一种悬臂方形薄平板共振模态理论分析方法

A Theoretical Investigation of Resonant Model on Cantilever Thin Square Plate

为了实现悬臂方形薄板的共振模态分析,本文基于AF-ESPI测量原理和瑞利利兹法对悬臂方形薄板共振模态的理论进行了完整分析,给出前8阶的共振频率和相对应悬臂方薄板的电子散斑共振条纹分布情况。为了验证理论计算的精确性,搭建了振幅波动电子散斑干涉测量系统,并利用该系统对悬臂方形薄板进行模态分析,测量该板的共振频率和振动模态。理论计算的结果和实验测量值对比发现,振动的条纹和理论计算的结果一致,共振频率的测量值和理论计算值之间的相对差值在0.1%～9.1%之间。

In order to analyze resonant model of the cantilever thin square plate, a theoretical interpretation of resonant vibration based on Rayleigh-Ritz method and amplitude-fluctuation electronic speckle pattern interferometry （AF-ESPI） is proposed. The resonant frequencies and deflection of the first eight orders are obtained. Based on this theory, we calculate the theoretical distribution of the speckled fringe pattern of the square thin cantilever plate. In order to verify the accuracy of theoretical expression and measure in experiment, AF-ESPI is employed to measure resonant frequency and mode shape of this cantilever square plate. The theoretical results are compared with the experimental measurement. Good agreement of vibration fringe patterns is obtained, and the relative errors of resonant frequencies between AF-ESPI and our method are 0.1%-9.1%.