基于改进傅里叶级数法的环扇形板三维自由振动分析  

3D free vibration analysis of annular sector plates based on improved fourier series method

作　　者：石先杰[1] 李春丽[1] 史冬岩[2] 

机构地区：[1]中国工程物理研究院总体工程研究所,四川绵阳621900 [2]哈尔滨工程大学机电工程学院,黑龙江哈尔滨150001

出　　处：《机械设计》2016年第10期75-80,共6页Journal of Machine Design

基　　金：国家自然科学基金资助项目(51505445);中国工程物理研究院重点学科项目"计算固体力学"

摘　　要：基于三维弹性理论,采用改进傅里叶级数法(Improved Fourier Series Method,IFSM)对环扇形板三维自由振动进行了数值分析。环扇形板的位移函数表示为一种改进的三角级数形式,而边界条件则通过均匀分布在各边界面的线性弹簧来模拟,通过改变边界约束弹簧的刚度值来实现不同的边界条件。将位移函数的未知级数展开系数看作广义坐标,并采用瑞利-里兹法进行求解,得到一个关于未知系数的标准特征值问题。环扇形板结构的三维自由振动特性可以通过求解标准特征值问题简单获得。数值计算结果充分表明,文中采用改进傅里叶级数法分析环扇形板三维自由振动问题的有效性和正确性。Based on the three dimensional elastic theory, the 3D free vibration problem of annular sector plates was analyzed using improved Fourier series method （IFSM）. The displacement function of annular sector plates was expressed as an improved trigonometric series. The boundary conditions were simulated using the linear-displacement springs distributed evenly at each boundary surface. Different boundary conditions could be easily realized by changing the stiffness of these restraining springs. All the unknown series expansion coefficients were treated as the generalized coordinates. The Rayleigh-Ritz technique was adopted to solution. A standard characteristic value problem was derived. The 3D free vibration characteristics can be solved though the solution of standard characteristic value. Numerical examples revealed that the present approach for 3D free vibration analysis of annular sector plates was efficient and accurate.

关 键 词：环扇形板 三维自由振动 改进傅里叶级数法 三角级数 

分 类 号：TB123[理学—工程力学]