谈一对边简支一对边自由矩形板自振频率解法

Discussion about the Solution of the Free Vibration Frequency of Rectangular Plate with Two Opposite Ends Simply Supported and Two Opposite Ends Free

一对边简支一对边自由矩形板自振频率传统求解方法认为该板对应的最低自振频率ωm1等于同跨度简支梁的自振频率ωm.在比较该矩形板与同跨度简支梁的刚度的基础上 ,得出矩形板最低自振频率ωm1应略小于同跨度简支梁的自振频率ωm,由此提出求解该矩形板ωm1的正确的振形函数表达式及频率方程 ,并计算了该板 2 5个自振频率及相应的振形曲线 ,前

The classical solution considers that the minimum free vibration frequency ( ω m1 ) of the rectangular plate with two opposite ends simply supported and two opposite ends free is equal to the free vibration frequency ( ω m ) of freely-supported beam with the same span. In this paper, the conclusion is proved to be wrong and the contrast of rigidity between the plate and the beam proves that ω m1 is little than ω m . Therefore, the correct vibration mode function and frequency equation, which used for finding out ω m1 , are advanced. Twenty-five free vibration frequencies and corresponding vibration mode curves are worked out in this paper. Five lowest frequencies and there corresponding modes of vibration are quite similar to the calculations with finite element method.