Study On The Nonlinear Acoustic Characteristics Of Parametric Array

Parametric array utilizes the nonlinear acoustic propagation characteristics in the medium to obtain the difference waves.Since the parametric array radiates through small apertures to obtain beams with low-frequency,high directivity and no side-lobes,the resolution of parametric array can overcome the Rayleigh limitation.As a result,parametric array is widely used in underwater acoustic navigation,underwater communication,target detection in seafloor sediments,shallow seabed topography mapping and material's acoustic property measurements.Meanwhile,the process of primary wave's energy into difference wave's energy is a nonlinear secondary effects,the conversion efficiency of parametric array is low.In order to improving the parametric array's conversion efficiency.In this dissertation,by improving the calculation model of parametric array's nonlinear sound field,the parametric array's nonlinear acoustic characteristics have been systematically studied including the primary waveform,media properties,transducer aperture,etc.The model analyzed a number of techniques to improve the parametric array conversion efficiency and to provide appropriate theoretical guidance for the practical applications of the parametric array.Considering the precision mismatch and step-length inconsistence in solving the near-field parametric array,this dissertation has modified the calculation model of the KZK equation that uses backward implicit finite difference(IBFD),and proposed a second order Runge-Kutta finite difference method(DIRK2)to solve the near-field parametric array.The proposed method has resulted a more precise and resolvable second-order decay.Numerical calculation showed that the method proposed has effectively improved the accuracy of the calculation and the stability needed for the KZK equation by using a bigger stride length.The calculation theory for KZK equation using frequency domain finite difference numerical solution suffers from exhaustive calculation and low efficiency.In this dissertation,a model for the calculation of parametric array near-field acoustic characteristics has been derived using conservation upwind scheme.The result shows that the method is highly consistent with the frequency-domain finite difference method,and can effectively reduce the amount of calculation and improve the calculation efficiency.Employing the parametric array near-field calculation model mentioned above,the sound field of the difference wave formed by multi-frequencies interaction has been systematically studied in this dissertation.These studies include:(1),the characteristics of the parametric array sound field formed by two primary waves with different magnitudes,initial phases andfrequencies at the stage of sound saturation and cavitation yet fully expanded;(2),the characteristics of parametric array sound field formed by multiple primary waves with different phases but the same amplitude;and specifically(3),the characteristics of parametric array sound field formed by multi-frequency arithmetic primary waves,and further exploration on the parametric array conversion efficiencies when the peak amplitudes are consistent.The results show that:(1),the characteristics of the parametric array sound field formed by two primary waves with different magnitudes are independent of the primary wave's initial phase;(2),the primary waves with multi-frequency spectrum could produce the parametric array radiating system with a plurality frequency component difference beams with low-frequency high direction,and produce the maximum information.For the multi-column arithmetic difference waves formed by interactions between the multi-frequency primary waves,the richer the primary wave frequencies,the greater the difference sound pressure amplitude with the same frequency,and the greater the conversion efficiency.Based on the brief derivation of the KZK equation's time domain,we have monitored and investigated the self-demodulation process of the time-domain waveforms including the short-and long-Gaussian pulse envelope with different rising edges,the rectangular envelope with different pulse width,and the positive and negative chirp signals modulated by center frequency.Furthermore,the parametric array's acoustic spectrum waveforms with the same peak power and their sound-field characteristics have been qualitatively analyzed.Simulation results show that: the demodulation process of the parametric array is related to the rising/decreasing edge of transient signal.The steeper the rising edge of the transient signal,the faster the nonlinear demodulation effect,the richer the corresponding spectrum waveform,the higher the low frequency spectral components of the sound pressure amplitude,and the higher conversion efficiency of the parametric array.In this dissertation,the parametric array sound field spatial characteristics in different propagation medium have been studied,and it is concluded that slow waveguide materials with lower velocity and higher nonlinear parameter can improve the sound saturation and increase the generation of difference wave.Based on these results,combining the modeling theory of J.D.Ryder,the parametric array sound characteristics in composite media system formed by slow waveguide materials and water were calculated in this dissertation.Simulation results show that higher sound pressure amplitude of the difference wave can be formed in the composite medium system during the energy accumulation process of the parametric array,so it is an effective system to improve the parametric array conversion efficiency.In this dissertation,based on the transducer(array)with different apertures,we analyzedthe sound's spatial distribution characteristics of the annular piston source and the circular piston source with the same radiation area.Subsequently,the differential evolution algorithm has been employed to analyze the difference frequency sound pressure amplitude formed by circular piston array source.Meanwhile,difference frequency sound pressure amplitude from the parametric array has been realized by increasing the coverage area of the primary wave's beam.The optimization results show that the sparse arrangement of the transducer array elements can be beneficial for a higher difference frequency sound pressure level.To verify the theoretical analysis and simulation results,the anechoic tank test was carried out in this dissertation.In addition,related experimental basis for further engineering applications of parametric array was also investigated.