矩形板边界支撑优化设计

采用瑞利-里兹法分析、计算矩形板附加弹性铰(简)支撑的最小刚度和最优支撑位置,使板的第一阶固有频率达到原结构的第二阶频率。矩形板仅有一边固定(固支或简支),其他边自由,弹性支撑位于固定边相对的自由边界上。由振动系统能量泛函取极小值原理,构建特征频率方程,利用拉格朗日乘子施加最优支撑位置应满足的设计条件。算例结果表明,该文提出的方法是可靠的,能得到满意的结果。

OPTIMIZATION OF BOUNDARY SUPPORT FOR NATURAL FREQUENCY CONTROL OF RECTANGULAR PLATE

The Rayleigh-Ritz method is utilized to determine the minimum stiffness and optimal position of elastic point (simple) supports,so that the fundamental natural frequency of a rectangular plate can be raised to the original second frequency. The plate has only one boundary edge restrained (clamped or simply supported),and the additional supports are placed along the free edge opposite to the restrained boundary. Lagrange multipliers are applied to enforce the optimality conditions for the position design of a support. The minimum stiffness of the support can be found numerically by solving a characteristic eigenvalue problem. Illustrative examples are employed to verify the solution procedure and show that the present method is feasible and effective for the optimal design of a flexible support of a finite stiffness.