Index of content:
Volume 128, Issue 6, December 2010
- NONLINEAR ACOUSTICS 
Nonlinear propagation of spark-generated N-waves in air: Modeling and measurements using acoustical and optical methods128(2010); http://dx.doi.org/10.1121/1.3505106View Description Hide Description
The propagation of nonlinear spherically diverging N-waves in homogeneous air is studied experimentally and theoretically. A spark source is used to generate high amplitude (1.4 kPa) short duration (40 μs) N-waves; acoustic measurements are performed using microphones (3 mm diameter, 150 kHz bandwidth). Numerical modeling with the generalized Burgers equation is used to reveal the relative effects of acoustic nonlinearity, thermoviscous absorption, and oxygen and nitrogen relaxation on the wave propagation. The results of modeling are in a good agreement with the measurements in respect to the wave amplitude and duration. However, the measured rise time of the front shock is ten times longer than the calculated one, which is attributed to the limited bandwidth of the microphone. To better resolve the shock thickness, a focused shadowgraphy technique is used. The recorded optical shadowgrams are compared with shadow patterns predicted by geometrical optics and scalar diffraction model of light propagation. It is shown that the geometrical optics approximation results in overestimation of the shock rise time, while the diffraction model allows to correctly resolve the shock width. A combination of microphonemeasurements and focused optical shadowgraphy is therefore a reliable way of studying evolution of spark-generated shock waves in air.
128(2010); http://dx.doi.org/10.1121/1.3505102View Description Hide Description
Consider the constitutive law for an isotropic elastic solid with the strain-energy function expanded up to the fourth order in the strain and the stress up to the third order in the strain. The stress–strain relation can then be inverted to give the strain in terms of the stress with a view to considering the incompressible limit. For this purpose, use of the logarithmic strain tensor is of particular value. It enables the limiting values of all nine fourth-order elastic constants in the incompressible limit to be evaluated precisely and rigorously. In particular, it is explained why the three constants of fourth-order incompressible elasticity μ, , and are of the same order of magnitude. Several examples of application of the results follow, including determination of the acoustoelastic coefficients in incompressible solids and the limiting values of the coefficients of nonlinearity for elastic wave propagation.
128(2010); http://dx.doi.org/10.1121/1.3502461View Description Hide Description
Dynamic acoustoelastictesting is applied to weakly pre-loaded unconsolidated water-saturated glass beads. The gravitational acceleration produces, on the probed beads, a static stress of order 130 Pa, thus the granular medium is close to the jamming transition. A low-frequency (LF) acoustic wave gently disturbs the medium, inducing successively slight expansion and compaction of the granular packing expected to modulate the number of contacts between beads. Ultrasound(US) pulses are emitted simultaneously to dynamically detect the induced modification of the granular skeleton. US propagation velocity and attenuation both increase when the LF pressure increases. The quadratic nonlinear elastic parameter β, related to the pressure dependence of US propagation velocity, was measured in the range 60–530 if water-saturated glass beads are considered as an effective medium. A dynamic modification of US scattering induced by beads is proposed to modulate USattenuation. Complex hysteretic behaviors and tension-compression asymmetry are also observed and analyzed by time-domain and spectral analyses. Furthermore acoustic nonlinearities are measured in cases of quasi-static and dynamic variations of the LF wave amplitude, providing quantitatively similar acoustic nonlinearities but qualitatively different.
Minimum radiation force target size for power measurements in focused ultrasonic fields with circular symmetry128(2010); http://dx.doi.org/10.1121/1.3505105View Description Hide Description
The time-averaged ultrasonic power emitted by medical ultrasonic equipment is mostly measured using a radiation force balance, and the question of the necessary target size is of practical importance. The question is answered here by calculations based on a Rayleigh integral algorithm for fields from circular, focusing transducers. This case occurs particularly in the field of high-intensity therapeuticultrasound. The calculation yields the necessary size of an absorbing target so that the radiation force is 98% of that exerted on an absorber of infinite lateral size, and this as a function of the transducer-to-target distance, of the transducer radius in comparison with the wavelength and of the focus (half-)angle. Several distributions of the transducer vibration amplitude are considered. The Rayleigh integral strictly applies only to planar transducers, but among the amplitude distributions there is also one that allows the simulation of the spherically curved transducer type often found in practice.