Acoustic Sounder Data Research Articles

Об идентификации характеристик неоднородных вязкоупругих тел в рамках модели дробного порядка

Nowadays, the development of models of viscoelastic materials with complex inhomogeneous structure is one of the hottest problems of continuum mechanics. Along with classical models, fractional-differential models of viscoelasticity have become increasingly popular. In this paper, we present a model for describing steady-state oscillations of inhomogeneous viscoelastic bodies in terms of fractional-order differential operators. Taking into account the fractional order of the model operators, the corresponding form of the complex module describing the material properties is constructed. The module includes four characteristics: instantaneous and long-term elastic moduli (in the case of material inhomogeneity, they are the functions of coordinates), relaxation time and fractionality parameter. The properties of the complex module are studied, and the ranges of the model parameters, at which the rheological properties are most pronounced, are identified. A general formulation of the inverse problem (IP) on the identification of function-parameters of the model based on the acoustic sounding data is proposed. In the framework of this formulation, the inverse problems for specific objects , namely, an inhomogeneous rod and a round plate, are considered. In both model problems, the influence of the fractionalization parameter on the amplitude-frequency characteristics is analyzed. It has been found that in the vicinity of viscoelastic resonances the fractionality parameter affects the parameters of the oscillatory process most significantly, which is typical for such problems. A solution to the nonlinear IPs under consideration is constructed based on the linearization method, which also serve as basis for the iterative processes supplemented with the elements of the projection approach. This allows one to determine corrections to the required functions in the specified classes of functions using regularization. For both IPs, a series of computational experiments were carried out. The analysis of the experimental results made it possible to formulate recommendations for the selection of optimal sensing modes.

Functionally graded cylinders: Vibration analysis

AbstractThe problems of steady‐state and free oscillations of functionally graded hollow cylinders are considered in the present article, with the cylinders' properties considered changing along the radial or longitudinal coordinates. The stress–strain state was described using the model of an isotropic body with the variable Lamé parameters and density. The cylinders were assumed to be subjected to the normal and tangential loads. In order to obtain the numerical problem solutions, the finite element method was employed. The effect of variable properties on the amplitude–frequency characteristics and the resonant frequencies values for various cylinders types is estimated. Some features, which can be used in solving new inverse coefficient problems on material properties identification based on acoustic sounding data, are revealed.

MODELLING AND ANALYSIS OF INITIAL STRESS STATE IN A THIN-WALL CYLINDER WITH VARIABLE CHARACTERISTICS

A linearized model of prestressed elastic body vibrations is described in terms of the nonsymmetric Piola stress tensor, and a weak statement of the original problem is given. With the help of the Lagrange variational principle, we construct a statement of the problem of steady axisymmetric oscillations of a thin-walled (shell-like) cylinder with variable material properties in the presence of an inhomogeneous prestress field. The motion equations, essential and natural boundary conditions are formulated. Integral characteristics are introduced that average the change in prestresses and material properties over the shell thickness. On the basis of the model presented, the problem on steady-state vibrations of a functionally graded prestressed cylindrical shell is numerically investigated via the shooting method; the influence of the laws of change in material modules and prestress components on dynamic characteristics (e.g., amplitude-frequency characteristics, natural vibration frequencies) is analyzed, a comparative analysis of the solutions is carried out depending on the thin-walled parameter. For the considered cylindrical shell with axial inhomogeneity, based on the acoustic sounding data, we study the inverse problem of restoring two laws of prestress inhomogeneity characterizing the nonuniform initial stress-strain state of tension or inflation. As additional information, we consider the measurement data of the displacement components on the cylinder's surface, given in a set of points at a certain frequency of steady-state oscillations; in such a case, the material characteristics are considered to be known and may depend on the axial coordinate, which makes it possible to set an arbitrary functional gradient along the axis of the cylinder. The mode of probing loading is determined by specifying the traction type and oscillation frequency. Explicit formulas for the desired laws of prestress inhomogeneity are obtained, and computational experiments are carried out to restore them. A high accuracy of reconstruction is revealed far from the ends of the cylinder when probing at a frequency in the vicinity of the first resonance.

Method for weak zones location at the coal-bed – host rock joint relative to the problem of sudden outbursts: theory and laboratory experiment

Within the framework of a geomechanical model that describes the deformation of a rock mass during the subhorizontal coal-bed extraction, the mechanism for the formation and implementation of a sudden outburst is substantiated: as working face gets close to the weak zone of coal-bed – host rock joint, areas of tensile stresses arise, which creates the prerequisites for face space spalling and coal loss with methane. The inverse problem of determining the conditions at the horizontal boundaries of a coal-bed is formulated and solved using tomography data (longitudinal wave velocity V distribution) and the empirical dependence of V on the mean normal stress σ. Lab tests results on stepwise compression of parallelepipeds made of artificial geomaterials are presented. Tomography of the specimens was performed by acoustic sounding data, and the distribution of velocities V* was found. Using the pre-established empirical dependence V(σ) for geomaterial, the distribution σ*=V-1(V*) in the specimen was calculated, which served as input data for inverse problem of determining the shear stresses σxy at the “specimen faces – press platens” joints. Lab data inversion confirmed the possibility of identifying weak zones of the boundaries where σxy=0. These zones are associated with probable nucleus of failure and sudden outbursts.

Localization the discontinuity lines of bottom scattering coefficient according to acoustic sounding data

Localization the discontinuity lines of bottom scattering coefficient according to acoustic sounding data

Localization of the Discontinuity Lines of the Bottom Scattering Coefficient According to Acoustic Sounding Data

Localization of the Discontinuity Lines of the Bottom Scattering Coefficient According to Acoustic Sounding Data

ЗАДАЧА О РАСПРОСТРАНЕНИИ АКУСТИЧЕСКИХ ВОЛН В ПОРИСТОЙ СРЕДЕ, НАСЫЩЕННОЙ ПУЗЫРЬКОВОЙ ЖИДКОСТЬЮ

In many cases, formation fluids contain gas. For example, a gas-liquid mixture in a porous medium is formed during acid treatment of low-permeability zones, during water-gas stimulation of reservoirs, etc. Therefore, it seems relevant to take into account the presence of gas bubbles when studying wave processes in porous media saturated with liquid. In this work, the propagation of acoustic waves in a porous medium saturated with a gas-liquid mixture is theoretically investigated taking into account the interfacial forces of interaction between the liquid and the matrix, and heat transfer between the gas and the liquid. A general system of equations and physical relations is written, which describes the propagation of waves in a porous medium filled with bubble liquid. A dispersion relation is obtained that describes the dependence of the complex wave vector on the frequency, on the basis of which the dependence of the phase velocity and attenuation coefficient on the frequency for “fast” and “slow” waves is investigated. The calculation results make it possible to evaluate the effect of gas bubbles on the propagation of sound waves in a porous medium saturated with bubble liquid. In addition, the results of the work can be used to interpret the data of acoustic sounding of porous media.

On the Determination of the Mechanical Characteristics of Rod Elements Made of Functionally Graded Materials

The determining problem of the variable characteristics of an elastic rod made of a functionally graded material based on acoustic sounding data is considered. The amplitude-frequency characteristics of the rod during longitudinal and bending vibrations are used as additional information. A system of nonlinear integral equations is derived, the solution of which is based on an iterative scheme. The conditions under which the reconstruction is carried out in a unique way are presented. The results of computational experiments are discussed.

Natural stress estimation by solving inverse problem using acoustic sounding data

Under consideration is the approach allowing quantitative estimation of natural stress field components in the vicinity of underground objects based on solution of an inverse boundary-value problem using the data on acoustic sounding in an extended mine working. To ensure solvability of an inverse problem, the optimal sonic transmitter–receivers positioning and the limiting nominal error of measurements are determined. The objective function is set as a root-mean-square difference between the theoretical and actual head P-wave arrival times at the receivers; unimodelity of the objective function is illustrated using synthetic input data.

Determination of stress state in coal seam based on inverse problem solution using acoustic sounding data

The paper presents an algorithm for calculating the horizontal, vertical and tangential stresses in a horizontal coal seam lying between galleries. These stresses are expressed in terms of the Airy function, which satisfies a homogeneous biharmonic equation. For its numerical solution it is necessary to set boundary conditions. Practical limitations do not allow us to determine the tangential stresses on horizontal boundaries of the coal seam. Calculations of stresses are proposed to be carried out in two steps. The first step is to solve the inverse problem for the biharmonic equation to find unknown tangential stresses on horizontal boundaries of the coal seam. The inverse problem is solved by minimizing the residual functional. Its strong convexity is proved, which implies the existence and uniqueness of the solution of the inverse problem. The second step is to solve the boundary value problem for the biharmonic equation to calculate stresses in the coal seam. The result of a numerical experiment is presented.

Results of Acoustic Diagnostics of Atmospheric Boundary Layer in Estimation of the Turbulence Effect on Laser Beam Parameters

The coherence length and possible broadening of a laser beam in the atmospheric boundary layer under the effect of random inhomogeneities of the refractive index are estimated from experimental data of remote acoustic sounding. The possibility of significant loss of coherence and noticeable broadening of the laser beam due to turbulence in nighttime are noted.

ANALYSIS OF METHODS FOR WIND SHEAR DETECTION IN AREA OF AIRPORTS BY DATA OF ATMOSPHERE ACOUSTIC SOUNDING

ANALYSIS OF METHODS FOR WIND SHEAR DETECTION IN AREA OF AIRPORTS BY DATA OF ATMOSPHERE ACOUSTIC SOUNDING

Estimating helicity in the atmospheric boundary layer from acoustic sounding data

Distributions of the velocity-field helicity in the atmospheric boundary layer have been obtained from acoustic sounding data. The helicity of large-scale motions (0.3–0.6 m/s2) exceeds (by an order of magnitude) its independently measured turbulent values, which are close to helicity averaged over the layer (0.02–0.12 m/s2). In the absence of strong convection, there is good correlation between helicity and wind velocity squared at upper sounding levels of 400 to 600 m.

Space and time variations in the fine structure of the upper atmosphere according to acoustic sounding data

The results of studying variations in the fine layered structure of the upper atmosphere (heights of 20–140 km) according to data obtained from acoustic sounding within the range of infrasonic waves are given. The sources of infrasounds were surface explosions equivalent to 10 kg to 70 t of TNT. These explosions were set off in different seasons in different regions of Russia. Experimental data obtained in 1981–2011 have been analyzed. It has been found that the fine structure in the form of vertically distributed layered formations occurs in the upper atmosphere in all seasons. Moreover, the vertical distribution of both air-temperature and wind-velocity inhomogeneities in the upper atmosphere may be invariable over a time interval of no less than several hours. It has also been found that, throughout the entire atmospheric thickness from the stratopause to the lower thermosphere heights (up to 140 km), the instantaneous height distribution of layered air-temperature and wind-velocity inhomogeneities may remain almost unchanged during a time interval of no less than 20 min.

Acoustic method for defining the stress state of a rock massif based on solution of the seismic inverse problem

A method for estimating the stress–strain state of a rock massif in the vicinity of underground facilities is substantiated. This method is based on solution of the boundary inverse problem of defining the components of an external stress field from the acoustic sounding data. The acoustic sounding data used are the arrival times of diving head longitudinal waves, recorded in a long mine shaft. Numerical experiments have revealed the optimal arrangement of the recording network and the limited relative error in the input data, which, taken together, provide for solvability of the inverse problem.

Wind regime in the lower atmosphere over Moscow from the long-term acoustic sounding data

Presented are the results of the sounding of the lower atmospheric 500-meter layer for the period of 2004–2012 carried out at the Meteorological Observatory of the Moscow State University (MSU) with the MODOS Doppler acoustic radar (sodar) produced by METEK (Germany). Discussed is the methodological basis of the sodar wind data analysis. It is demonstrated that in the air layer up to 200 m the maximum values in the annual course of the wind speed are observed more often in autumn and winter, and the minimum values, in summer; this is associated with the fact that during the cold period of the year Moscow is often located in the zones of intense gradient currents. The diurnal course of the wind speed is characterized by the daytime maximum and night-time minimum in the layer up to 40–60 m from the surface; it is poorly pronounced and characterized by the minimum in the morning in the layer of 80–120 m; and the daytime minimum and night-time maximum are observed above 140–160 m. The layer from 80 to 120 m approximately corresponds to the height of the wind rotation. The amplitude of diurnal variations of the wind speed increases from 0.3 m/s at the height of 7 m and 0.6 m/s at the height of 15 m, to 4.5 m/s at the height of 400 m; however, its secondary minimum (0.5 m/s) associated with the rotation height is registered at the altitude of 80 m. The statistical relationship between the wind speed and surface air temperature is direct during the cold season, inverse during the warm season, and is absent in April and October. The average maximum wind speed over Moscow for ten minutes in the layer up to 500 m from the surface reaches 30–35 m/s in some cases if two conditions concur: the capital is located on the periphery of vast pressure formations (usually of deep cyclones) and the local low-level jet stream is present in the wind profile.

Identifying the inhomogeneous properties of an orthotropic elastic layer

A scheme is proposed for reconstructing inhomogeneously thick elasticity modules of an orthotropic layer from acoustic sounding data. The problem of reconstruction has been reduced to stepwise reconstruction of the functions characterizing the elasticity modules, based on iteration regularization and A.N. Tikhonov’s regularization method, which utilize analysis of the averaged characteristics. A computer experiment is performed for different inhomogeneity layers, the effective frequency sounding regions for identification are revealed, and various aspects of numerical realization are discussed.

Comparison of wind measurements by means of industrially produced sodar and high-altitude meteorological mast in Obninsk

The real characteristics of the MFAS sodar industrially produced by Scintec AG (Germany) are given. The paper presents a wider range of altitudes as compared with the papers published before as a result of using the meteorological mast with the height of 310 m and longer duration of practically continuous testing embracing different weather conditions in the period from July to November 2008. During the comparison, the 10-min averaging time for the wind speed and direction is used. The comparison of the data of acoustic sounding and contact measurement methods indicates that the sodar provides reliable information on the vertical profiles of average wind speed within the considered altitude range up to 300 m except the cases of heavy rainfalls and low wind speed.

Temporal dynamics of longitudinal and transverse velocity structure functions retrieved from the data of acoustic sounding

Temporal dynamics of vertical profiles of the longitudinal and transverse velocity structure functions and characteristics retrieved using an original procedure from regular measurements of vertical profiles of the wind velocity vector with a minisodar operating at a frequency of 4900 Hz is discussed. It is established that the structure functions first increase with the separation of the observation points and then are saturated; moreover, in agreement with the data available from the literature, the longitudinal velocity structure function is much greater than the transverse one. The altitude behavior of the velocity structure characteristic is well described by a z −2/3 dependence predicted theoretically. In this case, the structure function calculated from one-point measurements of the vertical wind velocity component exceeds the corresponding structure function retrieved for the vertical separation of the observation points. This is also in agreement with generalizations from the theory of isotropic turbulence.

Acoustic evidence of a Baltic Ice lake drainage debrite in the northern Baltic Sea

The sudden drainage of the Baltic Ice Lake (BIL) at the end of the Younger Dryas Chron was one of the major events within the Pleistocene/Holocene boundary in Scandinavia. Thus far the effects it might have had on sedimentary environments have been inadequately recorded outside of central and southern Sweden. In the present study, high-quality acoustic sounding data was used to examine and describe possible traces of the event from the north eastern Baltic proper and Gulf of Finland sediments. Five acoustic facies were identified; two of them bearing frequent indications of sediment deformation, slumping, sliding and homogenization. The lower deformation zone is in the glacial clay deposited in the ice-proximal environment, the middle zone in the ice-distal glacial clay and the upper zone in late-glacial clay. We suggest that the middle deformation unit may have basin-wide significance because it represents a debrite system originating from sediment instability due to the sudden water-level drop associated with the BIL drainage at the transition of the Younger Dryas/Preboreal Chrons.