Abstract: Three random strategies are used to produce the position of the linear phased array to suppress grating lobes of High-Intensity Focused Ultrasound(HIFU) phased array.For the first and second strategies,elements move randomly based on the regular arrangement.However,for the third one,elements move randomly and directly.The element movable range is:the first <the second <the third.Based on the Rayleigh-Sommerfeld integral and nonlinear Westervelt equation,we calculate the linear and nonlinear acoustic field of random phased arrays generated by three strategies,and evaluate the results of suppressing grating lobes using three parameters,i.e.the normalized acoustic maximum pressure of grating lobes,normalized average acoustic intensity of the grating lobes and normalized average acoustic intensity of side lobes.The results show that the increase in element movable range is beneficial to suppress grating lobes in the linear acoustic field,and normalized acoustic maximum pressure of the grating lobes for three strategies are decreased by 30.7%,53.8%,and 55.8% compared to regular arrangement.In the nonlinear case,the increase of random degree can improve the suppression of grating lobes.For example,the peak positive and negative acoustic pressure of the grating lobes are decreased by 55.6% and 54.8% compared to regular arrangement when the random degree is 0.9 in the third random strategy.Moreover,the acoustic nonlinear performance of random array with focus shifting is studied.If the safe standard is-8 dB,only the second and third strategies can be used and their shifting distances are 6 mm and 10 mm,respectively.This study provides an attractive approach to suppress grating lobes and is helpful for the optimization of random HIFU phased array.