Transient Fields of Concave Annular Arrays

A new a n a l y t i c e x p r e s s i o n f o r t h e impulse response o f concave r a d i a t o r s is used to compute t h e t r a n s i e n t pressure d i s t r i b u t i o n s of phased a n n u l a r a r r a y s w i t h s p h e r i c a l geometry. The process of phasing t h e a r r a y to a c h i e v e v a r i a b l e focus ing is t r e a t e d by summing t h e delayed impulse responses o f t h e i n d i v i d u a l a n n u l i . The example of pressure d i s t r i b u t i o n s o f a f i v e element annular a r r a y is t r e a t e d i n d e t a i l , and some recommendations are g iven f o r practical computer s t u d i e s .