V. E. Nazarov

Nonlinear acoustics of micro-inhomogeneous media

Abstract Acoustic waves can interact in micro-inhomogeneous media much more intensively than in homogeneous media. This has been repeatedly observed in experiments with ground species, marine sediments, porous materials and metals. This paper considers two models of such media which seem to be applicable to the description of these results. One of them is based on the consideration of nonlinear sound scattering by separate spherical cavities in liquids and solids. The second model is based on the phenomenological stress-deformation relation in solids with microplasticity which often has hysteresis (heritage) properties associated with the micro-inhomogeneities. In metals, for example, it is caused by the movement of dislocations. Different nonlinear effects in such media (harmonic and combination frequency generation, nonlinear, variations of resonance frequency amplitude-dependent losses) are considered. Some results of experiments with metallic resonators supporting the theory developed here are also presented. These mechanisms may determine the nonlinear properties of real soils and rocks summarized in a table given in the paper.

Experimental investigations of nonlinear acoustic phenomena in polycrystalline zinc

The results of experimental and theoretical investigations of nonlinear acoustic phenomena (nonlinear losses, shift of resonance frequency, generation of the third harmonic, and nonlinear sound-by-sound damping) in polycrystalline zinc nonannealed and annealed resonating rods are presented. The measurements were carried out in the 10(-7)-10(-5) strain range at a frequency of about 3 kHz; the frequency of the weak ultrasonic pulse was about 270 kHz. The experimentally observed phenomena are described in frames of phenomenological equations of state containing elastic hysteresis and dissipative nonlinearity. The nonlinear acoustic parameters of these equations are determined by comparison between theoretical dependencies and experimental results. The influence of structural changes in zinc due to annealing on the nonlinear acoustic phenomena is shown.

Nonlinear Interaction of Acoustical Waves Due to Cracks and Its Possible Usage for Cracks Detection

An interaction of a CW acoustic wave and a powerful acoustic pulse due to nonlinear properties of a crack-type discontinuity in a solid is considered. Characteristics of nonstationary variations of the reflected wave amplitude and the phase of the transmitted wave, which are induced by the powerful pulse, are determined. The effects should allow one to distinguish cracks from other scatterers and can be used as a base of a new method of crack detection and positioning. Demonstrative signal estimates based on two simplified crack models are presented.

Wave processes in media with hysteretic nonlinearity: Part 2

Nonlinear processes caused by the propagation of low-frequency and high-frequency acoustic pulses in an unbounded medium and the propagation of continuous waves in a ring resonator are theoretically studied on the basis of two hysteretic equations of state for media with imperfect elasticity. The profiles and parameters of pulses, the resonance curve and the Q factor of the resonator, and the ratio of the nonlinear resonance frequency shift to the nonlinear damping decrement are determined. For nonlinear wave processes in such media, the distinctive features that allow one to choose an appropriate hysteretic equation of state for analytically describing the experimental data are revealed.

Experimental Study of Nonlinear Acoustic Effects in a Granular Medium

Results of a series of experimental studies of nonlinear acoustic effects in a granular medium are presented. Different effects observed in the experiments simultaneously testify that the nonlinearity of granular media is governed by the weakest intergrain contacts. The behavior of the observed dependences suggests that the distribution function of contact forces strongly increases in the range of forces much smaller than the mean force value, which is inaccessible for conventional experimental measuring techniques. For shear waves in a granular medium, the effects of demodulation and second harmonic generation with conversion to longitudinal waves are studied. These effects are caused by the nonlinear dilatancy of the medium, i.e., by the nonlinear law of its volume variation in the shear stress field. With the use of shear waves of different polarizations, the anisotropy of the nonlinearity of the medium is demonstrated. The observation of the cross-modulation effect shows that the nonlinearity-induced modulation components of the probe wave are much more sensitive to weak nonstationary perturbations of the medium, as compared to the linearly propagating fundamental harmonic. The nonlinear effects under study offer promise for diagnostic applications in laboratory measurements and in seismic monitoring systems.

Effect of an Intense Sound Wave on the Acoustic Properties of a Sandstone Bar Resonator. Experiment

Experimental results and a theoretical description are presented for the effect of an intense pumping wave on a weak wave in a sandstone bar resonator. From the amplitude dependences of the resonance frequency shift and of the nonlinear loss, which are measured for the weak wave in the presence of the intense one, it is inferred that sandstone exhibits a dissipative acoustic nonlinearity.

The equation of state of a microinhomogeneous medium and the frequency dependence of its elastic nonlinearity

In the framework of a rheological model, a nonlinear dynamic equation of state of a microinhomogeneous medium containing nonlinear viscoelastic inclusions is derived. The frequency dependences of the effective nonlinear parameters are determined for the difference frequency and second harmonic generation processes in the case of a quadratic elastic nonlinearity. It is shown that the frequency dependence of the nonlinear elasticity of the medium is governed by the linear relaxation response of the inclusions at the primary excitation frequency, as well as by the relaxation of the inclusions at the nonlinear generation frequencies.

Experimental study of nonlinear acoustical effects in limestone

Results of an experimental and theoretical study of nonlinear acoustic effects (amplitude-dependent loss, resonance frequency shift, second and third harmonic generation, and sound by sound damping) in a limestone bar resonator are reported. The observed effects are analytically described in the framework of phenomenological equations of state with allowance for the low-frequency hysteretic nonlinearity and the high-frequency dissipative nonlinearity. Experimental and analytical dependences of nonlinear effects are compared to find the parameters of the hysteretic and dissipative nonlinearities of the limestone sample studied.

Dissipative acoustic nonlinearity of polycrystalline zinc

Results of experimental studies of nonlinear acoustic effects, namely, the attenuation of a weak ultrasonic pulse under the action of an intense low-frequency pumping wave and the limitation of the ultrasonic pulse amplitude in rod-type resonators made of unannealed and annealed polycrystalline zinc, are presented. The measurements are performed for the first four longitudinal modes of the rods with the frequency of the ultrasonic pulses varying from 40 kHz to 1 MHz. An analytical description of this effect is presented in the framework of the phenomenological equation of state allowing for dissipative nonlinearity. A modification of the Granato-Lucke dislocation theory that explains the experimentally observed amplitude and frequency dependences of the coefficient of nonlinear attenuation of ultrasonic pulses is proposed. Estimates for the parameters of the modified model are obtained from the comparison of theoretical and experimental data.

Amplitude dependent internal friction and generation of harmonics in granite resonator

The results of experimental and theoretical studies of low-frequency effects of amplitude dependent internal friction (nonlinear losses and resonance frequency shift) and generation of second and third harmonics in an acoustic bar resonator made of Karelian granite are presented. The analytical description of the observed effects is performed within the framework of phenomenological hysteretic equations of state containing elastic and inelastic hysteresis. It was shown that elastic cubic hysteresis is manifested at small amplitudes of strains, whereas superposition of elastic and inelastic quadratic hysteresises occurs at large amplitudes of strain. Relative weights of these hysteresises and effective parameters of acoustic nonlinearity of granite are determined.