The optimum position and minimum restraint stiffness of a flexible point support to raise a natural frequency of a thin bending plate is investigated, with the inclusion of the corresponding additional support mass. First the derivatives of the natural frequencies of the plate structure are derived with respect to the support movement using a finite element model. Second, the minimum support stiffness is analyzed to raise a plate's natural frequency to a target value by solving a characteristic eigenvalue problem. Then the optimal support design is studied to find the optimal attachment point and the associated minimum stiffness. Several typical examples of plate systems are analyzed with addition of the point supports with non-negligible mass. It appears that including the support mass in the plate vibration analysis can significantly increase the minimum support stiffness required to raise a given natural frequency to its target, whereas the optimal support position remains consistent with the massless support design case.

研究了柔性点支撑的最佳位置和最小约束刚度，以提高薄弯板的固有频率，并包括相应的附加支撑质量。首先，使用有限元模型相对于支撑运动导出板结构固有频率的导数。其次，通过解决特征特征值问题，分析最小支撑刚度以将板的固有频率提高到目标值。然后研究最佳支撑设计，以找到最佳连接点和相关的最小刚度。通过添加质量不可忽略的点支撑来分析板系统的几个典型示例。