平面常应力弹性固支板基波频率映射解析

基于含平面常应力的复杂域弹性固支板基波频率的求解问题,应用共形映射数值理论,将复杂边界域分为奇数与偶数插值点,提出三角插值法和法向收敛法,求解了复杂域与单位圆相互转换的共形映射函数,将其与Galerkin的方法相结合,可完成含平面常应力的复杂板域的振动微分方程及基波频率解析。同时以含圆角的矩形弹性固支板振动微分方程与基波频率求解为示例,分别分析了边长比λ、面积A和常应力系数Sp对基波频率的影响。

MAPPING ANALYSIS OF FUNDAMENTAL FREQUENCY ON ELASTIC CLAMPED PLATES SUBJECTED TO IN-PLANE CONSTANT STRESS

Based on analyzing the fundamental frequency of complicated elastic clamped plates subjected to in-plane constant stress, with the help of Conformal Mapping theory, interpolating points of odd and even sequence in complicated boundary region are given, and both trigonometric interpolation and normal convergence method are proposed, so that Conformal Mapping function between complicated region and the unit dish region is carried out. Then by using Galerkin method, the analysis of vibration fundamental frequency of complicated plates subjected to in-planes constant stress can be achieved. Meanwhile, using a rectangular elastic clamped plate as an example, the effect on the fundamental frequency caused by boundary length ratio λ, its area A and in-plane constant stress coefficient Sp are analyzed, respectively.