沿对角线对称分布的点支撑超椭圆板的线性自由振动和屈曲分析

Free Linear Vibration and Buckling of Super-Elliptical Plates Resting on Symmetrically Distributed Point-Supports on the Diagonals

研究计算出了均匀厚度的点支撑超椭圆板的自振频率(对应前3阶对称和反对称振型)和最小屈曲荷载(假定平面内压力沿周边均布)。利用一个超椭圆函数来求解板的周长,该函数可以用来计算从椭圆形到矩形的截面形状。基于传统薄板理论,并采用Ritz方法实现计算求解。通过拉格朗日因子来模拟几何边界条件。与矩形板的计算结果对比发现,两者具有良好的一致性。

This computational study reports the free vibration frequencies （corresponding to the first three symmetrical and antisymmetrical modes） , and the minimum buckling load （in case of in-plane uniform pressure along the periphery） of point-supported super-elliptical plates of uniform thickness, The plate perimeter was defined by a super-elliptic function with a power corresponding to the shape ranging from an ellipse to a rectangle. The analysis was based on the classical theory of thin plates and the computations were carried out by the Ritz method. The geometrical boundary conditions were satisfied by the Lagrange multipliers, The results were compared with those of rectangular plates and good agreement was obtained.