Acoustic backscattering enhancements resulting from the interaction of an obliquely incident plane wave with an infinite cylinder

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

The classical Resonance Scattering Theory (RST) for plane waves in acoustics is generalized for the case of a 2D arbitrarily-shaped beam incident upon an elastic cylinder with arbitrary location that is immersed in a nonviscous fluid. The formulation is valid for an elastic (or viscoelastic) cylinder (or a cylindrical shell, a layered cylinder/shell, or a multilayered cylindrical shell, etc.) of any size and material. Partial-wave series expansions (PWSEs) for the incident, internal and scattered fields are derived, and numerical examples illustrate the theory. The wave-fields are expressed using a generalized PWSE involving the beam-shape coefficients (BSCs) and the scattering coefficients of the cylinder. When the beam is shifted off the center of the cylinder, the off-axial BSCs are evaluated by performing standard numerical integration. Acoustic resonance scattering directivity diagrams are calculated by subtracting an appropriate background from the expression of the scattered pressure field. The properties related to the arbitrary scattering of a zeroth-order quasi-Gaussian cylindrical beam (chosen as an example) by an elastic brass cylinder centered on the axis of wave propagation of the beam, and shifted off-axially are analyzed and discussed. Moreover, the total and resonance backscattering form function moduli are numerically computed, and the results discussed with emphasis on the contribution of the surface waves circumnavigating the cylinder circular surface to the resonance backscattering. Furthermore, the analysis is extended to derive general expressions for the axial and transverse acoustic radiation force functions for the cylinder in any 2D beam of arbitrary shape. Examples are provided for a zeroth-order quasi Gaussian cylindrical beam with different waist. Potential applications are in underwater and physical acoustics, however, ongoing research in biomedical ultrasound, non-destructive evaluation, imaging, manufacturing, instrumentation, and acoustic holography to name a few, would benefit from the results of this analysis.

Autonomous motion of metallic microrods propelled by ultrasound

Autonomously moving micro-objects, or micromotors, have attracted the attention of the scientific community over the past decade, but the incompatibility of phoretic motors with solutions of high ionic strength and the use of toxic fuels have limited their applications in biologically relevant media. In this letter we demonstrate that ultrasonic standing waves in the MHz frequency range can levitate, propel, rotate, align, and assemble metallic microrods (2 μm long and 330 nm diameter) in water as well as in solutions of high ionic strength. Metallic rods levitated to the midpoint plane of a cylindrical cell when the ultrasonic frequency was tuned to create a vertical standing wave. Fast axial motion of metallic microrods at ~200 μm/s was observed at the resonant frequency using continuous or pulsed ultrasound. Segmented metal rods (AuRu or AuPt) were propelled unidirectionally with one end (Ru or Pt, respectively) consistently forward. A self-acoustophoresis mechanism based on the shape asymmetry of the metallic rods is proposed to explain this axial propulsion. Metallic rods also aligned and self-assembled into long spinning chains, which in the case of bimetallic rods had a head-to-tail alternating structure. These chains formed ring or streak patterns in the levitation plane. The diameter or distance between streaks was roughly half the wavelength of the ultrasonic excitation. The ultrasonically driven movement of metallic rods was insensitive to the addition of salt to the solution, opening the possibility of driving and controlling metallic micromotors in biologically relevant media using ultrasound.

Conformal mapping for the Helmholtz equation: acoustic wave scattering by a two dimensional inclusion with irregular shape in an ideal fluid

The complex variables method with mapping function was extended to solve the linear acoustic wave scattering by an inclusion with sharp/smooth corners in an infinite ideal fluid domain. The improved solutions of Helmholtz equation, shown as Bessel function with mapping function as the argument and fractional order Bessel function, were analytically obtained. Based on the mapping function, the initial geometry as well as the original physical vector can be transformed into the corresponding expressions inside the mapping plane. As all the physical vectors are calculated in the mapping plane (η,η), this method can lead to potential vast savings of computational resources and memory. In this work, the results are validated against several published works in the literature. The different geometries of the inclusion with sharp corners based on the proposed mapping functions for irregular polygons are studied and discussed. The findings show that the variation of angles and frequencies of the incident waves have significant influence on the bistatic scattering pattern and the far-field form factor for the pressure in the fluid.

Correlation between helical surface waves and guided modes of an infinite immersed elastic cylinder

Scattering of obliquely incident plane acoustic waves from immersed infinite solid elastic cylinders is a complex phenomenon that involves generation of various types of surface waves on the body of the cylinder. Mitri [F.G. Mitri, Acoustic backscattering enhancement resulting from the interaction of an obliquely incident plane wave with an infinite cylinder, Ultrasonics 50 (2010) 675-682] recently showed that for a solid aluminum cylinder, there exist acoustic backscattering enhancements at a normalized frequency of ka⩽0.1. The incidence angle α(c) at which these enhancements are observed lies between the first (longitudinal) and second (shear) coupling angles of the cylinder. He also confirmed the observations previously reported by the authors that there exist backscattering enhancements of the dipole mode at large angles of incidence where no wave penetration into the cylinder is expected. In this paper, physical explanations are provided for the aforementioned observations by establishing a correlation between helical surface waves generated by oblique insonification of an immersed infinite solid elastic cylinder and the longitudinal and flexural guided modes that can propagate along the cylinder. In particular, it is shown that the backscattering enhancement observed at ka⩽0.1 is due to the excitation of the first longitudinal guided mode travelling at the bar velocity along the cylinder. It is also demonstrated that the dipole resonance mode observed at incidence angles larger than the Rayleigh coupling angle is associated with the first flexural guided mode of the cylinder. The correlation established between the scattering and propagation problems can be used in both numerical and experimental studies of interaction of mechanical waves with cylinders.