A direct robust supergain method in mode space for the circular array mounted on an infinite rigid cylinder was proposed,and then it was also applied to the circular array mounted on a finite rigid cylinder which is more practical.According to the concept of phase modes,the beam pattern is expanded into a series of eigen-beams multiplying by modal coefficients. The modal noise cross spectral matrix is calculated from sound scattering theory.In the original modal robust supergain method,the coefficient vector in mode space is transformed indirectly from the weighting vector in sensor space.The method presented here gives the most suitable modal coefficient vector directly under the related constraint conditions based on the second-order cone programming.The results of simulation show that the direct modal robust supergain method can not only improve robustness using the white noise gain constraint, but also change the mode orders to provide compromise between array gain and robustness in low frequencies.Beam performance measures such as sidelobe level can be optimized as well as array gain,so this method can give more effective schemes for designing practical robust supergain beamformers.
The acoustic radiation characteristics of free-flooded ring transducers made of PZT4 and PMN-PT materials are calculated and compared.First,the theoretical formulae for free-flooded ring transducers are studied.The resonant frequencies of a transducer made of PZT4 and PMN-PT materials are calculated.Then,the transmitting voltage responses of the free-flooded ring transducers are calculated using the finite element method.Finally,the acoustic radiation characteristics of the free-flooded ring transducers are calculated using the boundary element method.The calculated results show that the resonant frequencies of the free-flooded ring transducer made of PMN-PT are greatly reduced compared with those made of PZT4 with the same size.The transmitting voltage response of the transducer made of PMN-PT is much higher than that of the transducer made of PZT4.The calculated 3-dB beamwidth of the acoustic radiated far-field directivity of the free-flooded ring transducer made of PZT4 at the resonant frequency 1900 Hz is 63.6 and that of the transducer made of PMN-PT at the resonant frequency 1000 Hz is 64.6.The comparison results show that the free-flooded ring transducer made of PMN-PT material has many advantages over that made of PZT4.The PMN-PT is a promising material for improving the performance of free-flooded ring transducers.
