用于变厚度圆盘振动分析的动态环形元
The Finite Dynamic Annular Element for the Vibration Analysis of Variable Thickness Discs
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摘要: 本文利用动态位移的回转周期变化规律,将变厚度圆板弯曲振动的二维问题化为一维形式.并将环形单元的位移函数以频率的升幂形式展开,作为动态形状函数,进而推导了动态环形元的质量和刚度矩阵及其一次动态修正矩阵,并以简洁的形式给出.最后作为本文方法的直接应用,计算了叶盘组合件的固有特性与实验值及其它方法进行了比较,说明动态的变厚度环板元的优越性.Abstract: According to the gyro-periodicity of dynamic displacements,the two-dimensional problems of circular plates with variable thickness are simplified into one-dimensional ones in this paper.Taking the expanded form of frequency power series of the dynamic displacement functions as the dynamic shape functions of the finite annular element,the mass and stiffness matrices as well as their one-order revised matrices are given succinctly.The dynamic method is used to analyse the vibration characteristics of a bladed disc assembly and is compared with conventional finite element method and experiment,and is proved to be superior to other numerical methods.
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[1] Gupta,K.K.,On a finite dynamic element method for free vibration analysis of structures,Comput.Meth.Appl.Math.Eng.,9(1976),105-120. [2] Kirkhope,J.and G.J.Wilson,Vibration analysis of axial flow turbine disks using finite elements,ASME paper 75-DET-80,Design Engineering Technical Conference,Washington,Sept.(1975). [3] П.В.赫洛宁,《航空发动机振动理论和计算》,A D,731351,晏炳堂,谢竹虚等译(1979,10). [4] Gupta,K.K.,Solution of quadratic matrix equations for free vibration analysis of structures,Int.J.Num.Meth.Eng.,6(1973),129-135. [5] Salama,A.M.,Finite element dynamic analysis of blade packets and bladed disc assumbleies,Ph.D.Thesis,University of Southampton,Oct.(1976). [6] 高德平、张益松,回转周期结构的振动特性分析,南京航空学院学报,4(1986),7-16. -
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