基于改进傅里叶级数方法的旋转功能梯度圆柱壳振动特性分析  

Vibration characteristics analysis of the rotating functionally graded cylindrical shell structure using an improved Fourier series method

作　　者：李文达[1] 杜敬涛[1] 杨铁军[1] 刘志刚[1] 

机构地区：[1]哈尔滨工程大学动力与能源工程学院,黑龙江哈尔滨150001

出　　处：《哈尔滨工程大学学报》2016年第3期388-393,共6页Journal of Harbin Engineering University

基　　金：国家自然科学基金资助项目(11202056);中央高校基本科研业务费专项基金资助项目(HEUCFQ20150305)

摘　　要：通过在功能梯度圆柱壳结构两端引入轴向、环向、径向和径向旋转四组约束弹簧刚度,统一考虑了的弹性约束边界条件,将功能梯度材料特性表示成沿壳体厚度方向的连续性变化,根据Love薄壳理论,采用改进傅里叶级数方法和Rayleigh-Ritz法相结合,推导得到旋转功能梯度圆柱壳自由振动的频率计算方程。通过计算分析,模拟了任意边界条件,研究了弹性边界约束对旋转功能梯度圆柱壳结构自由振动频率的影响。结果表明:边界约束刚度对于功能梯度圆柱壳结构固有频率敏感影响区域不同,径向弹性约束对频率影响较明显,环向弹性约束其次,轴向弹性约束对频率影响较小,而径向旋转弹性约束对频率几乎无影响。In this paper we uniformly consider the elastic constraint boundary conditions on the two ends of a functionally graded cylindrical shell structure by introducing four types of spring stiffness restraints,including axial,circumferential,radial,and radial rotation. Based on the Love shell theory,where the functionally graded material properties are expressed as continuously changing along the shell thickness direction,we employ an improved Fourier series method and the Rayleigh-Ritz procedure to model the rotating functionally graded cylindrical shell in order to conduct a free vibration analysis. We then derive the system characteristics equation. Using numerical calculation and analysis,we simulate the arbitrary boundary conditions and examine the effect of the elastic boundary constraints on the natural frequencies of the rotating functionally graded cylindrical shell structure with respect to free vibration. The results show that the sensitivity range of the boundary constraint stiffness is diverse in the inherent frequency of the functionally graded cylindrical shell structure. The influence of the radial elastic restraint on frequency is obvious,followed by that of the circumferential elastic constraint. The axial elastic constraint has less effect,while the radial rotating elastic constraint has almost no effect.

关 键 词：旋转功能梯度圆柱壳 弹性边界约束 傅里叶级数 自由振动 频率参数 

分 类 号：O327[理学—一般力学与力学基础]