Radiation from finite phased and focused linear array including interaction

Resultant pressure of linear arrays, consisting of $N$ elementary transducers, are in general computed with the help of simplified assumptions for the displacement field of the transducer radiating surface. Moreover, interactions between neighboring elements are not included in most of the numerical approaches. In this paper, a new calculation scheme is proposed to compute the resultant pressure of such arrays, including interactions. For this purpose, using the finite element method (FEM), the far-field directivity pattern of a part of the array is computed using dipolar dampers and a previously described extrapolation algorithm [J. Assaad et al., J. Acoust. Soc. Am. 94, 562–573 (1993)]. This part is constituted of an active elementary transducer (electrically driven) mounted between $2Q$ passives (electrically grounded) neighboring transducers. Then, the resultant pressure of a finite phased and focused array can be obtained by summing up the far-field directivity patterns of the $2Q+1$ transducers sets weighted by the classical term which takes into account the geometrical and electrical phase shifts. This new calculation scheme is then used to compute the resultant pressure of a lithium niobate linear array. It will be shown that mechanical interaction must be taken into account for high frequency arrays.