基于能量变分原理的梁—圆柱壳耦合系统振动特性分析

聂睿1,3,李天匀1,2,3,朱翔1,2,3,陈旭1,3

振动与冲击 ›› 2022, Vol. 41 ›› Issue (7) : 1-10.

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振动与冲击 ›› 2022, Vol. 41 ›› Issue (7) : 1-10.
论文

基于能量变分原理的梁—圆柱壳耦合系统振动特性分析

  • 聂睿1,3,李天匀1,2,3,朱翔1,2,3,陈旭1,3
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Vibration characteristics of beam-cylindrical shell coupled system based on energy variational principle

  • NIE Rui1,3, LI Tianyun1,2,3, ZHU Xiang1,2,3, CHEN Xu1,3
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摘要

本文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,验证了本文方法正确性。此外,与传统Rayleigh-Ritz法相比,本文方法在面对复杂边界条件时,可构建准确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影响。

Abstract

In this paper, the energy variational principle is used to study the vibration characteristics of a beam-cylindrical shell coupling system. The whole coupling structure can be divided into two parts: beam substructure and shell substructure. Firstly, the improved Fourier series is used to describe the vibration displacement of the beam structure and the cylindrical shell structure, respectively. Then, the structural kinetic energy and the structural potential energy of the two structures are calculated. While, the boundary constraint of the structure will be transformed into the corresponding boundary potential energy by using the springs to simulate the boundary. At the same time, the springs are used to connect the beam structure and the shell structure, so that the coupling effect of the them will be shown as the corresponding coupling spring potential energy. The excitation forces can be added to the whole system in the form of external force work. Finally, by using the energy variational principle, the natural vibration characteristics and forced vibration responses of the coupled system can be calculated. Compared with the results of finite element software, the correctness of this method is verified. In addition, compared with the traditional Rayleigh-Ritz method, the proposed method can construct an accurate unified analysis model for complex boundary conditions without changing the displacement admissible function. More,the influence of some parameters on the vibration characteristics of the coupled system is discussed, also.

关键词

能量变分原理;梁&mdash / 壳耦合系统;改进傅里叶级数;振动特性;Rayleigh-Ritz法

Key words

energy variational principle / coupled beam-shell system / improved Fourier series / vibration characteristics / Rayleigh-Ritz method

引用本文

导出引用
聂睿1,3,李天匀1,2,3,朱翔1,2,3,陈旭1,3. 基于能量变分原理的梁—圆柱壳耦合系统振动特性分析[J]. 振动与冲击, 2022, 41(7): 1-10
NIE Rui1,3, LI Tianyun1,2,3, ZHU Xiang1,2,3, CHEN Xu1,3. Vibration characteristics of beam-cylindrical shell coupled system based on energy variational principle[J]. Journal of Vibration and Shock, 2022, 41(7): 1-10

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