Open AccessStudy on the property of the second harmonic in the nearfield of a Bessel ultrasonic field based on the Fourier-Bessel series
Author(s) -
Du Hong-Wei,
Peng Hu,
Z. Jiang,
Feng Huan-qing
Publication year - 2007
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.56.6496
Subject(s) - bessel function , harmonic , field (mathematics) , fourier series , series (stratigraphy) , mathematical analysis , fourier transform , diffraction , physics , cylindrical harmonics , bessel beam , acoustics , mathematics , optics , pure mathematics , classical orthogonal polynomials , paleontology , gegenbauer polynomials , orthogonal polynomials , biology
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 fieldthus solves the problem of radial distribution of the second harmonic in the nearfield of Bessel ultrasonic field. Moreoverthe conclusion implies that the second harmonic field has similar limited diffraction property as the fundamental. A numerical computation and simulation example is given subsequently.