On the added mass matrix and acoustic pressure of multiple circular cylinders vibrating in a compressible fluid

Abstract

The linear two‐dimensional acoustic wave equation is solved for multiple circular cylinders vibrating harmonically in an infinite compressible fluid. The solution is expressed in terms of series of cylindrical wave functions. To satisfy the interface boundary condition of a particular cylinder, all cylindrical wave functions are transformed to the coordinates associated with that cylinder. The resulting equations are a system of algebraic equations for the undetermined coefficients, which are solved numerically by digital computer. The velocity potential, pressure, and force acting in each cylinder are then obtained in terms of these coefficients. The added mass matrix is found symmetrical and dependent on the wave number, the cylinder radius, and the distance and orientation between cylinders. On the surface of each cylinder the pressure field also depends on those parameters as well as the orientation of point on that surface. Numerical values of added mass matrix and pressure distribution are obtained for many cases.