内边界固定情况下环形薄板二维驻波的研究

发布时间：2018-01-17 13:16

本文关键词：内边界固定情况下环形薄板二维驻波的研究　出处：《大学物理》2016年06期 　论文类型：期刊论文

【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.
[Abstract]:By separating variables from the small vibration equation in the vertical direction (vertical plate direction) in polar coordinates, the normal model of the analytical solution of the small vibration equation of a circular thin plate with fixed and outer boundary free conditions is obtained. The two-dimensional standing wave nodal figure (Clarney figure) is studied theoretically and experimentally. It is observed experimentally that only the radiative nodal line (excluding the inner boundary) is observed. Or there are two normal modes between the radial nodal line and the circular nodal line. The radius of the circular standing wave nodal line on the thin plate and the eigenvalue of the equation and the elastic modulus of the thin plate are further calculated and compared with the measured values. It is found that the theoretical results are in good agreement with the experiment.
【作者单位】：中山大学物理学院;
【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
【分类号】：O326
【正文快照】： 自从1787年克拉尼首先发现水平放置的撒有稀薄沙粒的薄金属板上竖向小振动的二维驻波波节图[1](现称为克拉尼图形)后,对克拉尼图形的研究已有重要的进展和应用[2-6].当初克拉尼采用粗沙粒,发现沙粒聚集在波节线上形成规则且对称的图形,称为正(或标准)克拉尼图形.若所用的沙粒

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