基于Fourier-Bessel级数的Bessel型超声场二次谐波近场特性研究

将Fourier-Bessel级数引入KZK方程的求解，用于计算黏滞媒质中零阶Bessel型超声场的二次谐波声场，得到其级数形式的解析解，并由此得出二次谐波声场在近场分布的一个新结论.设声源表面声压分布为J₀(α₀r)，则二次谐波声压在近场的径向分布服从J²₀(α₀r)函数规律.这一结论合理解释了相关的实验结果，表明二次谐波声场在近场和远场有不同的径向分布，从而解决了非线性Bessel型超声场二次谐波的近场分布问题.研究还发现二次谐波声场具有类似基波声场的有限衍射特性.给出了一个数值计算和仿真实例.

Study on the property of the second harmonic in the nearfield of a Bessel ultrasonic field based on the Fourier-Bessel series

A new method based on the Fourier-Bessel series is applied in KZK equation to calculate the second harmonic component of a zero-order Bessel ultrasonic field in viscous medium. An analytical solution of a series form is obtained and a new conclusion is drawn. Assuming the source sound pressure to be J₀(α₀r)，the second harmonic sound pressure has a radial distribution of J²₀(α₀r) function profile in the near field. This conclusion explains the experimental results reported in literature appropriately and indicates that the second harmonic field has different radial distributions in the near and far field，thus solves the problem of radial distribution of the second harmonic in the nearfield of Bessel ultrasonic field. Moreover，the conclusion implies that the second harmonic field has similar limited diffraction property as the fundamental. A numerical computation and simulation example is given subsequently.