Abstract:
A theoretical model to describe the behavior of a membrane loaded by gas films has recently been developed. This analytical model is required by the current level of miniaturization of acoustical transducers and by new devices and applications, especially in the high-frequency range (up to 100 kHz and more). It is based on the fundamental acoustical and mechanical equations (the Navier--Stokes equation, the conservation of mass equation, the Fourier equation for heat conduction, the equation of motion of the membrane) and includes realistic boundary conditions. These equations are simplified by making assumptions based on the fact that the thicknesses of fluid films are very small. Then, conventional models, based on equivalent electrical networks, generally used to describe the behavior of electrostatic or piezoelectric microphones or loudspeakers, are improved. For example, the influence of the viscosity, the heat conduction, and the deformation of the membrane in the high-frequency range can be accurately taken into account.