【摘要】：用分離變量法對(duì)極坐標(biāo)下垂直板面方向的金屬薄板的小振動(dòng)方程求解,解出扇形薄板在全部邊界均自由的條件下的解析解的簡(jiǎn)正模式及通解,并計(jì)算了不同頻率下對(duì)應(yīng)的簡(jiǎn)正振動(dòng)模式下薄板上的圓弧形駐波波節(jié)線的半徑和方程的本征值所滿足的規(guī)律及薄板的彈性模量,給出了駐波圖,與實(shí)驗(yàn)上觀察到的僅有輻射狀波節(jié)線或輻射狀波節(jié)線與圓弧形波節(jié)線同時(shí)存在這兩種簡(jiǎn)正模式(即克拉尼圖形)相比較,發(fā)現(xiàn)理論結(jié)果與實(shí)驗(yàn)符合得很好.
[Abstract]:The method of separating variables is used to solve the small vibration equation of the plate in the vertical direction of the plate in polar coordinates. The normal mode and the general solution of the analytical solution of the sector plate under the condition that all the boundaries are free are obtained. The radius of the arc standing wave nodal line and the eigenvalue of the equation and the elastic modulus of the thin plate under the normal vibration mode corresponding to different frequencies are calculated, and the standing wave diagram is given. Compared with the only radiative nodal line observed experimentally or the radial nodal line and the arc-shaped nodal line, there are two normal modes (i.e., the Clarney figure). It is found that the theoretical results are in good agreement with the experimental results.
【作者單位】： 中山大學(xué)物理學(xué)院;
【基金】：國(guó)家自然科學(xué)基金項(xiàng)目(11175268) 中山大學(xué)校級(jí)教學(xué)改革研究項(xiàng)目(74130-18822503和30000-1163124)資助
【分類號(hào)】：O302;O327
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本文編號(hào)：2269476