振动固支弹性板基波频率共形解析

CONFORMAL ANALYSIS OF THE FUNDAMENTAL FREQUENCY OF ELASTIC CLAMPED-PLATE VIBRATION

基于振动固支弹性异型板基波频率值的求解问题,采用共形映射理论,为了寻求复杂域与单位圆域的共形映射函数,将复杂边界域插值点序列分为奇偶两序列并相互迭代;提出了三角插值数学方法及其法向收敛方法,求得了共形映射函数的复系数。应用Galerkin的方法,完成复杂振动板域振动微分方程的基波频率解析。以椭圆板域求解为示例,分析了偏心率e和面积对基波频率系数的影响。

In order to calculate the fundamental vibration frequency of special-shaped, elastic clamped-plates, conformal mapping theory is used to separate the interpolating points of complicated boundary into odd and even sequences, both of which can be iterated mutually, so that the conformal mapping function between the complicated region and the unit dish region can be established. Trigonometric interpolation and its convergence along normal direction are provided. The complex coefficients of the conformal mapping function are then calculated. Furthermore, by using Galerkin method, the solution of the fundamental frequency of the complicated vibrating region is achieved. Finally, an ellipse elastic clamped-plate is used as an example to analyze the effects on fundamental frequency coefficient caused by eccentric ratio e and area size.