四边自由矩形板横向振动的近似解及其实验  

An approximate solution to transverse vibration of a rectangular plate with 4 free edges and its experimental verification

作　　者：付江松 徐鉴[1] FU Jiangsong;XU Jian(School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China)

机构地区：[1]同济大学航空航天与力学学院,上海200092

出　　处：《振动与冲击》2018年第5期92-97,107,共7页Journal of Vibration and Shock

基　　金：国家自然科学基金项目(11572224)

摘　　要：针对四边自由矩形板横向振动目前没有精确解的问题,构造出四边自由矩形板横向振动振型函数的一种近似解。由于矩形板发生横向振动时会形成驻波,按不同的驻波类型,我们采用不同的组合级数对驻波所反映的矩形板振型函数精确解进行逼近,进而得到了四边自由矩形板振型函数的近似解。为了验证近似解的有效性,搭建了四边自由矩形薄板横向振动的实验平台。通过简谐激励得到了薄板在0~2 000 Hz频带内的一系列二维驻波图形(克拉尼斑图)。将实验结果(克拉尼斑图)与近似解得到的驻波图形相比,发现两者从定性、定量两方面均吻合得较好,从而验证了近似解的正确性。Aiming at no exact solution to transverse vibration of a rectangular plate with4free edges,an approximate solution to transverse vibration mode functions of this plate was proposed here.Following the fact that transverse vibration of a rectangular plate induces various standing waves,trying to combine them and approach the exact solution to mode functions of the rectangular plate,then an approximate solution to transverse vibration mode functions of this plate was formed.In order to verify the validity of the approximate solution,an experimental platform for the transverse vibration of a rectangular plate with4free edges was designed and made.The experimental results showed that a series of two-dimensional standing wave patterns(Chladni patterns)of the plate are obtained within the simple harmonic excitation frequency range of0to2000Hz.Comparing the experiment results(Chladni patterns)to the standing wave patterns in the approximate solution,it was shown that they agree well each other qualitatively and quantitatively,so the correctness of the approximate solution is verified.

关 键 词：四边自由矩形板 克拉尼图形 驻波 振型函数 近似解 

分 类 号：TH212[机械工程—机械制造及自动化] TH213.3