摘要
自旋圆柱壳作为实际工程结构中的重要部件,其壳体端部边界条件复杂多样,对部件的振动特性有着重要影响。为研究多种边界条件下自旋圆柱壳的振动特性,基于Lagrange方程和Novozhilov壳体理论建立自旋圆柱壳的结构动力学模型;根据圆柱壳边界条件的数学描述,采用Chebyshev多项式构建满足边界条件且与壳体结构参数无关的位移场离散函数;通过求解与振动特性相关的特征方程得到静止圆柱壳的固有频率和模态,分析壳体转动惯性对固有频率的影响,讨论壳体理论在不同壳体几何尺寸下的适用性;此外,发现了环向波数相关的模态函数,并将其用于圆柱壳零阶环向模态固有频率的求解及多种边界条件下自旋圆柱壳行波固有频率的求解,讨论了自旋圆柱壳行波固有频率随结构参数变化的情况。
Spinning cylindrical shells are critical components in practical engineering structures.The boundary conditions at the shell ends are diverse and significantly influence the vibration characteristics of the shell.To study these characteristics under various boundary conditions,a dynamic model of the spinning cylindrical shell is established using Lagrange equations and Novozhilov’s shell theory.The mathematical description of the boundary conditions for the cylindrical shell is combined with the discretized displacement functions,which are constructed based on a linear combination of Chebyshev polynomials.These functions satisfy the boundary conditions and are independent of the cylindrical shell's parameters.The vibration characteristics of stationary cylindrical shells are determined by solving the eigenvalue problems,revealing the influence of rotary inertia on the vibration characteristics.The applicability of different shell theories with respect to various geometrical parameters of the shell is discussed.Additionally,circumferential wave-dependent mode functions are identified and used to compute the natural frequencies of shell modes with the zero circumferential waves,as well as the travelling waves of the spinning cylindrical shell under different boundary conditions.The impact of structural parameters on the natural frequencies of the travelling waves is also analyzed.
作者
董有恒
李映辉
李翔宇
茅晓晨
DONG You-heng;LI Ying-hui;LI Xiang-yu;MAO Xiao-chen(College of Mechanics and Engineering Science,Hohai University,Nanjing 211100,China;School of Mechanics and Aerospace Engineering,Southwest Jiaotong University,Chengdu 611756,China)
出处
《振动工程学报》
EI
CSCD
北大核心
2024年第10期1731-1738,共8页
Journal of Vibration Engineering
基金
国家自然科学基金资助项目(12102175)
中央高校基本科研业务费专项资金资助项目(B240201128)。
关键词
自旋圆柱壳
多种边界条件
转动惯性
位移场离散
spinning cylindrical shell
various boundary conditions
rotary inertia
displacement field discretization
作者简介
董有恒(1992-),男,博士,副研究员。E-mail:dyhe@hhu.edu.cn;通讯作者:李映辉(1964-),男,博士,教授。E-mail:yhli2007@sina.com。
