Acoustic radiation impedance and directional response of rectangular pistons on elliptic cylinders

The self- and mutual radiation impedances and the farfield directional response of rectangular pistons conformal to a rigid elliptic cylindrical baffle are formulated. The pistons are assumed to vibrate with uniform normal velocity and the solution for the acoustic pressure is expressed in terms of a modal series representation in Mathieu functions. The Mathieu functions are obtained using computer programs that have been recently developed to provide accurate values of the functions at high frequencies. Results for the normalized self- and mutual radiation resistance and reactance and the directional response of acoustic radiation are presented over a wide frequency range for different piston sizes and elliptic cylinder cross section shapes.