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.

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.