Elastic Solid Medium Research Articles

Internal absorbing boundary conditions for closed-aperture wavefield decomposition in solid media with unknown interiors.

We present a method to create an internal numerical absorbing boundary within elastic solid media whose properties are largely unknown and use it to create the first wavefield separation method that retrieves all orders of outgoing elastic wavefield constituents for real data recorded on a closed free surface. The recorded data are injected into a numerical finite-difference (FD) simulation along a closed, transparent surface, and the new internal numerical absorbing boundary condition achieves high attenuation of the ingoing waves radiated from the injection surface. This internal wave absorption enables the data injection to radiate all outgoing waves for experimental domains that include arbitrary unknown scatterers in the interior. The injection-absorption-based separation scheme is validated using three-dimensional (3D) synthetic modeling and a real data experiment acquired using a 3D laser Doppler vibrometer on a granite rock. The wavefield separation method forms a key component of an elastic immersive wave experimentation laboratory, and the ability to numerically absorb ingoing scattered energy in an uncharacterized medium while still radiating the true outgoing energy is intriguing and may lead to other development and applications in the future.

Rayleigh-Type Waves in a Rotating Fiber-Reinforced Half Space under the Action of Magnetic Field, Gravity and Surface Stress

The aim of the present article is to analyze the propagation of Rayleigh waves in a rotating fiber-reinforced electrically conducting elastic solid medium under the influence of surface stress, magnetic field and gravity. The magnetic field is applied in such a direction that the problem can be considered as a two dimensional one. The wave velocity equation for Rayleigh waves has been obtained. In the absence of gravity field, surface stress, rotation and fiberreinforcement, the frequency equation is in complete agreement with the corresponding classical results. The effects on various subjects of interest are discussed and shown graphically. Comparisons are made with the corresponding results in absence of surface stress

Time scale disparity yielding acoustic nonreciprocity in a two-dimensional granular-elastic solid interface with asymmetry.

We study nonreciprocal wave transmission across the interface of two dissimilar granular media separated by an elastic solid medium. Specifically, a left, larger-scale and a right smaller-scale granular media composed of two-dimensional, initially uncompressed hexagonally packed granules are interfacing with an intermediate linearly elastic solid, modeled either as a thin elastic plate or a linear Euler-Bernoulli beam. The granular media are modeled by discrete elements and the elastic solid by finite elements assuming a plane stress approximation for the thin plate. Accounting for the combined effects of Hertzian, frictional and rotational interactions in the granular media, as well as the highly discontinuous interfacial effects between the (discrete) granular media and the (continuous) intermediate elastic solid, the nonlinear acoustics of the integrated system is computationally studied subject to a half-sine shock excitation applied to a boundary granule of either the left or right granular medium. The highly discontinuous and nonlinear interaction forces coupling the granular media to the elastic solid are accurately computed through an algorithm with interrelated iteration and interpolation at successive adaptive time steps. Numerical convergence is ensured by monitoring the (linearized) eigenvalues of a nonlinear map of interface forces at each (variable) time step. Due to the strong nonlinearity and hierarchical asymmetry of the left and right granular media, time scale disparity occurs in the response of the interface which breaks acoustic reciprocity. Specifically, depending on the location and intensity of the applied shock, propagating wavefronts are excited in the granular media, which, in turn, excite either (slow) low-frequency vibrations or (fast) high-frequency acoustics in the intermediate elastic medium. This scale disparity is due to the size disparity of the left and right granular media, which yields drastically different wave speeds in the resulting propagating wavefronts. As a result, the continuum part of the interface responds with either low-frequency vibrations-when the shock is applied to the larger-scale granular medium, or high-frequency waves-when the shock is applied to the smaller-scale granular medium. This provides the fundamental mechanism for breaking reciprocity in the interface. The nonreciprocal interfacial acoustics studied here apply to a broad class of asymmetric hybrid (discrete-continuum) nonlinear systems and can inform predictive designs of highly effective granular shock protectors or granular acoustic diodes.

Generalized photo-thermo-microstretch elastic solid semiconductor medium due to the excitation process

A novel model in the photo-thermoelasticity theory with microstretch properties is studied. The plasma-elastic-thermal plane waves are propagated in a linear isotropic generalized photo-thermo-microstretch elastic semiconductor solid medium. The photothermal excitation occurs in the context of the microinertia of the microelement process during two-dimensional (2D) deformation. The harmonic wave techniques are used to get the solutions for the basic variables. The analytical solution of the main physical fields; carrier intensity, normal displacement components, temperature, stress load force, microstress and tangential coupled stress can be obtained. Some graphics illustrated when using the plasma, thermal and mechanical load boundary conditions are applied at the outer free surface of the elastic medium. Some semiconductor materials, as silicon (Si) and Germanium (Ge), are used to make the numerical simulation and some comparisons in different thermal memories are made. The main physical variables with new parameters are discussed theoretically and shown graphically.

Impact area and debonding line detection assessment by cross-correlation analysis and distributed sensing

Debonding at two components interface (f.i., skin & stringer) is a common defect of composite stiffened structures. It may result from inefficient manufacturing or impacts from foreign objects. Discontinuities within an elastic solid medium under mechanical loads may cause local anomalies in the strain field. On this basis, the current work investigates disbonding at skin/stringer interface of an aeronautical plate, generated by low/medium energy impacts. Distributed fiber optics records longitudinal strain values; data are then elaborated by a methodology using different deformation-based features providing Local High Edge Observation (LHEO) in both time and space domains. Cross correlation is implemented to improve signal to noise ratio. Proposed LHEO algorithm proves its capability to detect impact area and occurred skin-stringer debonding, without reference to applied loads or a certain baseline. A dedicated Matlab routine elaborates the output further, with the aim of visualizing and estimating impact region extension.

Strain-based health indicators for the structural health monitoring of stiffened composite panels

A common defect of composite-stiffened structures is the disbond at the interface between the two constituents (skin/stringer), as a result of inefficient manufacturing process or foreign object impacts in service. Generally, discontinuities within the volume of an elastic solid medium, subjected to mechanical load, cause anomalies on the strain field in the near vicinity of the discontinuity. Utilizing this observation, this work investigates the effect of artificially induced disbonds in the skin/stiffener interface of an aeronautical-grade generic element. A structural health monitoring methodology is developed, leveraging on numerically simulated strains along the stringer foot which aims to assess the health state of the panel as the size of the disbonds increases. The study is implemented using a parametric finite element model generating various disbond scenarios. Longitudinal strain values are acquired at the exact points where in reality actual fiber Bragg grating sensors will be located. Two types of commonly utilized strain-based health indicators are evaluated, and their drawbacks are revealed and discussed. A new health indicator is proposed that proves its capability to monitor growing disbonds while being both load- and baseline-independent.

RETRACTED: Flexural wave dispersion of nonlocal bi-Helmholtz-type stress gradient theory

In this study, harmonic wave propagation in elastic solid media is investigated. The accuracy of the proposed nonlocal bi-Helmholtz-type stress gradient theory with two nonlocal parameters is evalu...

Multiple scattering of plane compressional waves by two cylindrical core-shell inclusions with surface effect

Elastic wave propagation at nanoscale exhibits some special properties due to surface/interface effect. Scattering of plane compressional waves (P-wave) by two nanocylindrical core-shell inclusions in an elastic solid medium is investigated in this study. The wave fields of the core-shell structure are given by the eigenfunction expansion method and Graf addition theorem. The effect of factors such as surface energy, center distance, and thickness of the liner under different incident wave frequencies has been discussed. The results show that as the radius of the core-shell inclusions shrinks to nanometers, surface energy becomes a dominant factor that affects the scattering of elastic waves. The interaction between two core-shell inclusions in multiple scattering phenomena is discussed at the same time.

Couple Stress Impacton S-Wavesin an Anisotropic Pre-Stressed Medium under Gravity and Magnetic Field

The gravity fieldand magnetic field impact with the inclusion of couple stress s r onshear waves in a transversely isotropic elastic solid medium is studied. Thedispersion equations for the particular problem have been obtained. Severalparticular cases are also examined. The numerical calculations are carriedout for specific rigidity parameter A, density parameter C, anisotropic factor N , initial stress parameter P , gravity parameter G, magnetic fieldparameter H , couple stress parameter  as well as wave number κ and theoutcomes are visually represented by graph.

Математическое моделирование влияния релаксационных процессов на температурные поля в упругом полупространстве

The article examines the relaxation processes that occur in an elastic solid medium when it is heated and cooled, especially their influence on the temperature field. Besides, we considered in this paper the heat equation of parabolic type arising in the theory of thermal conductivity for different modes of heating the border. We present a solution of the boundary value problem of nonstationary heat conduction for an infinite plate with the following regimes of loading the boundaries: a single slow temperature change at the border, a single instantaneous temperature variation at the border, and, finally, multiple instantaneous changes of temperature at the border. In order to solve these three heat problems, they were brought to a dimensionless form. Then the operational calculus method was applied. The essence of the method consists in the following. According to the obtained analytical solutions three-dimensional graphics characterizing the relaxations processes were built in the computer algebra system Wolfram Mathematica for different ranges of the Fourier criterion.

Scattering of Stationary and Non-Stationary Sound by Ideal and Elastic Scatterers, Placed near Interface of Media, in Underwater Sound Channel and in Plane Waveguide

In the review we obtained a strict solution of problem of the sound diffraction by an elastic spheroidal shell, located near the interface of a liquid medium with an elastic solid medium. Calculation of the scattered sound field for ideal bodies (a spheroid and an elliptical cylinder) is performed. These bodies are placed on the interface between the liquid and the ideal medium; it is shown, that the main role is played not by interaction of scatterers (real and imaginary), but by interference of their scattered fields. The spectrum of the scattered impulse signal for the body in an underwater sound channel is calculated. It is shown, that at large distances the dominante role is played by the spectral characteristic of the channel itself. Based on the method of imaginary sources and imaginary scatterers, the solution of the current study is to solve the diffraction problem of sound pulse signals at ideal (soft) prolate spheroid, which is put in the plane waveguide with the hard elastic bottom. In the work, it is proved that with such a formulation of problems eliminated, there exists possibility of using the method of normal waves because pulses are bundies of energy and can therefore only be distributed to the group velocity which is inherent in just the method of imaginary sources. Calculations made in the article showed that imaginary sources with small numbers exert the effect of total internal reflection, as the result of the reflection coefficient V by the hard elastic bottom which is complex and the real part of V is close to 1.0 which corresponds to V absolutely hard bottom. Found sequences of reflected pulses for the elastic hard bottom and the absolutely hard bottom floor confirmed this approach. In the final part of the article, on the basis of the received results, a solution (the method integral equations) is given, which is a much more complex problem of the diffraction at the elastic non-analytical scatterer, put in the plane waveguide with the hard elastic bottom.

Reflecting and scattering of acoustic wave from sea ices

In order to build an efficient underwater acoustic sensor network in the Arctic Ocean environment, transmission characteristics of under-ice acoustic channels need comprehensive understanding. The reflecting and scattering of acoustic waves from sea ices have great influences on under-ice acoustic channels. Both topology and structure of sea surface ices are very complex and variable. The physical dimension, acoustic property and interface roughness of sea ices depend not only on local environment, but also on climate and formation time. Therefore, it is of great significance to develop a model of reflecting and scattering of acoustic waves from sea ices for investigating the sound propagation in the under-ice environment. Assuming that sea ices are a multi-layered elastic solid medium and the ice-water interface is rough and satisfies the boundary condition of perturbation, we develop a system of linear equations to solve the coherent reflection coefficient of the incident sound wave from water to sea ice. The coherent reflection coefficient is a function of the frequency of sound wave and incident grazing angle, and is numerically evaluated. The influences of ice thickness and ice-water interface roughness on the coherent reflection coefficient are analyzed. Furthermore, the method of calculating scattering coefficient by using the power spectrum density of the scattering field is introduced. The scattering coefficient as a function of the scattering grazing angle is numerically evaluated. The influences of ice thickness and ice-water interface roughness on scattering coefficient are analyzed. The results show that both the coherent reflection coefficient and the scattering coefficient are dependent on the frequency of acoustic wave, ice thickness and grazing angle. The coherent reflection coefficient is close to 1.0 and the scattering coefficient is less than 0.01 when incident grazing angle is less than 15°. In addition, the frequency of acoustic wave and ice thickness have weak influences on them. However, the frequency of acoustic wave and ice thickness have significant influences on the coherent reflection coefficient and the scattering coefficient when the incident grazing angle is big, say, greater than 30°. In general, the thicker the ice is, the smaller the coherent reflection coefficient and the scattering coefficient are. The coherent reflection coefficient is less than 0.18 when the ice thickness is greater than 10.0 m and the frequency of acoustic waves is greater than 2 kHz. The ice-water interface roughness has great influences on both the coherent reflection coefficient and the scattering coefficient. The rougher of the ice-water interface is, the smaller the coherent reflection coefficient is, and the bigger the scattering coefficient is.

Role of viscoelasticity in instability in plane shear flow over a deformable solid

The stability of the flow of a viscoelastic fluid over a deformable elastic solid medium is reviewed focusing on the role played by the fluid elasticity on the earlier known instability modes for the Newtonian fluids. In particular, two classes of modes are emphasized: the viscous mode for the creeping flow, and the wall mode for high Reynolds number flow. The flow geometry is restricted to plane Couette flow of fluid supported on elastic substrate of finite thickness. The viscoelastic fluid is described using the Oldroyd-B model and the dynamics of the deformable solid continuum is described by either Hookean or neo-Hookean elastic model. In the limit of \(Re \rightarrow 0\), the introduction of fluid elasticity delays the onset of instability and for sufficiently viscoelastic fluid with dilute polymer concentration, the instability is suppressed rendering the flow stable. For concentrated solution and polymer melt, the instability persists, but with higher value of critical shear rate than for the Newtonian fluid, indicating stabilizing role of fluid elasticity in creeping flow regime. However, for high Reynolds number flow of dilute polymer solution, the polymer addition plays a destabilizing role for wall modes, indicated by reduction in critical Reynolds number by an order of magnitude.

Wall-mode instability in plane shear flow of viscoelastic fluid over a deformable solid.

The linear stability analysis of a plane Couette flow of an Oldroyd-B viscoelastic fluid past a flexible solid medium is carried out to investigate the role of polymer addition in the stability behavior. The system consists of a viscoelastic fluid layer of thickness R, density ρ, viscosity η, relaxation time λ, and retardation time βλ flowing past a linear elastic solid medium of thickness HR, density ρ, and shear modulus G. The emphasis is on the high-Reynolds-number wall-mode instability, which has recently been shown in experiments to destabilize the laminar flow of Newtonian fluids in soft-walled tubes and channels at a significantly lower Reynolds number than that for flows in rigid conduits. For Newtonian fluids, the linear stability studies have shown that the wall modes become unstable when flow Reynolds number exceeds a certain critical value Re(c) which scales as Σ(3/4), where Reynolds number Re=ρVR/η,V is the top-plate velocity, and dimensionless parameter Σ=ρGR(2)/η(2) characterizes the fluid-solid system. For high-Reynolds-number flow, the addition of polymer tends to decrease the critical Reynolds number in comparison to that for the Newtonian fluid, indicating a destabilizing role for fluid viscoelasticity. Numerical calculations show that the critical Reynolds number could be decreased by up to a factor of 10 by the addition of small amount of polymer. The critical Reynolds number follows the same scaling Re(c)∼Σ(3/4) as the wall modes for a Newtonian fluid for very high Reynolds number. However, for moderate Reynolds number, there exists a narrow region in β-H parametric space, corresponding to very dilute polymer solution (0.9≲β<1) and thin solids (H≲1.1), in which the addition of polymer tends to increase the critical Reynolds number in comparison to the Newtonian fluid. Thus, Reynolds number and polymer properties can be tailored to either increase or decrease the critical Reynolds number for unstable modes, thus providing an additional degree of control over the laminar-turbulent transition.

Gas bubble dynamics in soft materials.

Epstein and Plesset's seminal work on the rate of gas bubble dissolution and growth in a simple liquid is generalized to render it applicable to a gas bubble embedded in a soft elastic solid. Both the underlying diffusion equation and the expression for the gas bubble pressure were modified to allow for the non-zero shear modulus of the medium. The extension of the diffusion equation results in a trivial shift (by an additive constant) in the value of the diffusion coefficient, and does not change the form of the rate equations. But the use of a generalized Young-Laplace equation for the bubble pressure resulted in significant differences on the dynamics of bubble dissolution and growth, relative to an inviscid liquid medium. Depending on whether the salient parameters (solute concentration, initial bubble radius, surface tension, and shear modulus) lead to bubble growth or dissolution, the effect of allowing for a non-zero shear modulus in the generalized Young-Laplace equation is to speed up the rate of bubble growth, or to reduce the rate of bubble dissolution, respectively. The relation to previous work on visco-elastic materials is discussed, as is the connection of this work to the problem of Decompression Sickness (specifically, "the bends"). Examples of tissues to which our expressions can be applied are provided. Also, a new phenomenon is predicted whereby, for some parameter values, a bubble can be metastable and persist for long times, or it may grow, when embedded in a homogeneous under-saturated soft elastic medium.

Propagation of Rayleigh waves in non-homogeneous orthotropic half space elastic media under the effect of magnetic field

The influence of magnetic field on the propagation of Rayleigh waves in an inhomogeneous, orthotropic elastic solid medium has been discussed. The method of variable separation of is used to find the frequency equation of the surface waves. The obtained dispersion equations are in agreement with the classical results when magnetic field and non-homogeneity are neglected.

Propagation of Rayleigh waves in non-homogeneous orthotropic half space elastic media under the effect of magnetic field

The influence of magnetic field on the propagation of Rayleigh waves in an inhomogeneous, orthotropic elastic solid medium has been discussed. The method of variable separation of is used to find the frequency equation of the surface waves. The obtained dispersion equations are in agreement with the classical results when magnetic field and non-homogeneity are neglected.

Surface Waves in Fibre-Reinforced Anisotropic Solid Elastic Media under the Influence of Gravity

The aim of the present paper is to investigate surface waves in an anisotropic, elastic solid medium under the influence of gravity. First, a theory of generalised surface waves was developed and then it was employed to investigate particular cases of waves, viz., Stoneley and Rayleigh, Love type. The wave velocity equations were obtained for different cases and they are in well agreement with the corresponding classical result, when the effect of gravity, viscosity as well as parameters for fibre-reinforcement of the material medium are ignored.

Scholte waves on fluid-solid interfaces by means of an integral formulation

The present work shows the propagation of Scholte interface waves at the boundary of a fluid in contact with an elastic solid, for a broad range of solid materials. It has been demonstrated that by an analysis of diffracted waves in a fluid it is possible to infer the mechanical properties of the elastic solid medium, specifically, its propagation velocities. For this purpose, the diffracted wave field of pressures and displacements, due to an initial wave of pressure in the fluid, are expressed using boundary integral representations, which satisfy the equation of motion. The source in the fluid is represented by a Hankel’s function of second kind and zero order. The solution to this wave propagation problem is obtained by means of the Indirect Boundary Element Method, which is equivalent to the well-known Somigliana representation theorem. The validation of the results is carried out by using the Discrete Wave Number Method and the Spectral Element Method. Firstly, we show spectra of pressures that illustrate the behavior of the fluid for each solid material considered, then, we apply the Fast Fourier Transform to show results in time domain. Snapshots to exemplify the emergence of Scholte’s waves are also included.

The Process Analysis of Commonly Used T-Shaped Tube Compound Bulging Media

As the important bearing structure of aircraft high pressure systems, the properties of air ducts are directly related to the flight safety. In order to improve air ducts formation quality and reduce the forming processing cost, improving the tube bulging processes is needed. The key technology of bulging processes is one of the choices of dielectric bulging, through to the liquid medium, plastic medium, the elastic medium, viscous medium and solid medium forming technology characteristic analysis, this study describes the advantages and disadvantages of various media.