Generalized theory of resonance excitation by sound scattering from an elastic spherical shell in a nonviscous fluid

Abstract

This work presents the general theory of resonance scattering (GTRS) by an elastic spherical shell immersed in a nonviscous fluid and placed arbitrarily in an acoustic beam. The GTRS formulation is valid for a spherical shell of any size and material regardless of its location relative to the incident beam. It is shown here that the scattering coefficients derived for a spherical shell immersed in water and placed in an arbitrary beam equal those obtained for plane wave incidence. Numerical examples for an elastic shell placed in the field of acoustical Bessel beams of different types, namely, a zero-order Bessel beam and first-order Bessel vortex and trigonometric (nonvortex) beams are provided. The scattered pressure is expressed using a generalized partial-wave series expansion involving the beam-shape coefficients (BSCs), the scattering coefficients of the spherical shell, and the half-cone angle of the beam. The BSCs are evaluated using the numerical discrete spherical harmonics transform (DSHT). The far-field acoustic resonance scattering directivity diagrams are calculated for an albuminoidal shell immersed in water and filled with perfluoropropane gas, by subtracting an appropriate background from the total far-field form function. The properties related to the arbitrary scattering are analyzed and discussed. The results are of particular importance in acoustical scattering applications involving imaging and beam-forming for transducer design. Moreover, the GTRS method can be applied to investigate the scattering of any beam of arbitrary shape that satisfies the source-free Helmholtz equation, and the method can be readily adapted to viscoelastic spherical shells or spheres.

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

“…30 This method has been employed in the generalized formalism developed for spheres. 4 It is emphasized that both methods are commensurate with the same result as long as an elastic isotropic cylinder is considered. Nevertheless, for an anisotropic cylinder, different equations have been established when decomposing the vector potential in terms of scalar potentials (See Section 2 in Ref.…”

“…It is of some importance to develop a formalism which accounts for the nature and finite character of the incident field, since the resulting resonance scattering process may be enhanced or suppressed depending on the beam's parameters, as recently demonstrated for the case of an elastic sphere (or a shell) placed arbitrarily in an acoustical beam of arbitrary wave-front. 4,5 Nevertheless, analyzing the arbitrary scattering with a cylinder using the formalism devoted to spheres 4,5 as a first approximation, leads to significant inaccuracies in the numerical predictions. Therefore, it is of particular importance to develop a method applicable to cylinders in order to numerically predict and compute the arbitrary scattering, and other phenomena such as the resulting acoustic radiation force for various applications.…”

Resonance scattering of a dielectric sphere illuminated by electromagnetic Bessel non-diffracting (vortex) beams with arbitrary incidence and selective polarizations

“…It has also been thoroughly described using semi-analytical (i.e., involving numerical integration procedures to evaluate the beam-shape coefficients (BSCs) in the arbitrary/off-axial configuration) formalisms in acoustics [23,24]. In the electromagnetic (EM) context, it can be studied by means of the Lorenz-Mie [25] theory for plane waves [26][27][28][29][30][31], or the rigorous generalized Lorenz-Mie theories (GLMTs) for arbitrary-shaped beams [32][33][34][35].…”

Interaction of an acoustical 2D-beam with an elastic cylinder with arbitrary location in a non-viscous fluid

“…Introduction 53 The generalization of the standard formalism of the Resonance 54 Scattering Theory (RST) in acoustics [1,2] that describes the reso- 55 nance excitation by sound scattering, has been devised for an elas-56 tic sphere (or a shell, layered sphere, etc.) placed arbitrarily in an 57 acoustical beam of arbitrary wave-front [3][4][5] instead of plane 58 waves of infinite extent. The Generalized Theory of Resonance 59 Scattering (GTRS) [3,5] is an important mathematical and physical 60 tool which allows efficient modeling and interpreting the arbitrary 61 scattering (from a sphere of any size and material) that plays a sig-62 nificant role in numerous applications including the generation of 63 the acoustic radiation force and torque on a particle (or a cluster of 64 particles).…”

“…placed arbitrarily in an 57 acoustical beam of arbitrary wave-front [3][4][5] instead of plane 58 waves of infinite extent. The Generalized Theory of Resonance 59 Scattering (GTRS) [3,5] is an important mathematical and physical 60 tool which allows efficient modeling and interpreting the arbitrary 61 scattering (from a sphere of any size and material) that plays a sig-62 nificant role in numerous applications including the generation of 63 the acoustic radiation force and torque on a particle (or a cluster of 64 particles). Despite the extensive analyses related to plane wave 65 scattering by an infinitely-long cylinder [2,[6][7][8][9] or shells [10][11][12][13][14], 66 analyzing the arbitrary scattering resulting from the interaction 67 of acoustical beams with cylindrical particles using the GTRS for-68 malism devoted to spheres [3,5] as a first approximation, leads to 69 significant inaccuracies in the evaluation of the scattering and 70 the resulting radiation force phenomena.…”