Abstract: 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.

Key words: square plate, free boundary, forced vibration, Cladni patter