;激励力则可通过外力功的形式加入到整个系统之中。再利用能量变分原理,即可计算耦合系统固有振动特性或受迫振动响应。通过与有限元软件计算结果对比,验证了该方法的正确性。此外,与传统Rayleigh-Ritz法相比,该方法在面对复杂边界条件时,可构建准确的统一分析模型而不需要重新选择位移容许函数。随后,进一步探讨了模型主要参数对耦合系统振动特性的影响。Here,vibration characteristics of a beam-cylindrical shell coupled system were studied by using the energy variational principle.The whole coupled structure was divided into two parts of beam substructure and shell substructure.Firstly,the improved Fourier series was used to describe vibration displacements of beam substructure and cylindrical shell substructure,and the two substructures’ kinetic energy and potential energy were solved.Springs were used to simulate the whole structure’s boundary,and constraints exerted on the whole structure by the boundary were converted into the corresponding boundary potential energy.At the same time,a spatially distributed spring group was used to connect beam substructure and shell substructure,and their coupling effect was expressed as the corresponding coupled spring potential energy.Excitation force could be added to the whole system in form of external work.Then,the energy variational principle was used to calculate natural vibration characteristics or forced vibration responses of the coupled system.The correctness of the proposed method was verified by comparing the calculation results obtained using the proposed method with those obtained using finite element software.It was shown that compared with the traditional Rayleigh-Ritz method,the proposed method can construct an accurate and unified analysis model to deal with complex boundary conditions without re-choosing displacement allowable functions.Finally,effects of model main parameters on vibration characteristics of the coupled system were further discussed.

关 键 词：能量变分原理 梁-壳耦合系统 改进傅里叶级数 振动特性 Rayleigh-Ritz法 

分 类 号：TB123[理学—工程力学]