Propagation of acoustic wave in viscoelastic medium permeated with air bubbles

Based on the modification of the radial pulsation equation of an individual bubble, an effective medium method （EMM） is presented for studying propagation of linear and nonlinear longitudinal acoustic waves in viscoelastic medium permeated with air bubbles. A classical theory developed previously by Gaunaurd （Gaunaurd GC and UEberall H, J. Acoust, Soc, Am., 1978; 63： 1699-1711） is employed to verify the EMM under linear approximation by comparing the dynamic （i.e. frequency-dependent） effective parameters, and an excellent agreement is obtained. The propagation of longitudinal waves is hereby studied in detail, The results illustrate that the nonlinear pulsation of bubbles serves as the source of second harmonic wave and the sound energy has the tendency to be transferred to second harmonic wave, Therefore the sound attenuation and acoustic nonlinearity of the viscoelastic matrix are remarkably enhanced due to the system＇s resonance induced by the existence of bubbles.

LINEAR THEORY OF GRAVITY WAVES ON A VOIGT VISCOELASTIC MEDIUM

Linear surface gravity waves on a semi-infinite incompressible Voigt medium are studied in this paper.Three dimensionless parameters,the dimensionless viscoelastic parameter (?),the dimensionless wave number and the dimensionless sur- face tension are introduced.A dimensionless characteristic equation describing the waves is derived.This is a sixth order complex algebraic equation which is solved to give the complex dispersion relation.Based on the numerical solution, two critical values of (?),(?)_A=0.607 and (?)_R=2.380,which represent the appearance of the cutoff region and the disappearance of the strong dispersion region,are found.The effects of (?) on the characteristic equation and the properties of the waves are discussed.

On the higher-order thermal vibrations of FG saturated porous cylindrical micro-shells integrated with nanocomposite skins in viscoelastic medium

Since the multi-layered structures are widely used nowadays, and due to interesting applications of cylindrical shells, this study is dedicated to analyzing free vibrational behaviors of functionally graded saturated porous micro cylindrical shells with two nanocomposite skins. Based on Biot's assumptions, constitutive relations for the core are presented and effective properties of the skins are determined via the rule of mixture. A sinusoidal theory is used to capture the shear deformation effects, and to account for the scale effects, the modified couple stress theory is employed which suggests a material length-scale parameter for predicting the results in small-dimension. With the aid of extended form of Hamilton's principle for dynamic systems, differential equations of motion are extracted. Fourier series functions are used to obtain natural frequencies and after validating them, a set of parametric studies are carried out. The results show the significant effects of porosity and Skempton coefficient, pores placement patterns, CNTs addition and distribution patterns, temperature variations, material length-scale parameter and viscoelastic medium on the natural frequencies of the microstructure. The outcomes of this work could be used to design and manufacture more reliable micro cylindrical structures in thermo-dynamical environments.

INVERSE PROBLEM FOR THE VISCOELASTIC MEDIUM WITH DISCONTINUOUS WAVE IMPEDANCE

In this paper, the inverse problem for the viscoelastic medium is investigated in the time domain, in which the wave impedance of the medium is discontinuous at the rear interface. The differentio-integral equations governing the behavior of the scattering and propagation operators are utilized to reconstruct the relaxation modulus of the viscoelastic medium. A new approach, in which only the one-side measurement reflection data for one round trip through the viscoelastic layer, is developed. The numerical examples are given at the end of the paper. Ir is shown that the curves of the reconstructed moduli coincide very well with the original relaxation moduli.

Acoustics of a viscoelastic medium with encapsulated bubbles

In this paper,a modified Rayleigh-Lamb equation is derived that takes into account the radial vibrations of a gas bubble coated with a viscoelastic shell and located in an elastic medium.For small oscillations of inclusion,the problem of heat exchange between a gas,a liquid phase,a viscoelastic shell,and an elastic medium is solved.The energy integral is determined.In the case of small disturbances,the dispersion relation is found from the Rayleigh-Lamb equations,energy,and the known wave equation for the bubbly medium.An analytical expression of the equilibrium speed of sound is written out and its dependence on the size of the viscoelastic shell and the disturbance frequency is established.An example of a mixture of polydimethylsiloxane with air bubbles coated with a rubber shell illustrates the influence of the elasticity of the carrier medium and the shell of the bubbles on the dependence of the phase velocity and attenuation coefficient on the perturbation frequency.For a mixture of water with air bubbles coated with a rubber shell,the influence of the dependences of the shear modulus and viscosity of butyl rubber on the frequency of disturbances at different temperature on the dispersion curves is shown.A comparison of the theory with experimental data is given.

Effect of Longitudinal Magnetic Field on Vibration Response of Double-Walled Carbon Nanotubes Embedded in Viscoelastic Medium

This paper aims to study the effect of externally applied longitudinal magnetic field on the transverse vibration of viscoelastic double-walled carbon nanotubes （visco-DWCNTs） embedded in a viscoelastic medium. The analyses are carried out based on the nonlocal viscoelastic model and Euler-Bernoulli beam theory. Governing equations are derived for the vibration of the embedded visco-DWCNT subjected to a magnetic field, where the Lorentz magnetic force, the surrounding viscoelastic medium, the intertube van der Waals forces and viscoelasticity of the DWCNT are taken into consideration. In this study, the transfer function method is employed to solve the governing equations, which enables one to obtain the natural frequencies and the corresponding mode shapes in closed form for the DWCNTs with arbitrary boundary conditions. Here the developed mechanics model is first compared with the existing techniques available in the literature in a few particular cases, where excellent agreement is achieved. The validation of the model is followed by a detailed parametric study of the effects of longitudinal magnetic field, nonlocal parameter, boundary conditions, structural damping coefficient and aspect ratio of the DWCNTs on their vibration. The study demonstrates the efficiency of the present technique designed for vibration analysis of a complicated multi-physics system comprising DWCNTs, the viscoelastic medium and a magnetic field in longitudinal direction.

Construction of constant-Q viscoelastic model with three parameters

The popularly used viscoelastic models have some shortcomings in describing relationship between quality factor （Q） and frequency, which is not consistent with the observation data. Based on the theory of viscoelasticity, a new approach to construct constant-Q viscoelastic model in given frequency band with three parameters is developed. The designed model describes the frequency-independence feature of quality factor very well, and the effect of viscoelasticity on seismic wave field can be studied relatively accurate in theory with this model. Furthermore, the number of required parameters in this model has been reduced fewer than that of other constant-Q models, this can simplify the solution of the viscoelastic problems to some extent. At last, the accuracy and application range have been analyzed through numerical tests. The effect of viscoelasticity on wave propagation has been briefly illustrated through the change of frequency spectra and waveform in several different viscoelastic models.

The Stochastic Stability of a Viscoelastic Cable with Small Sag

In this paper, the almost sure stability of a viscoelastic cable subjected to an initial stress on the uniform cross section is studied. The constitutive of the cable material is assumed to be the hereditary integral type, the relaxation kernels of which are represented by the sums of exponents. The initial stress and the damping coefficientto the environment and also relaxation kernel coefficients are a random wide band stationary process. The partial differential integral equation of motion is derived first. Then by applying Galerkins method, the governing equation is reduced to a set of second order differential integral equations. Based on the Liapunovs direct method, sufficient conditions for almost sure stability of viscoelstic cable are obtained.

On Estimating Magnitude of a Maximum Sequent Earthquake by Viscoelastic Coulomb Stress Change and a Discussion of the Relationship between the M_S7.3 Earthquakes in Yutian 2008 and 2014

On the basis of the previous studies of the layered crustal model in the Yutian area,combined with the field GPS continuous observation data,we roughly estimate the viscous coefficient of each layer. With the viscoelastic horizontal layer model,we calculate the viscoelastic co-seismic Coulomb stress change caused by the Yutian M_S7. 3 earthquakes 2008 and 2014 respectively. Based on the Coulomb stress change,using the calculation method of "direct "aftershock frequency,we come up with the theoretical earthquake frequency directly related to the mainshock and the co-seismic Coulomb stress change in the study area. Then we put forward a method,based on the comparison of theoretical and actual earthquake frequency or the comparison between theoretical and practical earthquake frequency-distance decay curve fitting residuals,to estimate the magnitude of a maximum sequent earthquake,directly related to the mainshock co-seismic Coulomb stress change. Results calculated by different methods show that the maximum follow-up earthquake magnitude caused by the coseismic Coulomb stress change lies from M_S7. 2 to M_S7. 5 following Yutian M_S7. 3 earthquake in 2008; but that of the 2014 Yutian M_S7. 3 earthquake is M_S6. 3. The former is very close to the Yutian M_S7. 3 earthquake in 2014.Because of the same magnitude,relatively close spatial distance,short time interval,the same region of the external force,the strong correlation between two seismic tectonic and a clear stress interaction,we thus consider that the two Yutian M_S7. 3 earthquakes in 2008 and 2014 constitute a pair of generalized double shock type earthquake. This is consistent with the sequence type characteristic of past "double shock"earthquakes in the region. In this paper,the influence of the magnitude lower limit and the b-value in the relationship of G-R on the results is discussed. As a result,when the viscoelastic coseismic Coulomb stress variation is determined,the lower limit of magnitude has little effect on the maximum sequent earthquake magnitude estimation,but b-value of G-R has a greater impact on the results.

Localisation and phase transition of acoustic waves in a soft medium containing air bubbles

We study via numerical experiments the localisation property of an acoustic wave in a viscoelastic soft medium containing randomly-distributed air bubbles. The behaviours of the oscillation phases of bubbles are particularly investigated in various cases for distinguishing efficiently the acoustic localisation from the effects of acoustic absorption caused by the viscosity of medium. The numerical results reveal the phenomenon of ＇phase transition＇ characterized by an unusual collective oscillation of bubbles, which is an effective criterion to unambiguously identify the acoustic localisation in the presence of viscosity. Within the localisation region, the phenomenon of phase transition persists, and a remarkable decrease in the fluctuation of the oscillation phases of bubbles is observed. The localisation phenomenon will be impaired by the enhancement of the viscosity factors, and the extent to which the acoustic wave is localised may be determined by appropriately analyzing the values of the oscillation phases or the amount of reduction of the phase fluctuation. The results are particularly significant for the practical experiments in an attempt to observe the acoustic localisation in such a medium, which is in general subjected to the interference of the great ambiguity resulting from the effect of acoustic absorption.

Joint inversion method for interval quality factor based on amplitude and phase information

Estimating the quality factor Q accurately signifi cantly improves the seismic data resolution and reservoir characterization.The commonly used log-spectral ratio method uses least-squares fi tting to obtain Q values and involves only the amplitude information of seismic data while neglecting phase information.This paper proposes a joint interval Q inversion method based on the spectral ratio method and employs both amplitude and phase information to improve the accuracy.Based on the assumption that Q is independent of frequency,the nonlinear relation between the Q value and the two types of information is jointly used to construct an objective function,which clarifies the quantitative relation between amplitude spectrum,phase information,and Q value.The interval Q value can be inverted by calculating the minimum value of the objective function.The model test exhibits that the proposed method has higher precision and stability than the spectral ratio method;furthermore,the application to field data demonstrates that accurate Q inversion results are consistent with reservoir characteristics.

Research on seismic stress triggering

This paper briefly reviews basic theory of seismic stress triggering. Recent development on seismic stress triggering has been reviewed in the views of seismic static and dynamic stress triggering, application of viscoelastic model in seismic stress triggering, the relation between earthquake triggering and volcanic eruption or explosion, other explanation of earthquake triggering, etc. And some suggestions for further study on seismic stress triggering in near future are given.