A new calculation method for the radiation impedance of square piston

In ultrasonic transducers, the calculation of radiation impedance is fundamental to predict the acoustic behavior of the transducers. Although the self and the mutual radiation impedance have been studied by many authors, the expressions of formulas for a rectangular piston are very complicated and hard to obtain analytic solutions. Accordingly, the solutions have been obtained by numerical integration with approximation. Because computational algorithms include multiple loops due to multiple integration, it takes a long calculation time and the results have low accuracy. In this paper, we propose a new algorithm in that the vibrating surface of the rectangular piston is divided into small elements and the duplicate calculations are recognized in the calculating process of mutual effects of each element. Using the algorithm, quadruple loops due to quadruple integration are simplified to single loop or double loops and the short calculation time and high accuracy can be obtained. As a demonstration, the self and the mutual radiation impedance for a vibrating piston with regular square surface are calculated and its calculation accuracy is evaluated