Improved Integral Formulation for Acoustic Radiation Using Integral Equation of Frequency Averaged Quadratic Pressure

Abstract

This paper is concerned with the problem of obtaining a unique solution for radiation at irregular frequencies when an integral equation of frequency averaged quadratic pressure (FAQP) is used to get robust predictions at medium and high frequencies. It is proved that there is no unique solution of the integral equation of FAQP at irregular frequencies, and existence and uniqueness of solutions under four types of boundary conditions are discussed. A combined energy boundary integral equation formulation (CEBIEF) is presented and proves to be efficient to overcome the nonuniqueness of the integral equation of FAQP. The numerical examples are given to demonstrate the versatility of the CEBIEF method with a proposed function correctly indicating a solution.