THE RESEARCH OF 2-DIMENSIONAL STANDINGWAVES ON ANNULAR PLATE

The analytical solution of Chladni figures on a thin metal plate is a difficult problem in theoretical acoustics. The problem can be solved quite completely if the plate is circular or rectangular and the vibration frequency is low, but the solution becomes rather difficult if the plate is annular and the frequency is high. In this paper, the two-dimensional standing waves on an annular plate (Chladni figures) are investigated both experimentally and theoretically at two kinds of boundary conditions, the free outer edge with simply supported inner edge and both free edges , respectively. It is found that the Chladni figures can be precisely controlled by adjusting the vibrating frequency and position of the vibration source. Three kinds of patterns have been observed, only having circular nodal lines, only having radial nodal lines, and having both of the two kinds of nodal lines, distinguishedly. Furthermore, the approximate radial wave velocities, the radii of standing wave nodal circles in different frequencies, and the elastic modulus of the plate are also obtained. The results of experiments well correspond with those from the analytical solutions.