An Improved Series Expansion Method to Accelerate the Multi-Frequency Acoustic Radiation Prediction

Multi-frequency calculation is usually very time-consuming due to the repeated numerical integration for numerous frequencies in acoustic scattering or radiation problems. A series expansion method has been proposed to speed up this process just by taking the frequency-dependent terms out of the integral sign. However, this method, constrained by the number of truncation terms, is only applicable to low and medium frequencies and/or small-size structures. This paper develops an improved series expansion method that can be employed in a wider frequency band and larger-scale problems but with less computing expense. In the present method, the frequency-dependent term kr in the integral kernel is firstly transformed into the range from -π to π due to the periodicity of sine and cosine functions. Afterwards, truncation error would be kept reasonably small while the number of expansion terms would not increase with kr. Test cases of acoustic radiation from a pulsating sphere and a cat's eye structure are conducted and numerical results show significant reduction of computational time but suffering little accuracy loss for multi-frequency problems with this approach.