Treating the Phenomenon of Irregular Frequencies

Abstract

This chapter reviews a number of techniques developed to overcome the well– known non–uniqueness difficulty in the boundary element method for acoustic radiation and scattering in an exterior domain. The non–uniqueness difficulty occurs at a set of irregular frequencies associated with the eigenfrequencies of the corresponding interior problem. The chapter focuses on the comparison of two commonly used techniques, the CHIEF method and the Burton and Miller method, along with their variations. After briefly revisiting the example of the pulsating sphere, a cat’s eye radiation problem is used as a test case for evaluating the effectiveness of different techniques. Numerical results confirm that the Burton and Miller method is a very reliable technique at all frequencies, while the CHIEF method is effective only at low frequencies. One potential drawback of Burton and Miller method is the requirement of the C ¹ continuity condition at collocation points, which may rule out the use of any C ⁰ continuous elements. Modified versions of the Burton and Miller method, which compute the normal–derivative integral equation only at the center of each C ⁰ element, have been proposed in the past to partially alleviate the strict C ¹ requirement. It is still uncertain that any of these modified versions is as theoretically robust as the original Burton and Miller method. Nonetheless, the cat’s eye radiation test case demonstrates that a modified version that uses 9–node quadrilateral elements is as effective as the original Burton and Miller method in practical use. The paper is completed by applying the Burton and Miller method to the industrial problem of a radiating diesel engine for which the radiated sound power is evaluated.