内边界固定情况下环形薄板二维驻波的研究  

Two-dimensional standing waves on annular plate as the inner boundary being cramped

作　　者：方奕忠[1] 沈韩[1] 王钢[1] 崔新图[1] 廖德驹[1] 冯饶慧[1] 

机构地区：[1]中山大学物理学院,广东广州510275

出　　处：《大学物理》2016年第6期15-19,28,共6页College Physics

基　　金：国家自然科学基金资助项目(11175268);中山大学实验教学研究(改革)基金项目(YJ201109)资助

摘　　要：通过极坐标下对竖向(垂直板面方向)的小振动方程分离变量,解出环形薄板的小振动方程在内边界固定外边界自由条件下解析解的简正模式,并在理论上和实验上对其二维驻波波节图形(克拉尼图形)进行了研究.实验上观察到仅有辐射状波节线(不包含内边界)或辐射状波节线与圆形波节线同时存在两种简正模式,进一步计算了此时薄板上的圆形驻波波节线的半径和方程的本征值所满足的规律以及薄板的弹性模量,并与实际测量值进行比较,发现理论结果跟实验符合得很好.The two- dimensional standing wave figures of an annular plate（Chladni patterns）as the inner boundary is clamped,are investigated experimentally and theoretically. It is found that the Chladni patterns can be precisely controlled by adjusting the frequency and position of the vibration source. Two kinds of patterns have been observed,one kind only has radial nodal lines（excepting the inner boundary）and the other has both of radial nodal lines and circular nodal lines. Furthermore,the radii of the circular nodal lines,the change rules of the eigen values,and the elastic modulus of the thin plate have been obtained. The results of experiments are consistent with the analytical solutions.

关 键 词：驻波 m阶贝塞尔函数 克拉尼图形 环形薄板 

分 类 号：O347.42[理学—固体力学] O4-33[理学—力学]