Index of content:
Volume 117, Issue 2, February 2005
- NONLINEAR ACOUSTICS 
117(2005); http://dx.doi.org/10.1121/1.1841551View Description Hide Description
The present study investigates the focusing of acoustical weak shock waves incoming on a cusped caustic. The theoretical model is based on the Khokhlov–Zabolotskaya equation and its specific boundary conditions. Based on the so-called Guiraud’s similitude law for a step shock, a new explanation about the wavefront unfolding due to nonlinear self-refraction is proposed. This effect is shown to be associated not only to nonlinearities, as expected by previous authors, but also to the nonlocal geometry of the wavefront. Numerical simulations confirm the sensitivity of the process to wavefront geometry. Theoreticalmodeling and numerical simulations are substantiated by an original experiment. This one is carried out in two steps. First, the canonical Pearcey function is synthesized in linear regime by the inverse filter technique. In the second step, the same wavefront is emitted but with a high amplitude to generate shock waves during the propagation. The experimental results are compared with remarkable agreement to the numerical ones. Finally, applications to sonic boom are briefly discussed.
117(2005); http://dx.doi.org/10.1121/1.1841711View Description Hide Description
Analyses of rocketnoise data measured at far-field locations during the launch of a large rocket and a smaller rocket are presented. Weak shocks are present in all of the data sets. In order to characterize these shocks, those segments of the waveforms where the acoustic pressure is increasing are isolated and the rate of increase in pressure plotted versus magnitude of pressure rise. The plots follow a trend consistent with random noise at low values of pressure rise, then transition to the pressure-squared dependence expected for weak shocks at higher pressure rise values. Power spectral densities of the noise during the period of maximum overall sound-pressure levels display high- and low-frequency spectral slopes that are close to those predicted for shock-dominated noise. It is concluded that shocks must be included in propagation models if high frequency levels are to be estimated as a function of distance from the source. Initial shock thicknesses will have to be characterized experimentally and will require instrumentation with a bandwidth well in excess of 20 kHz. Reflection-free data are essential if meaningful assessments of the statistical properties of the noise are to be made.
117(2005); http://dx.doi.org/10.1121/1.1850052View Description Hide Description
A theoreticalmodel describing the nonlinear scattering of acoustic waves by surface-breaking cracks with faces in partial contact is presented. The nonlinear properties of the crack are accounted for by suitable boundary conditions that are derived from micromechanical models of the dynamics of elastic rough surfaces in contact. Both linear and nonlinear responses of the crack are shown to be largest for a shear vertical wave incident on the surface containing the crack at an angle just above the critical angle for longitudinal waves. These findings question the fitness for the purpose of a conventional inspection method, which utilizes shear vertical waves at 45° of incidence to search for surface-breaking cracks in many engineering components. For angles of incidence proximal to the critical angle of longitudinal waves, the efficiency of the second harmonic’s generation appears to be the highest. Thanks to the increased sensitivity to surface-breaking cracks, this configuration seems to offer a solution to the localization problem, a task that has eluded nonlinear techniques operating under other circumstances. Finally, this model suggests a simple interpretation of the highly localized nonlinear response of delaminations in composite materials.
Resonant properties of a nonlinear dissipative layer excited by a vibrating boundary: Q-factor and frequency response117(2005); http://dx.doi.org/10.1121/1.1828548View Description Hide Description
Simplified nonlinear evolution equations describing non-steady-state forced vibrations in an acoustic resonator having one closed end and the other end periodically oscillating are derived. An approach based on a nonlinear functional equation is used. The nonlinear Q-factor and the nonlinear frequency response of the resonator are calculated for steady-state oscillations of both inviscid and dissipative media. The general expression for the mean intensity of the acoustic wave in terms of the characteristic value of a Mathieu function is derived. The process of development of a standing wave is described analytically on the base of exact nonlinear solutions for different laws of periodic motion of the wall. For harmonic excitation the wave profiles are described by Mathieu functions, and their mean energycharacteristics by the corresponding eigenvalues. The sawtooth-shaped motion of the boundary leads to a similar process of evolution of the profile, but the solution has a very simple form. Some possibilities to enhance the Q-factor of a nonlinear system by suppression of nonlinear energy losses are discussed.