Resonance scattering and radiation force calculations for an elastic cylinder using the translational addition theorem for cylindrical wave functions

Abstract

The standard Resonance Scattering Theory (RST) of plane waves is extended for the case of any two-dimensional (2D) arbitrarily-shaped monochromatic beam incident upon an elastic cylinder with arbitrary location using an exact methodology based on Graf's translational addition theorem for the cylindrical wave functions. The analysis is exact as it does not require numerical integration procedures. The formulation is valid for any cylinder of finite size and material that is immersed in a nonviscous fluid. Partial-wave series expansions (PWSEs) for the incident, internal and scattered linear pressure fields are derived, and the analysis is further extended to obtain generalized expressions for the on-axis and off-axis acoustic radiation force components. The wave-fields are expressed using generalized PWSEs involving the beam-shape coefficients (BSCs) and the scattering coefficients of the cylinder. The off-axial BSCs are expressed analytically in terms of an infinite PWSE with emphasis on the translational offset distance d. Numerical computations are considered for a zeroth-order quasi-Gaussian beam chosen as an example to illustrate the analysis. Acoustic resonance scattering directivity diagrams are calculated by subtracting an appropriate background from the expression of the scattered pressure field. In addition, computations for the radiation force exerted on an elastic cylinder centered on the axis of wave propagation of the beam, and shifted off-axially are analyzed and discussed. C 2015 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License.

Radiation force and torque on a two-dimensional circular cross-section of a non-viscous eccentric layered compressible cylinder in acoustical standing waves

“…For experimental design purposes and instrumentation optimization, analyses have relied on theoretical formalisms for the time-averaged radiation force for cylindrical rigid, [8][9][10][11] fluid, [12] elastic, [12][13][14][15][16] and viscoelastic materials. [12,17,18] The effects of the host medium viscosity have been also considered, [19] and further generalizations taking into consideration the profile of the incident wavefront (unlike plane waves) [20,21] and particle shape [22][23][24] have been examined. Numerical computations for the radiation force of non-paraxial [25][26][27][28] wavefronts showed interesting capabilities from the standpoint of particle attraction, as well as linear, parabolic and reverse cylindrical particle movement dynamics.…”

Acoustic radiation force on a cylindrical particle near a planar rigid boundary

“…Several investigations were previously developed for a cylindrical particle in an unbounded fluid [5][6][7][8][9][10][11][12][13][14] , where some recent analyses (not limited to a particular range of frequencies) considered the elliptical geometry [15][16][17][18] . Nonetheless, those formalisms cannot be applied to a cylindrical particle nearby a boundary, and it is important to develop an improved methodology taking the multiple reflections/scattering effects between the wall and the particle into account.…”

Acoustic radiation force and torque on a lossless eccentric layered fluid cylinder

“…[10] Formalisms accounting for the viscosity of the host fluid medium have been also developed. [11,12] Lately, further extensions to take into account the shape of the incident insonifying wave-field (differing from plane waves) have been considered, [13,14] and showed interesting properties for non-paraxial focused Gaussian, [15] Hermite-Gaussian, [16] and Airy [17,18] acoustical sheet tweezers from the standpoint of negative pulling force generation acting in opposite direction of wave motion, and linear, parabolic and reverse particle transport.…”