弛豫媒质中有限束超声波的非线性传播畸变理论

NONLINEAR THEORY OF DISTORTION OF BOUNDED ULTRA- SONIC BEAM IN RELAXATING MEDIA

文中提出弛豫媒质中有限束非线性声波方程,并采用微扰法求得由非线性传播畸变产生的高次谐波的一般解.研究表明,对高斯型声波,其谐波畸变解可以解析给出,而且其径向分布始终维持高斯函数.虽然其频散量大小会影响各次谐波的振幅,但其相速的变化却仍与对在频率的小振幅波相同.文中还用Blackstock算子将所得的结果应用于任何吸收-频散媒质,包括只能从经验得到其吸收与频率关系的一些生物媒质.

In this article, a nonlinear wave equation of bounded acoustic beam in relaxating media is presented and a general solution of higher harmonics resulting from the nonlinear distortion of propagation is found by using the pertubation approach. Investigation shows that for the Gaussian ultrasonic field, the solution of higher harmonics can be given analytically, moreover their corresponding radical distributions of amplitude always maintain the Gaussian profiles. Although the dispersion may affect the amplitude of various harmonics, the variation of phase velocity of those keep the same law as the small amplitude waves of corresponding frequencies do. We also show that by means of Blackstock' operator the obtained results can be applied te the case of media with arbitrary dissipation and dispersion, including some biomedia in which the relationship between the absorption and frequency may be obtained only empirically.