A simple approach to determine the mode shapes of Chladni plates based on the optical lever method

Abstract

This article introduces a simple approach based on the optical lever method to quantitatively determine the Chladni patterns of 2D plane standing waves on an elastic plate. Only an ordinary laser pen and a light screen made of ground glass are auxiliarily used during the measurement, which can be done quickly during classroom demonstrations in college physics courses. Three circular acrylic plates each with a thickness of 1 mm are tested under different center harmonic excitations. The beam from the laser pen is projected to the vibrating plate perpendicularly and reflected to the light screen in the distance, and the slope of the mode shape at the laser point can be determined with the length of the light spot on the light screen. Then, the observed mode shape can be obtained by integrating the slope distribution. Theoretical models and numerical simulations are also conducted to verify the accuracy of the present method, and results show that they compare very well. The present approach can be further applied to determine the full-field mode shapes of Chladni plates in a rather simple fashion.