Wijnant Y., van Blijderveen M., de Boer A.

Previous research has shown that viscothermal wave propagation in narrow gaps can efficiently be described by means of the low reduced frequency model. For simple geometries and boundary conditions, analytical solutions are available. For example, Beltman [1] gives the acoustic pressure in the gap between an oscillating, rigid, rectangular plate and a rigid surface. Assuming a pressure release boundary condition at the circumference of the plate (p=0) excellent agreement with experiments was obtained. Generally however, the boundary conditions in many engineering applications are arbitrary. For instance, the vibrating membranes in hearing aid receivers are attached to complex structures and a simple pressure release (p=0) or zero velocity boundary condition (dp/dn=0) is only valid on parts of the circumference of the vibrating structure. One can use numerical methods, like FEM or BEM, but often a large number of degrees of freedom is needed to obtain accurate results. Furthermore, a thorough understanding of the various phenomena involved can only be gained through a large number of calculations. In the paper a semi-analytical solution is presented for the viscothermal wave propagation in the gap between an oscillating, rigid, circular plate and a rigid surface for arbitrary boundary conditions. The solution is written as a series expansion of solutions satisfying the equations in the interior domain. Subsequently, either the pressure release or the zero velocity boundary condition is imposed on arbitrary parts of the circumference. The unknown constants in the series expansion are determined using a weak form of the boundary conditions. It is shown that only a small number of terms is needed to accurately describe the pressure in the gap. In addition, experimental results will be presented which validate the theory used. [1] W.M. Beltman. Viscothermal wave propagation including acousto-elastic interaction. PhD thesis, University of Twente, The Netherlands, 1998. ISBN 90-365-1217-4.