摘要
连接壳结构广泛应用于船舶推进系统中,其边界条件复杂,而且在旋转运动下会产生行波模态,对推进器的动力学性能具有重要影响。为了推进功能梯度材料在船舶海洋工程中的应用,本文通过弹簧模拟壳体结构的边界条件,建立旋转功能梯度锥-柱连接壳的动力学模型,探讨旋转功能梯度锥-柱连接壳的行波模态特性。基于Love薄壳理论,运用弹簧模拟结构两端的边界条件以及圆锥壳和圆柱壳连接界面的连续性条件,推导考虑旋转运动引发的科氏力和离心力的功能梯度连接壳能量方程;以Chebyshev多项式为基底构造位移函数,建立旋转功能梯度连接壳的模态频率方程;利用Rayleigh-Ritz法求解连接壳的行波模态频率;通过收敛性分析确定边界弹簧和接触弹簧的刚度取值范围以及Chebyshev多项式所需要展开的项数;分析环向波数、陶瓷体积分数指数、圆锥角、转速以及任意边界对行波模态频率的影响。结果表明:旋转转速越大,连接壳的前后行波分叉行为越明显;轴向弹簧刚度对行波模态频率影响最大;相比于传统的能量法,采用弹簧模拟边界提高了计算效率,而且连接壳在弹性边界下的行波特性变化较大,说明了采用弹簧模拟任意边界的必要性。
The joined shell with complex boundary condition is widely employed in the marine propulsion.And the traveling wave mode of the joined shell with rotational motion usually plays an important role in the marine propulsion.For prompting the application of functionally graded materials(FGMs)in ships and ocean engineering,the boundary conditions of a shell structure were simulated by the spring,the dynamical model of the rotating FGMs joined conical-cylindrical shell was derived,and the traveling wave mode of the rotating FGMs joined conical-cylindrical shell was analyzed.Firstly,considering the influence of the Coriolis force and centrifugal force produced by rotation,energy equations of the joined shell with the boundary spring and connecting spring were derived based on the Love’s thin shell theory.Then,the displacement function could be assumed based the Chebyshev polynomial,and the modal frequency equation was derived.Finally,the modal frequency of the traveling wave was solved by the Rayleigh-Ritz method.Based on the convergence analysis,the stiffness values of corresponding springs and the truncated terms of the Chebyshev polynomial were given.The effects of the circumferential wave number,volume fraction exponent,cone angle,rotational speed and the general boundary condition on the traveling wave mode were discussed.Results indicate that the bifurcation behavior with respect to the forward wave and backward wave are notable with the increase of rotating speed;the stiffness of axial spring has a greater effect compared with other springs;compared with the traditional energy method,the efficiency can be reduced for the repeated calculation and the elastic boundary condition has a large influence on the traveling wave mode,meaning the necessity of employing the spring to simulate the boundary condition.
作者
张宇航
刘文光
刘超
ZHANG Yu-hang;LIU Wen-guang;LIU Chao(School of Aeronautical Manufacturing Engineering,Nanchang Hangkong University,Nanchang 330063,China;Graduate School at Shenzhen,Harbin Institute of Technology,Shenzhen 150001,China)
出处
《船舶力学》
EI
CSCD
北大核心
2024年第1期154-168,共15页
Journal of Ship Mechanics
基金
国家自然科学基金项目(51965042)。
关键词
功能梯度材料
锥-柱连接壳
旋转运动
任意边界
CHEBYSHEV多项式
行波模态
functionally graded materials
joined conical-cylindrical shell
rotational motion
general boundary condition
Chebyshev polynomial
traveling wave mode
