自由边界条件下方形平板受迫振动模式的探究  

Research on forced vibration mode for a square plate with free boundary

作　　者：严琪琪[1] 陈彦[1] 胡湘 YAN Qi-qi;CHEN Yah;HU Xiang(School of Physics and Nuclear Energy Engineering,Beihang University,Beijing 100083,China)

机构地区：[1]北京航空航天大学物理科学与核能工程学院,北京100083

出　　处：《大学物理》2018年第12期11-15,25,共6页College Physics

摘　　要：以自由边界条件下方形平板为研究对象,探究了其受迫振动的特性.首先假设其位移解为余弦级数的形式,并将其代入对应的控制方程和边界方程中;然后再利用三角函数的正交性构造多个等式求解出位移解中的未知系数;进而得到不同频率下平板上各点所对应的位移解,并根据该位移解模拟出相应的波节线图.结果显示,理论计算得到的波节线图与实验观察到的克拉尼图形十分吻合,且对应的理论计算频率值与实验观测得到的共振频率值接近,这很好的验证了该研究方法的准确性与可靠性.The forced vibration mode for a square plate with free boundary is studied.Its displacement solution is assumed to a Fourier series,which is plugged into the corresponding control equation and boundary conditions to solve the unknown displacement coefficient by using the orthogonality of trigonometric function.Then displacement solutions under different frequencies are calculated and the corresponding nodal charts can be drawn.The results show that the nodal charts of simulation and the Cladni patter of experimental observations match very well,and the corresponding frequency values of theoretical calculation and the experiment observation are also very closed,which prove that the displacement solution is efficient and accurate.

关 键 词：方形平板 自由边界 受迫振动 克拉尼图形 

分 类 号：O433[机械工程—光学工程]