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.
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.
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 seismic wave propagation and significantly influence the relationship of seismic signal to seismic source.
Hearing protection devices (HPDs) such as earplugs offer to mitigate noise exposure and reduce the incidence of hearing loss among persons frequently exposed to intense sound. However, distortions of spatial acoustic information and reduced audibility of low-intensity sounds caused by many existing HPDs can make their use untenable in high-risk (e.g., military or law enforcement) environments where auditory situational awareness is imperative. Here we assessed (1) sound source localization accuracy using a head-turning paradigm, (2) speech-in-noise recognition using a modified version of the QuickSIN test, and (3) tone detection thresholds using a two-alternative forced-choice task. Subjects were 10 young normal-hearing males. Four different HPDs were tested (two active, two passive), including two new and previously untested devices. Relative to unoccluded (control) performance, all tested HPDs significantly degraded performance across tasks, although one active HPD slightly improved high-frequency tone detection thresholds and did not degrade speech recognition. Behavioral data were examined with respect to head-related transfer functions measured using a binaural manikin with and without tested HPDs in place. Data reinforce previous reports that HPDs significantly compromise a variety of auditory perceptual facilities, particularly sound localization due to distortions of high-frequency spectral cues that are important for the avoidance of front-back confusions.
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.
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