Index of content:
Volume 125, Issue 3, March 2009
- NONLINEAR ACOUSTICS 
Two-dimensional wave propagation in an elastic half-space with quadratic nonlinearity: A numerical study125(2009); http://dx.doi.org/10.1121/1.3075597View Description Hide Description
This study investigates two-dimensional wave propagation in an elastic half-space with quadratic nonlinearity. The problem is formulated as a hyperbolic system of conservation laws, which is solved numerically using a semi-discrete central scheme. These numerical results are then analyzed in the frequency domain to interpret the nonlinear effects, specifically the excitation of higher-order harmonics. To quantify and compare the nonlinearity of different materials, a new parameter is introduced, which is similar to the acoustic nonlinearity parameter for one-dimensional longitudinal waves. By using this new parameter, it is found that the nonlinear effects of a material depend on the point of observation in the half-space, both the angle and the distance to the excitation source. Furthermore it is illustrated that the third-order elastic constants have a linear effect on the acoustic nonlinearity of a material.
Nonlinear nonclassical elasticity applied to the analysis of low frequency flexural vibrations: Theory and experiments125(2009); http://dx.doi.org/10.1121/1.3075595View Description Hide Description
Motivated by the increasing interest on nonlinear nondestructive damage detection, a comparison of the nonlinear elastic behavior of damaged samples and their intact state is presented. Flexural vibration is induced in thin glass plates with laser thermal shock induced micro-cracks by means of two thin piezo-ceramic patches glued in a bimorph configuration. The cases of direct excitation of a resonance and excitation of an internal resonance cases are considered. The resulting nonlinear vibrations exhibit the main features of quadratic hysteresis: linear variation of the resonance frequency and quadratic production of the third harmonic. A theoretical model for nonlinear resonant flexural vibrations based on the Preisach–Mayergoyz constitutive relations is proposed for damage quantification. Experimental comparison between the intact and damaged sample indicates an increase in the relevant nonlinearity parameter, indicating a widening of the hysteresis loop due to damage.
125(2009); http://dx.doi.org/10.1121/1.3075585View Description Hide Description
The frequency response and nonlinear resonance frequency shift of an acoustical resonator with losses and having a varying cross section were investigated previously using Lagrangian mechanics and perturbation for resonator shapes that are close to cylindrical [M. F. Hamilton, et al., J. Acoust. Soc. Am.110, 109–119 (2001)]. The same approach is extended here to include resonators having any shape for which the Webster horn equation is a valid model in the linear approximation. Admissible shapes include cones and bulbs proposed for acoustical compressors. The approach is appropriate for approximate but rapid parameter estimations for resonators with complicated shapes, requiring far less computation time than for direct numerical solution of the one-dimensional modelequation frequently used for such resonators [Ilinskii et al., J. Acoust. Soc. Am.104, 2664–2674 (1998)]. Results for cone and bulb shaped resonators with losses are compared with results from the direct numerical solution. The direction of the resonance frequency shift is determined by the efficiency of second-harmonic generation in modes having natural frequencies below versus above the frequency of the second harmonic, and how the net effect of this coupling compares with the frequency shifts due to cubic nonlinearity and static deformation.
125(2009); http://dx.doi.org/10.1121/1.3075552View Description Hide Description
An analytical theory has been developed to calculate microstreaming velocity inside and outside an encapsulated microbubble (EMB) in a viscousliquid produced by its oscillations driven by an ultrasound field, taking account of two predominant modes of the EMB’s motion: a monopole (pulsation) and a dipole (translational harmonic vibrations). Analytical expressions of radial as well as tangential stresses are derived near the shell of the EMB. Numerical calculations in parameter regimes applicable to sonoporation are presented. For the calculation the following parameters unless specified otherwise are used: , , , , , , , , , , and . The calculated results show that the streaming velocity and stresses near an EMB are functions of the mechanical properties of shell and gas. Overall, the streaming velocity and stresses for an EMB are found to be greater than those for a similar size free bubble under the same ultrasound excitation. This finding is consistent with the existing theory of acoustic streaming of an oscillating bubble near a boundary given by Nyborg (1958) [J. Acoust. Soc. Am.30, 329–339].
125(2009); http://dx.doi.org/10.1121/1.3077216View Description Hide Description
A model of the interaction of a spherical gas bubble and a rigid spherical particle is derived as a coupled system of second-order differential equations using Lagrangian mechanics. The model accounts for pulsation and translation of the bubble as well as translation of the particle in an infinite, incompressible liquid. The model derived here is accurate to order , where is a characteristic radius and is the separation distance between the bubble and particle. This order is the minimum accuracy required to account for the interaction of the bubble and particle. Dependence on the size and density of the particle is demonstrated through numerical integration of the dynamical equations for both the free and forced response of the system. Numerical results are presented for models accurate to orders higher than to demonstrate the consequences of truncating the equations at order .