任意边界条件下环扇形板面内振动特性分析  

In-plane vibration analysis of annular sector plates with arbitrary boundary supports

作　　者：史冬岩[1] 石先杰[1,2] 李文龙[2] 

机构地区：[1]哈尔滨工程大学机电工程学院,黑龙江哈尔滨150001 [2]韦恩州立大学机械工程系,美国底特律48202

出　　处：《振动工程学报》2014年第1期1-8,共8页Journal of Vibration Engineering

基　　金：科技部国际科技合作计划(2011DFR90440);国家留学基金资助项目(2011668004)

摘　　要：基于改进傅里叶级数方法(Improved Fourier Series Method,IFSM)对任意边界条件下环扇形板的面内自由振动特性进行计算分析,任意边界条件可采用沿各边界均匀分布的法向和切向线性弹簧来模拟。环扇形板的径向和切向位移函数被不变地表示为改进傅里叶级数形式,并通过引入正弦函数项来克服弹性边界的不连续或跳跃现象。将位移函数的傅里叶展开系数看作广义坐标,并采用瑞利-里兹方法对其进行求解,得到一个关于未知傅里叶系数的标准特征值问题。通过求解标准特征值问题而简单地求解环扇形板面内振动的固有频率及其振型。通过不同边界条件下环扇形板模型结果与文献解及有限元法结果相对比来验证了本文方法的正确性及可靠性。In this study,the free in-plane vibrations of the annular sector plates with arbitrary boundary conditions are investigated with the improved Fourier series method （IFSM）.Arbitrary boundary supports can be physically realized by setting tangential and normal springs along each edge in the current method.Regardless of the boundary conditions,the tangential and radial displacement functions were invariantly sought as an improved Fourier cosine series,and a sine series was introduced to overcome all the relevant discontinuities or jumps of elastic boundary conditions.The expansion coefficients were considered as the generalized coordinates and hence determined using the Rayleigh-Ritz technique,which resulted in a standard eigenvalue problem concerning the unknown displacement expansion coefficient.The natural frequencies and mode shapes were thereby solved readily.The results of annular sector plates with various boundary conditions were presented and compared with those published in literatures and obtained by finite element method,so as to demonstrate the effectiveness and reliability of the current method.

关 键 词：结构动力分析 环扇形板 改进傅里叶级数方法 任意边界条件 面内振动 

分 类 号：O327[理学—一般力学与力学基础]