G. Douglas Meegan

Observations of nonlinear elastic wave behavior in sandstone

An experimental investigation of nonlinear elastic wave behavior was conducted using a 2‐m‐long cylindrical rod of Berea sandstone in order to study the strong elastic nonlinearity that is characteristic of microcracked materials. Measurements of the displacement field at distance x from the source show rich harmonic content with harmonic amplitudes depending on x, source frequency, and source amplitude. The amplitude of the 2ω harmonic is found to grow linearly with x and as the square of both the source frequency ω and the source amplitude U. This behavior is in agreement with the predictions of nonlinear elasticity theory for a system with cubic anharmonicity. From the measured amplitude of the 2ω harmonic the parameter ‖β‖, a measure of the strength of the cubic anharmonicity, is found to be of order 104 (7.0×103±25%). This value is orders of magnitude greater than that found in ordinary uncracked materials. These results suggest that wave distortion effects due to nonlinear elasticity can be large in...

Modeling of nonlinear shear waves in soft solids

An evolution equation for nonlinear shear waves in soft isotropic solids is derived using an expansion of the strain energy density that permits separation of compressibility and shear deformation. The advantage of this approach is that the coefficient of nonlinearity for shear waves depends on only three elastic constants, one each at second, third, and fourth order, and these coefficients have comparable numerical values. In contrast, previous formulations yield coefficients of nonlinearity that depend on elastic constants whose values may differ by many orders of magnitude because they account for effects of compressibility as well as shear. It is proposed that the present formulation is a more natural description of nonlinear shear waves in soft solids, and therefore it is especially applicable to biomaterials like soft tissues. Calculations are presented for harmonic generation and shock formation in both linearly and elliptically polarized shear waves.

Gas bubble and solid sphere motion in elastic media in response to acoustic radiation force.

The general approach to estimate the displacement of rounded objects (specifically, gas bubbles and solid spheres) in elastic incompressible media in response to applied acoustic radiation force is presented. In this study, both static displacement and transient motion are analyzed using the linear approximation. To evaluate the static displacement of the spherical inclusion, equations coupling the applied force, displacement, and shear modulus of the elastic medium are derived. Analytical expressions to estimate the static displacement of solid spheres and gas bubbles are presented. Under a continuously applied static force, both the solid sphere and the initially spherical gas bubble are displaced, and the bubble is deformed. The transient responses of the inclusions are described using motion equations. The displacements of the inclusion in elastic incompressible lossless media are analyzed using both frequency-domain and time-domain formalism, and the equations of motion are derived for both a solid sphere and a gas bubble. For a short pulsed force, an analytical solution for the equations of motion is presented. Finally, transient displacement of the gas bubble in viscoelastic media is considered.

Interaction of bubbles in a cluster near a rigid surface

A model for the interaction of two bubbles in a sound field [E. A. Zabolotskaya, Sov. Phys. Acoust. 30, 365–368 (1984)] is extended to account for an arbitrary number of bubbles interacting in a cluster. Compressibility of the liquid is taken into account through radiation damping and time delays due to the finite sound speed. Bubble coalescence is also included. A numerical method for implementing the model is described, and simulations of the growth and collapse of a bubble cluster near a rigid surface are presented. The relative effects of compressibility and coalescence are discussed.

Modifications of the equation for gas bubble dynamics in a soft elastic medium

A model equation for the oscillation of a pressurized gas bubble in a nonlinear incompressible elastic medium [Emelianov et al., J. Acoust. Soc. Am. 115, 581 (2004)] is extended to include effects of surface tension, viscosity, weak compressibility, and confinement by an elastic shell. The significance of this work is that starting from first principles, the full nonlinearity of the incompressible elastic medium surrounding the bubble and forming its shell is taken into account. Measurements of equilibrium radius as a function of external pressure for a gas bubble in a tissue-like gel are also presented. A general approach to including hysteresis is also discussed.

Acoustic agglomeration experiments and modeling

Acoustic agglomeration of aerosols has been known since at least 1931 when it was observed that particles tend to ‘‘stick’’ together in the presence of an intense acoustic field, thereby forming larger particles. Since the 1970s acoustic agglomeration has been an active area of research because of its potential applications for the control of particulate emissions resulting from fossil fuel combustion. In this talk, experimental methods used in the past to study acoustic agglomeration are described, along with improvements we have introduced. A simple standing wave tube is one of the devices used in our laboratory to measure the dependence of acoustic agglomeration on sound pressure level, frequency, and exposure time. Results are presented and compared with theoretical predictions based on existing models. The potential application to diesel engine emissions and the filtration of hazardous particulate will be discussed.

Bubble translation and deformation induced by ultrasound radiation force

Measurement of small‐bubble dynamics has been proposed for the remote evaluation of tissue elasticity [Erpelding et al., Proc. IEEE Ultrasonics Symp., 554–557, 2003]. For example, a microbubble can be produced within the cornea during femtosecond laser surgery and its response to a pulsed ultrasonic radiation force can be measured. The bubble’s translation, deformation, and oscillation can be directly related to the mechanical properties of surrounding tissue information that is required for optimization of the surgical procedure. In the work reported here, a model was developed to predict the translation and deformation of an initially spherical bubble in a soft viscoelastic medium as induced by radiation pressure. The extent of bubble translation and deformation is dictated by the elastic stress and viscous forces that oppose the radiation pressure. Numerical simulations predict static, periodic, and transient translation of the bubble in response to continuous, periodic, and pulsed waveforms, respectiv...

Analysis of engine noise for application in predictive maintenance

The analysis of radiated sound and vibrational signatures of engines may be useful for monitoring an engine’s performance and assessing the need for maintenance. Measurements of the vibrational signatures and exhaust noise produced by normal engines and engines with known faults will be presented along with a corresponding model for engine exhaust noise. The results of power spectral and higher‐order spectral processing of the engine noise will be compared and their usefulness as a means of detecting faulty engine operation will be discussed. [Work supported by the Office of Naval Research, Contract No. N00014‐96‐1‐0298‐7.]

Evaluation of level-dependent performance of in-ear hearing protection devices using an enclosed sound source

Hearing protection devices are increasingly designed with the capability to protect against impulsive sound. Current methods used to test protection from impulsive noise, such as blasts and gunshots, suffer from various drawbacks and complex, manual experimental procedures. For example, the use of a shock tube to emulate blast waves typically produces a blast wind of a much higher magnitude than that generated by an explosive, a specific but important inconsistency between the test conditions and final application. Shock tube test procedures are also very inflexible and provide only minimal insight into the function and performance of advanced electronic hearing protection devices that may have relatively complex response as a function of amplitude and frequency content. To address the issue of measuring the amplitude-dependent attenuation provided by a hearing protection device, a method using a compression driver attached to an enclosed waveguide was developed. The hearing protection device is placed at...

Model for interaction of bubbles in a cloud near a rigid surface

Bubble clouds produced during lithotripsy undergo complicated motions including bubble interactions that may inhibit kidney stone comminution. Our study of bubble interactions is motivated by high‐speed photographs reported by Pishchalnikov et al. [J. Acoust. Soc. Am. 114, 2386 (2003)]. In the work reported here, we simulated the observed bubble motion with a model based on the equations derived by Zabolotskaya [Sov. Phys. Acoust. 30, 365 (1984)]. The equations for interaction of two bubbles were generalized and solved numerically for a cluster of n bubbles near a rigid boundary, which represents the stone. The initial spatial distribution of bubbles in three dimensions was assumed to be random. When a short negative pressure pulse was applied, the simulated bubbles grew in size. When two bubbles touched each other, they were merged into a single bubble that conserved mass of the gas. Results are presented in selected planes intersecting the bubble cloud for different instants of time. Bubble interaction ...