NUMERICAL-ANALYSIS OF THE RADIATED FIELDS OF CIRCULAR PISTONS AND TIME-DELAY SPHERICALLY FOCUSED ARRAYS

Radiated fields of a circular transducer and a time-delay spherically focused transducer array are analyzed and compared using classical imp ulse response method and finite element analysis. In the first approac h, the velocity potential at an observation point is expressed as the convolution of the excitation velocity and the impulse response, while the pressure is obtained by the differentiation of the velocity poten tial. The impulse response for an array is expressed as the superposit ion of those of a series of circular pistons and is dependent on the o bservation point and piston/array structure. The finite element method starts with the formulation for elastic waves, and the pressure field s are obtained through the pressure analog method. No paraxial or farf ield approximation is needed and excellent agreement is observed betwe en results from the two methods.