Timothy D. Daniel

Scattering from multiple elastic targets using the coupled finite element/boundary element method

The fluid-structure interaction technique provides a paradigm for solving scattering from elastic targets embedded in a fluid by a combination of finite and boundary element methods. In this technique, the finite element method is used to compute the target’s elastic response and the boundary element method with the appropriate Green’s function is used to compute the field in the exterior medium. The two methods are coupled at the surface of the target by imposing the continuity of pressure and normal displacement. This results in a self-consistent boundary element method that can be used to compute the scattered field anywhere in the surrounding environment. The method reduces a finite element problem to a boundary element one with drastic reduction in the number of unknowns, which translates to a significant reduction in numerical cost. In this talk, the method is extended to compute scattering from multiple targets by self-consistently accounting for all interactions between them. The model allows to identify block matrices responsible for the interaction between targets, which proves useful in many applications. The model is tested by comparing its results with those measured involving two aluminum cylinders one of which is excited by modulated radiation pressure.The fluid-structure interaction technique provides a paradigm for solving scattering from elastic targets embedded in a fluid by a combination of finite and boundary element methods. In this technique, the finite element method is used to compute the target’s elastic response and the boundary element method with the appropriate Green’s function is used to compute the field in the exterior medium. The two methods are coupled at the surface of the target by imposing the continuity of pressure and normal displacement. This results in a self-consistent boundary element method that can be used to compute the scattered field anywhere in the surrounding environment. The method reduces a finite element problem to a boundary element one with drastic reduction in the number of unknowns, which translates to a significant reduction in numerical cost. In this talk, the method is extended to compute scattering from multiple targets by self-consistently accounting for all interactions between them. The model allows to i...

Geometric approximation of radiation stress projections for canonical objects

Modulated ultrasonic radiation pressure facilitates the selective excitation of modes of objects through modulation of appropriate surface stress projections [P. L. Marston and R. E. Apfel, J. Acoust. Soc. Am. 67, 27–37 (1980)]. For some large objects, it can be impractical to evaluate the needed stress projections using standard analytical or computational methods. For highly reflecting objects geometric approximations may provide useful insight into the relevant stress projections. The simplest projection gives the translational radiation force on the object. In that case, ray analysis of the far-field scattering was shown to recover the radiation force on large perfectly reflecting spheres in plane waves [P. L. Marston, J. Acoust. Soc. Am. 120, 3518–3524 (2006)]. In the present research, the appropriate force limit is also recovered through integrating a geometrically approximated local stress projection on the object’s surface. Appropriate limiting forces for other canonical objects or situations invo...

Backscattering enhancement due to weakly damped, leaky, guided waves on cylinders and associated images

In this work, distinct but related targets were studied using a circular synthetic aperture sonar system. Backscattering data from a solid brass cylinder were recorded. The response of the target was significantly spread out in time because leaky guided waves were weakly radiation damped. They gave significant backscattering contributions for a range of tilt angles. The associated meridional and helical wave contributions are also obvious in the frequency domain. (For comparison helical contributions are relatively weak for aluminum cylinders.) The second target is a bi-metallic cylinder made of a 1:1 brass cylinder bonded to a 3:1 aluminum cylinder. For a single-material cylinder, only 90 degrees of data are necessary due to symmetry. This target breaks that symmetry and requires a full 180 degrees of rotation. The distinction between the brass and aluminum ends is discernible in both the time and frequency domain. The join between the two metals affects the timing of certain guided waves that no longer travel the whole length of the compound cylinder. Image reconstruction was performed using Fourier based algorithms for both targets. The location of the compound cylinder joint is deducible from the location of features in the image domain. [Research supported by ONR.]In this work, distinct but related targets were studied using a circular synthetic aperture sonar system. Backscattering data from a solid brass cylinder were recorded. The response of the target was significantly spread out in time because leaky guided waves were weakly radiation damped. They gave significant backscattering contributions for a range of tilt angles. The associated meridional and helical wave contributions are also obvious in the frequency domain. (For comparison helical contributions are relatively weak for aluminum cylinders.) The second target is a bi-metallic cylinder made of a 1:1 brass cylinder bonded to a 3:1 aluminum cylinder. For a single-material cylinder, only 90 degrees of data are necessary due to symmetry. This target breaks that symmetry and requires a full 180 degrees of rotation. The distinction between the brass and aluminum ends is discernible in both the time and frequency domain. The join between the two metals affects the timing of certain guided waves that no longer ...

An examination of the scaling rules for sound emissions from targets excited by point-like forces

In earlier work [T. Daniel et al., JASA 140, 3123 (2016)] we had showed experimentally that the modes of small elastic targets in water could be excited using modulated radiation pressure (MRP) generated by focused ultrasound to create detectable sound emissions. A potential advantage of the MRP approach is that the narrow beam of the ultrasound beam permits the generation of point-like forces on the target’s surface with surgical precision. But an important question is how this technique scales with target size, e.g., the amount of force required to achieve a desired sound emission level. Here we examine how the sound emission levels and surface velocities of target modes driven by a point force scale with target size a. We will show that for a constant driving force, the far-field sound emission pressure levels scale as 1/a and the surface velocity as 1/a2. Specific examples are presented for circular plates, spheres, and cylindrical-like targets. Finally, results will be shown from a recent tank experiment at Washington State University where we attempted to experimentally determine the scaling rules using small targets excited by MRP.In earlier work [T. Daniel et al., JASA 140, 3123 (2016)] we had showed experimentally that the modes of small elastic targets in water could be excited using modulated radiation pressure (MRP) generated by focused ultrasound to create detectable sound emissions. A potential advantage of the MRP approach is that the narrow beam of the ultrasound beam permits the generation of point-like forces on the target’s surface with surgical precision. But an important question is how this technique scales with target size, e.g., the amount of force required to achieve a desired sound emission level. Here we examine how the sound emission levels and surface velocities of target modes driven by a point force scale with target size a. We will show that for a constant driving force, the far-field sound emission pressure levels scale as 1/a and the surface velocity as 1/a2. Specific examples are presented for circular plates, spheres, and cylindrical-like targets. Finally, results will be shown from a recent tank experi...

Target response in a focused, modulated sound field: Modeling and experiment

In a previous work, we had shown that low frequency flexural modes of circular plates and cylinders could be excited using modulated radiation pressure generated by focused ultrasound [ J. Acoust. Soc. Am. 139, 2053 (2016)]. We recently conducted experiments probing how the response of these targets varied as a function of position in the focused ultrasound field. Surprisingly, the response of the circular plate was found to change sign as it was moved away from the source. Two different models were developed to analyze the target response and understand this sign change. A purely geometric model based on ray optics and a semi-physical optics model that uses the incident intensity calculated for the focused source, using a Rayleigh-Sommerfeld integral. Both geometric and semi-physical optics models predict a sign change for the plate response at approximately the correct distance from the source. The sign change is due to a factor in a mode projection that more strongly weights points farther from the center of the plate. The physical optics model was also applied to cylindrical targets. [Work supported by ONR.]In a previous work, we had shown that low frequency flexural modes of circular plates and cylinders could be excited using modulated radiation pressure generated by focused ultrasound [ J. Acoust. Soc. Am. 139, 2053 (2016)]. We recently conducted experiments probing how the response of these targets varied as a function of position in the focused ultrasound field. Surprisingly, the response of the circular plate was found to change sign as it was moved away from the source. Two different models were developed to analyze the target response and understand this sign change. A purely geometric model based on ray optics and a semi-physical optics model that uses the incident intensity calculated for the focused source, using a Rayleigh-Sommerfeld integral. Both geometric and semi-physical optics models predict a sign change for the plate response at approximately the correct distance from the source. The sign change is due to a factor in a mode projection that more strongly weights points farther from the cen...

Acoustic vortex beam created with a continuous phase ramp lens and resulting radiation torque response of a sphere

An acoustic vortex beam was created in water using a lens with a phase ramp placed in front of a focused transducer. The lens was made from a polystyrene disk and CAD machine milled to have a continuous ramp in height about the center axis, with the ramp step height corresponding to a 2π phase difference between waves propagating in water and polystyrene at 500 kHz. This causes the transmitted beam through the lens to exit as a vortex beam with an angular phase ramp. It has been predicted [L. Zhang and P. L. Marston, J. Acoust. Soc. Am. 136, 2917–2921 (2014)] that the torque exerted by a vortex beam on an impenetrable sphere in a viscous fluid is proportional to the incident intensity due to dissipation of angular momentum in the viscous boundary layer near the sphere. This should result in steady rotation of the sphere with viscous drag proportional to angular velocity. Our upward-directed vortex beam was used to trap and spin a Styrofoam (closed foam) ball floating at the water surface. The spin rate was approximately proportional to the square of the source voltage as expected. [Work supported by ONR.]An acoustic vortex beam was created in water using a lens with a phase ramp placed in front of a focused transducer. The lens was made from a polystyrene disk and CAD machine milled to have a continuous ramp in height about the center axis, with the ramp step height corresponding to a 2π phase difference between waves propagating in water and polystyrene at 500 kHz. This causes the transmitted beam through the lens to exit as a vortex beam with an angular phase ramp. It has been predicted [L. Zhang and P. L. Marston, J. Acoust. Soc. Am. 136, 2917–2921 (2014)] that the torque exerted by a vortex beam on an impenetrable sphere in a viscous fluid is proportional to the incident intensity due to dissipation of angular momentum in the viscous boundary layer near the sphere. This should result in steady rotation of the sphere with viscous drag proportional to angular velocity. Our upward-directed vortex beam was used to trap and spin a Styrofoam (closed foam) ball floating at the water surface. The spin rate wa...

Observation and modeling of acoustic scattering from a rubber spherical shell

Acoustic backscattering from a rubber spherical shell in water is observed to contain a delayed enhancement, demonstrated to be associated with a waveguide path along the shell. This path is somewhat analogous to that of the Lamb wave observed on metallic shells. Rubber is a unique material because of its subsonic sound speed relative to water, and because shear coupling is often small enough to be neglected in typical models, making it fluid-like. This makes rubber a material of interest for coating and cloaking underwater devices and vehicles. Both fluid and elastic rubber partial wave series models are tested, using experimentally measured longitudinal and shear speeds, attenuation, and rubber density. A finite element model for the shell is also developed. Comparison of the models and experiments highlights the importance of the waveguide path to the overall scattering. Estimates for the group and phase velocities of the lowest order propagating mode in the shell are determined through waveguide normal mode analysis and Sommerfeld-Watson theory, and are shown to give good agreement with experiments in predicting the time of arrival of the waveguide path.

Creating synthetic aperture images using experimental and simulated backscattering of solid elastic cubes

To study aspect and material dependent backscattering of objects, we used cubes as their geometry has distinct exposure points for different backscattering mechanisms. We insonified two solid cubes, one brass and the other steel, in underwater tank scale experiments, measuring their backscattering using circular, linear, and cylindrical synthetic aperture sonar. The right angles of the edges allow for enhanced backscattering by Rayleigh waves, which couple in at material-specific angles, since the waves are retroreflected by the cube’s edges [K. Gipson and P. L. Marston, J. Acoust. Soc. Am. 105, 700-710 (1998)]. In concert with the experiments, we model the backscattering from our cubes using Kirchhoff-Integration based simulations. The simulation isolates the specular responses, simplifying the complex responses from the cube’s geometry and allowing us to identify specific effects, such as splitting from the corner reflections of a cube when its top ridge is tilted. Using Fourier based back-projection al...

On target excitation by modulated radiation pressure

Modulated radiation pressure (MRP), which can be produced by modulating an ultrasound carrier beam with a low-frequency signal provides the capability to interrogate elastic objects in a novel manner: The high-frequency carrier beam enables surgical investigation of target of interest, while the low-frequency modulation signal “shakes” the target to extract useful physical information. By sweeping the modulation frequency, target resonances can be identified, and by physically scanning the target at a modulation frequency that is commensurate with one of its resonant frequencies, the corresponding mode shape can be extracted. Up until now, the application of this technique has been limited to medical ultrasound, where it has been used to look for tumors and kidney stones among other things. The other applications of this technique have been particle trapping and non-contact manipulations. In this presentation, we will show results from experiments conducted at Washington State University involving scaled ...

Late backscattering enhancement from a rubber spherical shell associated with waveguide coupling and propagation

Acoustic scattering from rubber targets has received modest attention in the past due in part to rubber’s subsonic sound speeds. In particular, slow shear waves in rubber get rapidly attenuated, giving rubber the fluid-like property of negligible shear coupling. This makes rubber a material of interest for coating or cloaking underwater objects and vehicles. In this study, backscatter from a rubber spherical shell in water is considered experimentally and through such models as partial wave series, finite elements, and waveguide normal mode analysis. The target is a commercially available American handball of unspecified rubber composition. Experimental and modeled results exhibit the importance of a strong, slightly subsonic late echo, which is demonstrated through path timing models and frequency analysis to be due to waveguide propagation through the shell wall. The various models use wave speeds for the rubber determined experimentally, allowing for determination of the phase and group velocities of t...