Interactions of a Forced Vibrating Membrane with a Cylindrical Acoustic Cavity

Acoustic cavities play a role in many technological applications in civil, naval, and aerospace engineering. This study examines the vibroacoustic performance of a forced oscillating top membrane of a cylindrical container fully filled with a compressible and nonviscous fluid. For the case of harmonic motion and using Helmholtz's equation, the velocity potential is deduced, and the acoustic pressure is obtained using Bernoulli's linearized equation. Taking into account the dynamic equation for the membrane with the interacting fluid with the different terms expanded in a modal series and after an integration procedure over the membrane surface, a simple analytical quadratic equation is deduced, and the coupled natural frequencies of the membrane are obtained. For the case of forced vibrations, a transfer function is obtained for calculating the frequency spectrum response of the fluid-membrane interacting system. In particular, the membrane deformation spectrum and the acoustic cavity pressure spectrum are obtained for different location points. Moreover, the spectrum of the mean quadratic values of the membrane deflexion and acoustic pressure are deduced, along with its variation with different parameters such as drum height, membrane radius, fluid density, load position, sound speed, and membrane tension. The variation in sensitivity with frequency and other different parameters is also analysed. The results are contrasted with those obtained by other authors to validate the present work.