Mark F. Hamilton

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

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Publications (247)329.58 Total impact

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    Full-text · Article · Jul 2015 · AIAA Journal
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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.]
    No preview · Article · Apr 2015 · The Journal of the Acoustical Society of America
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    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.]
    No preview · Article · Apr 2015 · The Journal of the Acoustical Society of America
  • 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.]
    No preview · Article · Apr 2015 · The Journal of the Acoustical Society of America
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    Woutijn J. Baars · Charles E. Tinney · Mark F. Hamilton
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    ABSTRACT: Discrepancies between linear predictions and direct measurements of the far-field sound produced by highspeed jet flows are typically ascribed to nonlinear distortion. Here we employ an effective Gol'dberg number to investigate the likelihood of nonlinear distortion in the noise fields of supersonic jets. This simplified approach relies on an isolated view of a ray tube along the Mach wave angle. It is known that the acoustic pressure obeys by cylindrical spreading in close vicinity to the jet before advancing to a spherical decay in the far-field. Therefore, a 'piecewise-spreading regime' model is employed in order to compute effective Gol'dberg numbers for these jet flows. Our first-principal approach suggests that cumulative nonlinear distortion can only be present within 20 jet exit diameters along the Mach wave angle when laboratory-scale jets are being considered. Effective Gol'dberg numbers for full-scale jet noise scenarios reveal that a high-degree of cumulative distortion can likewise be present in the spherical decay regime. Hence, full-scale jet noise fields are more affected by cumulative distortion.
    Full-text · Article · Oct 2014
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    ABSTRACT: Snapping acoustic metamaterial (SAMM) inclusions are engineered sub-wavelength structures that exhibit regimes of both positive and negative stiffness. Snapping is defined as large, rapid deformations resulting from the application of an infinitesimal change in externally applied pressure. This snapping leads to a large hysteretic response at the inclusion scale and is thus of interest for enhancing absorption of energy in acoustic waves. The research presented here models the forced dynamics of a multiscale material consisting of SAMM inclusions embedded in a nearly incompressible viscoelastic matrix material to explore the influence of small-scale snapping on enhanced macroscopic absorption. The microscale is characterized by a single SAMM inclusion, while the macroscale is sufficiently large to encompass a low volume fraction of non-interacting SAMM inclusions within the nearly incompressible matrix. A model of the forced dynamical response of this heterogeneous material is achieved by coupling the two scales in time and space using a generalized Rayleigh-Plesset analysis, which has been adapted from the field of bubble dynamics. A loss factor for the heterogeneous medium is examined to characterize energy dissipation due to the forced behavior of these metamaterial inclusions. [Work supported by the ARL:UT McKinney Fellowship in Acoustics and Office of Naval Research.]
    No preview · Article · Oct 2014 · The Journal of the Acoustical Society of America
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    ABSTRACT: The theory for acoustic radiation force on a viscoelastic sphere of arbitrary size in tissue was extended recently to account for nonaxisymmetric incident fields [Ilinskii et al., POMA 19, 045004 (2013)]. A spherical harmonic expansion was used to describe the incident field. This work was specialized at the spring 2014 ASA meeting to focused axisymmetric sound beams with various focal spot sizes and a scatterer located at the focus. The emphasis of the present contribution is nonaxisymmetric fields, either through moving the scatterer off the axis of an axisymmetric beam or through explicitly defining a nonaxisymmetric beam. This is accomplished via angular spectrum decomposition of the incident field, spherical wave expansions of the resulting plane waves about the center of the scatterer, Wigner D-matrix transformations to express these spherical waves in a coordinate system with the polar axis aligned with the desired radiation force component, and finally integration over solid angle to obtain spherical wave amplitudes as required in the theory. Various scatterer sizes and positions relative to the focus are considered, and the effects of changing properties of both the scatterer and the surrounding tissue are examined. [Work supported by the ARL:UT McKinney Fellowship in Acoustics.]
    No preview · Article · Oct 2014 · The Journal of the Acoustical Society of America
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    ABSTRACT: The University of Texas at Austin has supported education and research in acoustics since the 1930s. The Cockrell School of Engineering currently offers a wide range of graduate courses and two undergraduate courses in acoustics, not counting the many courses in hearing, speech, seismology, and other areas of acoustics at the university. An important adjunct to the academic program in acoustics has been the Applied Research Laboratories (ARL). Spun off in 1945 from the WW II Harvard Underwater Sound Laboratory (1941–1949) and founded as the Defense Research Laboratory, ARL is one of five University Affiliated Research Centers formally recognized by the US Navy for their prominence in underwater acoustics research and development. ARL is an integral part of UT Austin, and this symbiotic combination of graduate and undergraduate courses, and laboratory and field work, provides one of the leading underwater acoustics education programs in the nation. In this talk, the underwater acoustics education program will be described with special emphasis on the underwater acoustics course and its place in the larger acoustics program. Statistics on education, funding, and placement of graduate students in the program will also be presented.
    No preview · Article · Oct 2014 · The Journal of the Acoustical Society of America
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    ABSTRACT: While graduate study in acoustics takes place in several colleges and schools at The University of Texas at Austin (UT Austin), including Communication, Fine Arts, Geosciences, and Natural Sciences, this poster focuses on the acoustics program in Engineering. The core of this program resides in the Departments of Mechanical Engineering (ME) and Electrical and Computer Engineering (ECE). Acoustics faculty in each department supervise graduate students in both departments. One undergraduate and seven graduate acoustics courses are cross-listed in ME and ECE. Instructors for these courses include staff at Applied Research Laboratories at UT Austin, where many of the graduate students have research assistantships. The undergraduate course, taught every fall, begins with basic physical acoustics and proceeds to draw examples from different areas of engineering acoustics. Three of the graduate courses are taught every year: a two-course sequence on physical acoustics, and a transducers course. The remaining four graduate acoustics courses, taught in alternate years, are on nonlinear acoustics, underwater acoustics, ultrasonics, and architectural acoustics. An acoustics seminar is held most Fridays during the long semesters, averaging over ten per semester since 1984. The ME and ECE departments both offer Ph.D. qualifying exams in acoustics.
    No preview · Article · Oct 2014 · The Journal of the Acoustical Society of America
  • S. G. Konarski · M. F. Hamilton · M. R. Haberman
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    ABSTRACT: This paper demonstrates the enhancement of acoustic nonlinearities in a heterogeneous elastic material consisting of negative stiffness metamaterial structures embedded in an isotropic linear elastic matrix. Standard formulations of nonlinear elasticity are employed to determine the effective isotropic nonlinear bulk modulus of the composite. Acoustic parameters of nonlinearity, which characterize the distortion of a propagating acoustic wave through this heterogeneous material, are determined by relating the bulk modulus to the nonlinear equation of state. The effects of varying the values of the inclusion and matrix parameters are presented and discussed.
    No preview · Conference Paper · Aug 2014
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    W. J. Baars · C. E. Tinney · M. S. Wochner · M. F. Hamilton
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    ABSTRACT: A model is proposed for predicting the presence of cumulative nonlinear distortions in the acoustic waveforms produced by high-speed jet flows. The model relies on the conventional definition of the acoustic shock formation distance and employs an effective Gol'dberg number A for diverging acoustic waves. The latter properly accounts for spherical spreading, whereas the classical Gol'dberg number F is restricted to plane wave applications. Scaling laws are then derived to account for the effects imposed by jet exit conditions of practical interest and includes Mach number, temperature ratio, Strouhal number and an absolute observer distance relative to a broadband Gaussian source. Surveys of the acoustic pressure produced by a laboratory-scale, shock-free and unheated Mach 3 jet are used to support findings of the model. Acoustic waveforms are acquired on a two-dimensional grid extending out to 145 nozzle diameters from the jet exit plane. Various statistical metrics are employed to examine the degree of local and cumulative nonlinearity in the measured waveforms and their temporal derivatives. This includes a wave steepening factor (WSF), skewness, kurtosis and the normalized quadrature spectral density. The analysed data are shown to collapse reasonably well along rays emanating from the post-potential-core region of the jet. An application of the generalized Burgers equation is used to demonstrate the effect of cumulative nonlinear distortion on an arbitrary acoustic waveform produced by a high-convective-Mach-number supersonic jet. It is advocated that cumulative nonlinear distortion effects during far-field sound propagation are too subtle in this range-restricted environment and over the region covered, which may be true for other laboratory-scale jet noise facilities.
    Full-text · Article · Jun 2014 · Journal of Fluid Mechanics
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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.
    No preview · Article · Apr 2014 · The Journal of the Acoustical Society of America
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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.].
    No preview · Article · Apr 2014 · The Journal of the Acoustical Society of America
  • 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.
    No preview · Article · Apr 2014 · The Journal of the Acoustical Society of America
  • 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.
    No preview · Article · Apr 2014 · The Journal of the Acoustical Society of America
  • 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.].
    No preview · Article · Apr 2014 · The Journal of the Acoustical Society of America
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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.].
    No preview · Article · Apr 2014 · The Journal of the Acoustical Society of America
  • 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.
    No preview · Article · Nov 2013 · The Journal of the Acoustical Society of America
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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.].
    No preview · Article · Nov 2013 · The Journal of the Acoustical Society of America
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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.
    No preview · Article · Nov 2013 · The Journal of the Acoustical Society of America

Publication Stats

2k Citations
329.58 Total Impact Points

Institutions

  • 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
    • Stanford University
      • E. L. Ginzton Laboratory
      Palo Alto, CA, United States
  • 1998
    • Acoustical Society of America
      Norfolk, Virginia, United States
  • 1995
    • University of Washington Seattle
      Seattle, Washington, United States
  • 1985
    • University of Bergen
      • Department of Mathematics
      Bergen, Hordaland, Norway