两径向边简支时环状扇形薄板二维驻波的研究

RESEARCH OF TWO-DIMENSIONAL STANDING WAVES ON ANNULAR SECTORIAL THIN PLATE WITH TWO SIMPLY-SUPPORTED RADIAL EDGES

本文在理论和实验上分别对张角为钝角、锐角,两辐射线方向边界简单支承、内外两圆弧边均悬空时水平放置的环状扇形薄板的小振动问题进行了研究。根据小挠度理论,采用极坐标系,用分离变量法求出环状扇形薄板给定边条件下不同本征频率及对应的本征振动模式,得出了通解,计算并讨论了不同本征振动模式下的圆弧状驻波波节线的半径及径向波节线的分布,求出薄板的弹性模量,给出仿真模拟驻波图,与实验上观察到的不同本征频率下的几种Chladni图形相比,理论与实验及仿真模拟结果符合得很好。

In this paper,the vertical small vibrations separately on obtuse-angled and acute-angled annular sectorial thin plate which placed horizontally with two simply-supported radial edges and two cantilevered arc edges are studied theoretically and experimentally.Based on the small flexivity theory,under polar coordinates,using the method of separation of variables,the normal vibration modes on different eigenfrequencies of annular sectorial thin plate under definite boundary conditions are investigated.The exactly analytical solution of vibrations is obtained,and the radical values of arc-shaped standing waves node-lines on the plate are calculated and measured.Furthermore,the values of elastic modulus of plate are acquired,and the patterns of standing waves are observed and simulated.The theoretical values show good agreement to the experiment and simulation results.