Abstract: Transverse vibration analysis of membranes is widely used in musical instrument membranes, ear membranes and plant cell membranes. Comparing with free vibration, the study of forced membrane vibration is more practical. In this paper, the vibration problem of a uniform rectangular thin film fixed on all sides is studied by using the Fourier series method and the impulse theorem, the analytical solution of the problem under forced vibration is obtained, and its vibration state is analyzed visually. It is found that the solution of one-dimensional string vibration can also provide a simple and convenient way to solve the problem of two-dimensional bounded membrane vibration, and the membrane vibration will present more abundant characteristics. The impulse theorem solution of the two-dimensional non-homogeneous vibration problem can also be extended to the two-dimensional active (sink) transport problem.

Key words: rectangular thin film, forced vibration, theorem of impulse, Fourier series