Calculation method of the velocity weighting vector for a conformal array of underwater acoustic projecting transducers

The boundary element theory together with optimization method is used to calculate the vibration velocity weighting vector of a complicated conformal array of underwater acoustic projecting transducers for an expected beam pattern. At first, the relationship between the acoustic radiated field and the vibration velocity weighting vector of the array is formulated. Then two weight calculation methods are presented, i.e., the phase compensation method and the least 2-norm method in which the acoustic mutual effect of the baffle and the transducers are considered. The calculation results show that the two methods are both able to correct the directivity deviation of the conventional beamforming method in which the plane wave model is used and the acoustic mutual effect of the baffle and the transducers are not taken into account. Moreover, the least 2-norm method provides the least 2-norm of the vibration velocity weighting vector of the array while producing the same amplitude of pressure in the axial direction