基于简支弹性矩形板含集中质量振动基波频率共形映射解析

借助共形映射理论,采用矩形板边界域奇偶插值点两序列的三角插值方法,寻求了带圆角矩形板等复杂域与单位圆域的共形映射函数;针对含有集中质量振动简支弹性异型板基波频率值的求解,在平面常应力状态下,完成该复杂弹性板以单位圆域方法描述的振动方程,求解板基波频率系数。以带圆角矩形简支板域求解为示例,分析了集中质量大小与位置、矩形长宽比值e、平面常应力系数Sp对基波频率的影响。

CONFORMAL MAPPING ANALYSIS OF FUNDAMENTAL VIBRATION FREQUENCY OF SIMPLE-SUPPORTED ELASTIC RECTANGLE-PLATES WITH CONCENTRATED MASS

With the help of Conformal Mapping theory, trigonometric interpolation method between odd and even sequences in rectangle boundary regions is used, and the conformal mapping function between unit dish region and complicated region such as rectangle-plates with arc radius is carried out. Aiming at determining the fundamental vibrating frequency of a special-shaped, simple-supported elastic rectangle-plate, in the in-plane state of constant stress, the vibration function of this complicated plate is obtained by unit dish region, and the coefficient of fundamental frequency are analyzed. Using simple-supported elastic rectangle-plates with arc radius as an example, the effects on fundamental frequency caused by the concentrated mass and position, the ratio between the width and length of rectangle-plates, as well as the coefficient Sp of constant in-plane stress are analyzed respectively.