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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 5个频率及振形与有限元结果十分相近
The traditional method of natural frequency of a free rectangular plate with one pair of edge simply supported and a pair of sides is that the lowest natural frequency ωm1 corresponding to the plate is equal to the natural frequency ωm of the same span with the spanned beam. The minimum natural frequency ωm1 of the rectangular plate should be slightly smaller than the natural frequency ωm of the simple span beam with the same span. Therefore, the correct shape function formula and frequency equation for solving this rectangular plate ωm1 are proposed The natural frequencies and corresponding vibration curves of 25 plates were calculated. The first five frequencies and vibration shapes are very similar to the finite element results