Mark F. Hamilton

University of Texas at Austin, Austin, Texas, United States

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Publications (237)328.89 Total impact

  • [Show abstract] [Hide abstract]
    ABSTRACT: Large encapsulated bubbles have recently been used for abating low-frequency anthropogenic underwater noise [J. Acoust. Soc. Am. 135, 1700-1708 (2014)]. The use of encapsulation allows for the possibility of bubbles that are significantly nonspherical in their equilibrium state. Strasberg [J. Acoust. Soc. Am. 25, 536-537 (1953)] investigated the resonance frequency of an ideal bubble with arbitrary shape and found that the dependence of resonance frequency on the shape of the bubble reduced to a well-known problem in electrostatics. The present work extends that analysis to include the effects of radiation damping on the oscillation of a bubble, and does so by including a loss term due to Ilinskii and Zabolotskaya [J. Acoust. Soc. Am. 92, 2837-2841 (1992)] in the volume-frame dynamical equation for the bubble. An expression is given for the amplitude of the acoustic field scattered from the bubble, and it is shown that radiation damping scales as resonance frequency cubed for arbitrarily shaped bubbles having the same volume. Comparisons are made with previous work on scattering from spherical and prolate spheroidal bubbles, and various new bubble shapes are considered. [Work supported by AdBm Technologies, the ARL:UT McKinney Fellowship in Acoustics and ONR.]
    The Journal of the Acoustical Society of America 04/2015; 137(4):2254-2254. DOI:10.1121/1.4920221 · 1.56 Impact Factor
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    ABSTRACT: A theory for acoustic radiation force on a viscoelastic sphere of arbitrary size in soft tissue has been reported previously for a nonaxisymmetric incident field described via spherical harmonic expansion [Ilinskii et al., POMA 19, 045004 (2013)]. At the Fall 2014 ASA meeting, the model was used to compute the radiation force on scatterers with different sizes and properties at various positions relative to the focus of an axisymmetric incident beam. For a particle located away from the focus, the model predicts a change in the direction of the axial or the transverse component of the radiation force depending on properties of both the particle and the host medium. The focus of the present contribution is this change in direction. Scatterers with various sizes and mechanical properties are considered, and small particles are found to be more prone to this phenomenon. Additionally, the reversal in direction is found to be sensitive to variations in the shear modulus of the host medium. Comparisons are made with liquid as the shear modulus of the host medium spans the range of values encountered in soft tissue. [Work supported by the ARL:UT McKinney Fellowship in Acoustics.]
    The Journal of the Acoustical Society of America 04/2015; 137(4):2313-2313. DOI:10.1121/1.4920438 · 1.56 Impact Factor
  • John Cormack, Mark F. Hamilton
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    ABSTRACT: Due to very low shear moduli for soft tissue or tissue-like media, shear waves propagate very slowly, on the order of meters per second, making it relatively easy to produce shear waves exhibiting waveform distortion and even shock formation. Finite amplitude effects in plane shear waves result from cubic nonlinearity, compared with quadratic nonlinearity in compressional waves. Both attenuation and dispersion also significantly affect propagation of shear waves in tissue. Here we account for these complex viscoelastic effects by considering a medium with one relaxation mechanism. An analytical solution similar to that of Polyakova, Soluyan, and Khokhlov [Sov. Phys. Acoust. 8, 78 (1962)] for a compressional wave with a step shock in a relaxing medium is obtained for a shear wave with a step shock in a relaxing medium. The wave profile with cubic nonlinearity closely resembles that with quadratic nonlinearity. For weak nonlinearity the solution reduces to an expression obtained by Crighton [J. Fluid Mech. 173, 625 (1986)] for a Taylor shock in a viscous medium with cubic nonlinearity. Numerical simulations are presented comparing shock formation with quadratic and cubic nonlinearity for other wave profiles in relaxing media. [Work supported by the ARL:UT McKinney Fellowship in Acoustics.]
    The Journal of the Acoustical Society of America 04/2015; 137(4):2364-2365. DOI:10.1121/1.4920592 · 1.56 Impact Factor
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    ABSTRACT: The theory for acoustic radiation force on a viscoelastic sphere of arbitrary size in tissue was extended at the spring 2013 ASA meeting to account for nonaxisymmetric fields incident on the scatterer [Ilinskii et al., POMA 19, 045004 (2013)]. The results were presented in a form that permits inclusion of as many spherical harmonics as needed to describe the field structure. At the fall 2013 ASA meeting, it was shown that for spheres having sizes up to about one wavelength, only four or five spherical harmonics are required for convergence of the solution when plane waves are incident on the scatterer. At the present meeting, the model is applied to diffracting sound beams incident on the scatterer. The analysis is based on angular spectrum decomposition of the incident field, expansion of the resulting plane waves in spherical waves, then a Wigner transformation of the latter back into spherical coordinates with polar axis coinciding with the beam axis, and finally integration over solid angle to obtain the spherical wave amplitudes used in the theory. Results are presented for different radiation patterns illustrating dependence of the radiation force both on beamwidth and on wavelength relative to the size of the scatterer.
    The Journal of the Acoustical Society of America 04/2014; 135(4):2210. DOI:10.1121/1.4877218 · 1.56 Impact Factor
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    ABSTRACT: This work studies the forced dynamical behavior of a heterogeneous material containing metamaterial inclusions undergoing large deformations. The inclusions exhibit non-monotonic stress-strain behavior, modeled with an expansion to third order in volume strain, where the coefficients of the expansion depend on the metamaterial structure. The resulting constitutive behavior of interest displays regimes of both positive and negative stiffness and the inclusion therefore exhibits hysteretic snapping when forced by an acoustic pressure. Two cases are explored using a generalized Rayleigh-Plesset analysis to model the large-deformation dynamics of the metamaterial inclusion following an approach similar to Emelianov et al. [J. Acoust. Soc. Am., 115, 581 (2004)]. The first case focuses on the forced dynamics of a single inclusion embedded in a weakly compressible elastic medium. The second case broadens the model to analyze the behavior of a heterogeneous material comprised of a low volume fraction of non-interacting metamaterial inclusions embedded in a weakly compressible material. Finally, estimates of the effective bulk modulus and loss factor of the heterogeneous medium are presented for instances of the forcing pressure inducing either large or small inclusion deformation. [Work supported by the ARL:UT McKinney Fellowship in Acoustics and the Office of Naval Research.].
    The Journal of the Acoustical Society of America 04/2014; 135(4):2255. DOI:10.1121/1.4877389 · 1.56 Impact Factor
  • Preston S Wilson, Craig N Dolder, Mark F Hamilton
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    ABSTRACT: Highly directional light sources such as flashlights and lasers are well known to most people. In contrast, highly directional acoustic sources, or in other words, sources of sound that are audible in only a very narrow region of space, are far less common. Many people have never experienced such a source, and the phenomenon is not found in nature. A highly directional source of sound known as a parametric array is used underwater for sonar applications, but the frequency (pitch) of the sound is often above the human hearing range. Similarly, highly directional, focused sound sources are regularly used in medical applications, but again, the frequency is too high to be heard. The narrowness of the acoustic beam cannot be experienced by human listeners. Recently, parametric array technology has been commercialized for use in air at frequencies in the human auditory range. These devices produce extremely narrow (on the order of 2 degrees) beams of audible sound. When pointed directly at one listener, the sound is virtually inaudible to another listener only a few feet away. Such a device will be demonstrated and the basic physics behind its operation will be explained.
    The Journal of the Acoustical Society of America 04/2014; 135(4):2249. DOI:10.1121/1.4877368 · 1.56 Impact Factor
  • Mark F Hamilton
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    ABSTRACT: Several years ago, the author was contacted by the legal team representing a major smartphone manufacturer and asked if he would serve as an expert witness in a patent-dispute case to be tried before an administrative law judge at the International Trade Commission. The author had no significant prior experience as an expert witness, and he therefore had no inkling of what responsibilities lay ahead of him. The author will describe his experiences in this case, beginning with assisting the legal team with understanding the relevant acoustics, then writing expert reports, and finally preparing for deposition and trial.
    The Journal of the Acoustical Society of America 04/2014; 135(4):2341. DOI:10.1121/1.4877688 · 1.56 Impact Factor
  • Craig N Dolder, Preston S Wilson, Mark F Hamilton
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    ABSTRACT: William M. Carey is well known for his interest in sound propagation through bubbly liquids. He was also a champion of re-attributing the low frequency effective medium model widely known as Wood's law to its original author Arnulph Mallock, who published a paper titled "The Damping of Sound by Frothy Liquids" in 1910. In the same spirit, this presentation will discuss the evolution of theories involving sound propagation through bubbly liquids over time from Mallock to modern day. Since bubble pulsations can exhibit strong nonlinearity, the presentation will conclude by reintroducing another often-overlooked modeling advance, at least in the western literature, that of Zabolotskya and Soluyan [Sov. Phys. Acoust. 13, 254-256 (1967)] describing the nonlinear propagation of sound in bubbly liquids. [Work supported by ONR.].
    The Journal of the Acoustical Society of America 04/2014; 135(4):2232. DOI:10.1121/1.4877308 · 1.56 Impact Factor
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    ABSTRACT: Surface acoustic waves (SAW) are used frequently in microfluidic devices. Normally SAWs are generated on the surface of a piezoelectric material. Commonly used PZT is not appropriate for biomedical applications because of its high lead content, over 60% by weight. In this talk, a study of nonlinear SAW propagation in a piezoelectric substrate is presented. Model equations describing nonlinear SAW propagation in a piezoelectric crystal are derived from first principles. Elastic, piezoelectric, dielectric, and electrostrictive properties of a crystal with arbitrary symmetry are taken into account. The derived evolution equations are integrated numerically to illustrate nonlinear distortion of an initially sinusoidal wave of finite amplitude. As an example, SAW propagation along the X axis on single crystal 127.680 YX-cut lithium niobate (LiNbO3), referred to as 128-YX-LN, is considered. This LiNbO3 cut is typically used in microfluidic devices because it provides large mechanical displacements in the substrate. Analysis of the nonlinearity matrix permits quantification of the relative contributions to surface wave distortion from each physical phenomenon. [Work supported by the IR&D program at ARL:UT.].
    The Journal of the Acoustical Society of America 04/2014; 135(4):2218. DOI:10.1121/1.4877244 · 1.56 Impact Factor
  • Mark F Hamilton
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    ABSTRACT: Interest in characterizing nonlinearity in jet noise has motivated consideration of an effective Gol'dberg number for diverging waves [Baars and Tinney, Bull. Am. Phys. Soc. 57, 17 (2012)]. Fenlon [J. Acoust. Soc. Am. 50, 1299 (1971)] developed expressions for the minimum value of Γ, the Gol'dberg number as defined for plane waves, for which shock formation occurs in diverging spherical and cylindrical waves. The conditions were deduced from a generalized Khokhlov solution and depend on the ratio xsh/r0, where r0 is source radius, and xsh the plane-wave shock formation distance for Γ=∞. Alternatively, by taking the ratio of the nonlinear and thermoviscous terms in Fenlon's Eq. (2), it is proposed here that effective Gol'dberg numbers may be identified for spherical and cylindrical waves: Λ=Γexp(-πxsh/2r0) and Λ=Γ/(1 + πxsh/4r0), respectively. For a given value of Λ, the diverging waves achieve approximately the same degree of nonlinear distortion as a plane wave for which the value of Γ is the same. Conversely, to achieve the same degree of nonlinear distortion as a plane wave with a given value of Γ, the value of Γ for, e.g., a spherical wave must be larger by a factor of exp(πxsh/2r0). Extensions to other spreading laws are presented.
    The Journal of the Acoustical Society of America 11/2013; 134(5):4099. DOI:10.1121/1.4830972 · 1.56 Impact Factor
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    ABSTRACT: There is concern that underwater noise generated by marine construction activities and radiated by towers supporting offshore wind turbines may disturb marine mammals, or interfere with passive sensors and communication equipment. In order to understand these effects a semi-analytic frequency-domain model was developed previously for the sound radiated in the water column by a pulsating cylindrical structure embedded in horizontally stratified layers of viscoelastic sediment. This model was in turn coupled to a parabolic equation code for long-range propagation over range-dependent environments [Hay et al., J. Acoust. Soc. Am. 133, 3396 (2013)]. A time-domain version of this model is now presented which enables simulation of impulsive sound sources such as those due to underwater pile driving, and pulsed tonal sources appropriate for use in a finite-sized laboratory tank. In order to validate the model a scaled physical model, consisting of a laboratory tank and metallic cylindrical tube driven in the high kilohertz frequency range, was constructed. Simulations will be presented for a variety of sound sources, and preliminary comparisons with measurements from the scaled model experiments will be made.
    The Journal of the Acoustical Society of America 11/2013; 134(5):4023. DOI:10.1121/1.4830686 · 1.56 Impact Factor
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    ABSTRACT: A parabolic equation describing the propagation of collimated shear wave beams in isotropic elastic solids was derived by Zabolotskaya [Sov. Phys. Acoust. 32, 296-299 (1986)], and was seen to contain both cubic and quadratic nonlinear terms at leading order. While second-order nonlinear effects vanish for the quasi-planar case of linearly-polarized shear wave beams, the importance of quadratic nonlinearity for more complicated polarizations is not yet well understood. The current work investigates the significance of quadratic nonlinearity by considering second-harmonic generation in shear wave beams generated by a certain class of source polarizations that includes such cases as radial and torsional polarization, among others. Corresponding to such beams with Gaussian amplitude shading, analytic solutions are derived for the propagated beam at the source frequency and the second harmonic. Diffraction characteristics are discussed, and special attention is paid to the relationship between the source polarization of the beam and the polarization of the subsequently generated second harmonic. Finally, suggestions are made for possible experiments that could be performed in tissue phantoms, exploiting the theoretical results of this work. [Work supported by the ARL:UT McKinney Fellowship in Acoustics.].
    The Journal of the Acoustical Society of America 11/2013; 134(5):3997. DOI:10.1121/1.4830579 · 1.56 Impact Factor
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    ABSTRACT: This work considers nonlinear propagation in a medium consisting of a low volume fraction of metamaterial inclusions dispersed in a fluid-like material. The metamaterial inclusions of interest are assumed to possess non-monotonic stress-strain constitutive relations, which results in regimes of negative stiffness. For modeling purposes, the constitutive relation for these inclusions is approximated with an expansion to third order in volume strain with coefficients that can be tuned with the geometry of the metamaterial structure and ambient pressure. A far-reaching goal of this research is to model the hysteretic response of the heterogeneous medium resulting from metamaterial inclusion snapping events and the associated effect on acoustic disturbances that cycle through regimes of both positive and negative stiffness. As an initial step, results are presented here for small but finite-amplitude disturbances limited to local regions of the constitutive relation. For this case, the quadratic and cubic nonlinearity parameters B/A and C/A, respectively, as traditionally defined for fluids are obtained. An evolution equation with both quadratic and cubic nonlinearity is also obtained. Numerical solutions of the evolution equation illustrate nonlinear waveform distortion as a function of the volume fraction and constitutive behavior of the inclusions. [Work supported by ARL:UT McKinney Fellowship in Acoustics.].
    The Journal of the Acoustical Society of America 11/2013; 134(5):4027. DOI:10.1121/1.4830700 · 1.56 Impact Factor
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    ABSTRACT: Underwater noise due to both marine pile driving and offshore wind farm operation is not only radiated directly from the pile into the water, but also from the seabed surrounding the pile. While there is much interest in mitigating the noise from these activities, a better understanding of the source mechanisms and propagation is needed to determine optimal strategies for noise abatement. A recent analytical model of the acoustic field radiated by submerged piles includes radiation from the pile directly into the water and into a stratified viscoelastic sediment as well as propagation into a shallow water waveguide from both the direct and sediment radiation paths [Hay et al., Proceedings of Meetings on Acoustics 19, 070038 (2013)]. As a step towards validating this model, scale-model experiments were conducted in the high kilohertz frequency range with a model pile consisting of a mechanically excited metallic tube inserted into a laboratory tank filled with two stratified layers to simulate the water/sediment interface. Measurements of the acoustic field in the experiment are compared with the model predictions, and the relevance of these results to implementing noise abatement strategies will be discussed. [Work supported by ARL:UT IR&D.].
    The Journal of the Acoustical Society of America 11/2013; 134(5):4060. DOI:10.1121/1.4830818 · 1.56 Impact Factor
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    ABSTRACT: In a previous presentation [J. Acoust. Soc. Am. 133, 3327 (2013)], an experimental model study of a pneumatic infrasound source that utilizes the pulsation of compressed air was discussed. The present paper discusses new measurements and theoretical modeling efforts that are currently underway. Measurements of the source level, directivity patterns, propagation loss, and frequency response are presented and analyzed. Acoustic and aerodynamic models are presented and discussed with a focus on modeling and predicting nearfield system performance using multipole (monopole, dipole, and quadrupole) representations of the sound source. Measurement techniques and engineering considerations are addressed, as are physical interpretations of the process. [Work supported by ARL:UT Austin.].
    The Journal of the Acoustical Society of America 11/2013; 134(5):4192. DOI:10.1121/1.4831377 · 1.56 Impact Factor
  • Derek C Thomas, Yurii A Ilinskii, Mark F Hamilton
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    ABSTRACT: Most common methods to include the effects of liquid compressibility in models for single-bubble dynamics rely on series expansions to some order in the inverse of the sound speed in the liquid. It has been shown that the Keller-Miksis model for single-bubble dynamics can be obtained from a series expansion of a delay differential equation related to the Rayleigh-Plesset equation for a single bubble. The iterative approach used to obtain the series expansion of the delay-based model becomes unworkable for more complicated models of bubble dynamics. Therefore, to provide an alternative, simpler method to model the effects of liquid compressibility, the delay differential equation model proposed by Ilinskii and Zabolotskaya [J. Acoust. Soc. Am. 92, 2837 (1992)] is analyzed directly. The results of the delay-based formulations are compared to those produced by models based on common series expansions. Alternative formulations of the delay differential equation are also considered and compared.
    The Journal of the Acoustical Society of America 11/2013; 134(5):3991. DOI:10.1121/1.4830554 · 1.56 Impact Factor
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    ABSTRACT: Acoustic radiation force on a scatterer in tissue depends on the compressibility and shear modulus of both the tissue and the scatterer. This force is related to the monopole and dipole scattering coefficients. The finite shear modulus of the tissue decreases the radiation force in comparison with the force exerted on the same scatterer surrounded by liquid. Shear moduli for soft tissue range from several kilopascals (breast, liver) to tens of kilopascals and higher for cornea, cartilage, and cancerous tissue. As reported previously, the radiation force on a bubble in tissue having 100 kPa shear modulus is 50% less than if the bubble is in water. This difference decreases for scatterers with finite shear moduli, examples of which are reported here. Additionally, displacement of a scatterer due to radiation force is inversely proportional to the shear modulus of the tissue, which permits measurement of the latter. Experiments demonstrating this technique are reviewed. In these experiments, the radiation force is applied to a gas microbubble produced by laser-induced optical breakdown, while displacement of the microbubble is measured by high-frequency ultrasound as a function of time. Results are reported for tissue-mimicking phantoms and animal crystalline lenses in vitro.
    The Journal of the Acoustical Society of America 11/2013; 134(5):4009. DOI:10.1121/1.4830623 · 1.56 Impact Factor
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    ABSTRACT: To help resolve certain practical issues with acoustical methods for humanitarian landmine detection, we have researched using a pulsed, standoff source method for acoustical excitation of the buried mine [J. Acoust. Soc. Am. 130, 2541 (2011); J. Acoust. Soc. Am. 133, 3457 (2013)]. Pulses consisting of two primary frequencies are used in order to search for induced nonlinear vibrations at interaction frequencies such as the sum frequency, which arise due to nonlinear interaction at the mine/soil interface. To model the pulsed excitation, we employ a fully nonlinear time-domain implementation of the lumped-element model of nonlinear soil/mine interaction introduced by Donskoy et al. [J. Acoust. Soc. Am. 117, 690 (2005)]. Modeling is compared with experimental results, which are obtained with bi-frequency pulses exciting a soil with a buried landmine replica, instrumented with a geophone and a nearby microphone. Cases investigated include: (1) target only, (2) buried target under disturbed soil, (3) disturbed soil only, and (4) undisturbed soil. Excitation both on and off the resonance of the buried mine is also investigated, as is burial in different soil types at various depths. [Work supported by the ARL:UT McKinney Fellowship in Acoustics.].
    The Journal of the Acoustical Society of America 11/2013; 134(5):4129. DOI:10.1121/1.4831168 · 1.56 Impact Factor
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    Derek C. Thomas, Yurii A. Ilinskii, Mark F. Hamilton
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    ABSTRACT: Various models for interacting spherical bubbles in a compressible liquid based on delay differential equations are considered. It is shown that most previously proposed models for interacting spherical bubbles in a compressible liquid based on the Keller-Miksis and Gilmore-Akulichev models are unstable for closely spaced bubbles. A new model for a single spherical bubble in a compressible liquid is proposed and used to derive a stable model for interacting bubbles. A qualitative comparison to the results of direct numerical integration of the fluid equations of motion suggests that the new model provides more accurate results than the standard Keller-Miksis or Gilmore-Akulichev models for single bubble dynamics.
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Publication Stats

2k Citations
328.89 Total Impact Points


  • 1987–2015
    • University of Texas at Austin
      • Department of Mechanical Engineering
      Austin, Texas, United States
  • 2012–2013
    • Brigham Young University - Provo Main Campus
      • Department of Physics and Astronomy
      Provo, Utah, United States
  • 2009
    • Universiteit Twente
      Enschede, Overijssel, Netherlands
  • 2007
    • Stanford University
      • E. L. Ginzton Laboratory
      Palo Alto, CA, United States
  • 1998
    • Acoustical Society of America
      Norfolk, Virginia, United States
  • 1985–1987
    • University of Bergen
      • Department of Mathematics
      Bergen, Hordaland, Norway