扇形薄板二维驻波的研究
发布时间：2018-10-13 18:06
【摘要】：用分离变量法对极坐标下垂直板面方向的金属薄板的小振动方程求解,解出扇形薄板在全部边界均自由的条件下的解析解的简正模式及通解,并计算了不同频率下对应的简正振动模式下薄板上的圆弧形驻波波节线的半径和方程的本征值所满足的规律及薄板的弹性模量,给出了驻波图,与实验上观察到的仅有辐射状波节线或辐射状波节线与圆弧形波节线同时存在这两种简正模式(即克拉尼图形)相比较,发现理论结果与实验符合得很好.
[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.
【作者单位】： 中山大学物理学院;
【基金】：国家自然科学基金项目(11175268) 中山大学校级教学改革研究项目(74130-18822503和30000-1163124)资助
【分类号】：O302;O327
，
本文编号：2269476
[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.
【作者单位】： 中山大学物理学院;
【基金】：国家自然科学基金项目(11175268) 中山大学校级教学改革研究项目(74130-18822503和30000-1163124)资助
【分类号】：O302;O327
，
本文编号：2269476
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