Propagation Of Compressional Waves Research Articles

The development of shear and compression elastic moduli in curing epoxy adhesives measured using non-contact ultrasonic transducers

Thin epoxy resin adhesive samples were ultrasonically measured during cure using normal incidence radially polarized shear wave electromagnetic acoustic transducers (EMATs). Although the EMATs used predominantly generated shear waves (SH) they were designed so that they also generated/detected compression waves allowing the simultaneous measurement of shear and compression wave propagation through a curing polymer in a non-contact regime. The adhesive thickness examined in the experiments was approximately 1 mm, which was optimal for experimental measurement using our apparatus. The epoxy resin systems (rapid cure and a standard cure) described in this paper were supplied in a two-part cartridge form, mixed by injection through a mixing nozzle. Five different samples have been investigated at this stage, and there appears to be a fundamental difference in the way that the elastic moduli develop in the rapid cure and longer cure time epoxies. This can possibly be explained in terms of the reaction kinetics and the development of the structure on a microscopic scale. The rapid cure systems initially develop a shear elastic modulus at a faster rate which suddenly decreases at approximately the same time that the temperature of the adhesive reaches its maximum value during the exothermic reaction. This is consistent with an initial rapid reaction rate which is then greatly reduced as the remaining un-reacted polymer chains require a finite time to move into a position where they can react and join the network.

Surface response of a viscoelastic medium to subsurface acoustic sources with application to medical diagnosis.

The response at the surface of an isotropic viscoelastic medium to buried fundamental acoustic sources is studied theoretically, computationally and experimentally. Finite and infinitesimal monopole and dipole sources within the low audible frequency range (40-400 Hz) are considered. Analytical and numerical integral solutions that account for compression, shear and surface wave response to the buried sources are formulated and compared with numerical finite element simulations and experimental studies on finite dimension phantom models. It is found that at low audible frequencies, compression and shear wave propagation from point sources can both be significant, with shear wave effects becoming less significant as frequency increases. Additionally, it is shown that simple closed-form analytical approximations based on an infinite medium model agree well with numerically obtained "exact" half-space solutions for the frequency range and material of interest in this study. The focus here is on developing a better understanding of how biological soft tissue affects the transmission of vibro-acoustic energy from biological acoustic sources below the skin surface, whose typical spectral content is in the low audible frequency range. Examples include sound radiated from pulmonary, gastro-intestinal and cardiovascular system functions, such as breath sounds, bowel sounds and vascular bruits, respectively.

Method to Simulate Generation of Compression Wave Inside a Tunnel at Train Entry with a Simple Geometry Model (Influence of the Offset of Train Axis and the Ground Plane)

A method to simulate the generation of tunnel compression wave at train entry is investigated by using a simple geometry model. The tunnel is represented by a circular and the train by an axisymmetric body which has a cross-sectional area distribution equivalent to that of an actual train. In order to simulate the entry into a double tracked tunnel, the train center axis is positioned offset from the tunnel axis and the effect of the ground plane is treated by the mirror image method. Analysis and model experiments are performed to confirm the validity of the present method to use a simple geometry model. The difference of the peak pressure gradient of the compression wave has turned out to be within a few percent between field measurements and model experiments.

Numerical and experimental investigation of wave dynamic processes in high-speed train/tunnels

Numerical and experimental investigation on wave dynamic processes induced by high-speed trains entering railway tunnels are presented. Experiments were conducted by using a 1:250 scaled train-tunnel simulator. Numerical simulations were carried out by solving the axisymmetric Euler equations with the dispersion-controlled scheme implemented with moving boundary conditions. Pressure histories at various positions inside the train-tunnel simulator at different distance measured from the entrance of the simulator are recorded both numerically and experimentally, and then compared with each other for two train speeds. After the validation of nonlinear wave phenomena, detailed numerical simulations were then conducted to account for the generation of compression waves near the entrance, the propagation of these waves along the train tunnel, and their gradual development into a weak shock wave. Four wave dynamic processes observed are interpreted by combining numerical results with experiments. They are: high-speed trains moving over a free terrain before entering railway tunnels; the abrupt-entering of high-speed trains into railway tunnels; the abrupt-entering of the tail of high-speed trains into railway tunnels; and the interaction of compression and expansion waves ahead of high-speed trains. The effects of train-tunnel configurations, such as the train length and the train-tunnel blockage ratio, on these wave processes have been investigated as well.

Attenuation or enhancement—a one-dimensional analysis on shock transmission in the solid phase of a cellular material

The characteristics of compressive shock wave propagation in the solid phase of a cellular material are studied in the present paper using a one-dimensional mass-spring model. The unique compressive stress–strain relation of a cellular material leads to several interesting observations on the characteristic of one-dimensional stress wave transmission in a cellular material, which are important for understanding the blast and impact mitigation and attenuation through a cellular material. Generally, cellular material attenuates impact- or blast-induced loads by cell collapse mechanism at low impact velocities or low pulse pressure intensities when the stress transmission in a cellular material is limited by the plateau stress before the densification stage starts. This feature leads to wide applications of cellular materials in structural crashworthiness design where low speed impact is considered as potential survivable scenarios. However, scattered information has shown that stress enhancement in cellular material may occur when an intensive loading is applied, which, in contrast to the stress attenuation function of a cellular material, could produce more severe damage on the protected structures. This phenomenon is studied qualitatively in the present paper using a one-dimensional spring-mass model.

Mindlin's problem for an anisotropic piezoelectric half–space with general boundary conditions

This paper considers Mindlin's problem in an anisotropic and piezoelectric halfspace with general boundary conditions, including 16 different sets of surface conditions. The Green's function due to...

111 単純な形状の模型を用いてトンネル突入時の圧縮波形成を模擬する方法(列車中心軸の偏心と地面の影響)

111 単純な形状の模型を用いてトンネル突入時の圧縮波形成を模擬する方法(列車中心軸の偏心と地面の影響)

Generation of Compression Waves by Simultaneously Imposing a Static Magnetic Field and an Alternating Current and Its Use for Refinement of Solidified Structure

A new generating method of compression waves in a liquid metal has been proposed in which a static magnetic field and an alternating current are simultaneously imposed. The theoretical expressions of intensities and distributions of pressure and velocity accompanied with the compression waves have been derived. The pressure change in liquid gallium excited by the method proposed here was measured under different intensities of the magnetic field and the alternating current. The measured pressures approximately agreed with the theoretical evaluation. The structure of a Sn–Pb alloy that was solidified under the imposition of the compression waves, was completely refined.

A three-dimensional model of the propagation of Alfvén waves through the auroral ionosphere: first results

The propagation of Alfvén waves in the auroral ionosphere is important in the determination of ground signatures of time-varying currents, in the formation of Pc1 compressional waves that can be ducted in the ionospheric waveguide, and in the development of field-aligned currents and parallel electric fields during auroral acceleration processes. This report presents the first results from a three-dimensional model of the linear propagation of these waves. In this model, the ionosphere is treated as a thin slab carrying Pedersen and Hall currents. The jump conditions across this boundary lead to the coupling of shear and compressional MHD modes at the ionosphere and also allow the ground signatures of these waves to be calculated within the context of the model. This model has been used to study this coupling and to illustrate the excitation and propagation of compressional MHD waves within the ionospheric waveguide. A new numerical scheme for the modeling of parallel electric fields is introduced and the excitation of resonance cone structures by narrow impulses is demonstrated.

DENSITY MAPPING OF CERAMIC TILES BY COMPRESSION-WAVE ULTRASOUND

A range of disc shaped ceramic powder compact samples with controlled densities were produced using manufacturing conditions that mimic those used for industrial tile manufacture. Ultrasonic compression-wave velocity measurements were made, and a straight-line relationship was seen to exist between the ceramic sample bulk density and velocity. This relationship can be used to measure density ultrasonically. This type of relationship for powder compacts has been explained before by incorporating the density or pore fraction dependence of Young's modulus into the expression which relates compressionwave propagation velocity to Young's modulus, density and Poisson's ratio. The dependence of Young's modulus on density in the wall tile material was found to deviate from the form assumed in the theory. However, when the range of densities considered is restricted to the range typically achieved industrially, the existing theory is found to be generally applicable. Using results from production line samples it is inferred that the most significant cause of density variations is the variability in the filling and pressing operation.

Wave propagation, stress relaxation, and grain-to-grain shearing in saturated, unconsolidated marine sediments

A linear theory of wave propagation in saturated, unconsolidated granular materials, including marine sediments, is developed in this article. Since the grains are unbonded, it is assumed that the shear rigidity modulus of the medium is zero, implying the absence of a skeletal elastic frame. The analysis is based on two types of shearing, translational and radial, which occur at grain contacts during the passage of a wave. These shearing processes act as stress-relaxation mechanisms, which tend to return the material to equilibrium after the application of a dynamic strain. The stress arising from shearing is represented as a random stick-slip process, consisting of a random succession of deterministic stress pulses. Each pulse is produced when micro-asperities on opposite surfaces of a contact slide against each other. The quantity relevant to wave propagation is the average stress from all the micro-sliding events, which is shown to be a temporal convolution between the deterministic stress, h(t), from a single event and the probability, q(t), of an event occurring between times t and t+dt. This probability is proportional to the velocity gradient normal to the tangent plane of contact between grains. The pulse shape function, h(t), is derived by treating the micro-sliding as a strain-hardening process, which yields an inverse-fractional-power-law dependence on time. Based on two convolutions, one for the stress relaxation from translational and the other from radial shearing, the Navier–Stokes equation for the granular medium is derived. In a standard way, it is split into two equations representing compressional and shear wave propagation. From these wave equations, algebraic expressions are derived for the wave speeds and attenuations as functions of the porosity and frequency. Both wave speeds exhibit weak, near-logarithmic dispersion, and the attenuations scale essentially as the first power of frequency. A test of the theory shows that it is consistent with wave speed and attenuation data acquired recently from a sandy sediment in the Gulf of Mexico during the SAX99 experiment. If dispersion is neglected, the predicted expressions for the wave speeds reduce to forms which are exactly the same as those in the empirical elastic model of a sediment proposed by Hamilton. On this basis, the concept of a “skeletal elastic frame” is interpreted as an approximate, but not equivalent, representation of the rigidity introduced by grain-to-grain interactions.

Gradient-dependent plasticity model and dynamic strain localisation analysis of saturated and partially saturated porous media: one dimensional model

Dynamic strain localisation in saturated and partially saturated porous media is investigated with a one-dimensional model in this paper. The porous medium is treated as a multiphase continuum, with the pores filled by water and air, this last one at atmospheric pressure. A gradient-dependent plasticity model is introduced to describe the plastic behaviour of the solid skeleton. Material instability due to the softening behaviour of the solid skeleton and the well-posedness of the initial value problem are studied. The advantages of the enhanced model are that the governing equations remain hyperbolic even in the softening regime and convergent solutions with mesh refinements are obtained. Moreover, the influence of permeability in the seepage process for the development of the localised zones is discussed. We find that the permeability plays an important part in the compressive wave propagation, but not in the shear wave cases. For numerical implementation of the present method, a parametric variational principle is introduced by which the original problem is reduced to a standard linear complementary problem in mathematical programming. The results of a one dimensional example are given to illustrate the efficiency of the techniques presented here.

Absorbing boundary and free-surface conditions in the phononic lattice solid by interpolation

We have recently developed a new lattice-Boltzmann-based approach for modelling compressional wave propagation in heterogeneous media, which we call the phononic lattice solid by interpolation (PLSI). In this paper, we propose an absorbing boundary condition for the PLSI method in which the microscopic reflection coefficients at the boundaries of a model are set to zero and viscous layers are added to the boundaries. Numerical simulation examples using the PLSI method and comparisons with exact solutions demonstrate that artificial boundary reflections can be almost completely eliminated when the incidence angle is less than approximately 70°, Beyond this angle, remanent artificial boundary reflections become visible. We propose four methods for modelling free-surface reflections in PLSI simu-lations. In the first three methods, special collision rules at a free surface are specified to take into account the effect of a free surface on quasi-particle movements (i.e. wave propagation) They are termed the specular bouncing, backward bouncing I, and combined bouncing methods. They involve quasi-particle reflections with a coefficient of − 1 and require the free surface to be located exactly along lattice nodes. For the fourth method, we modify the backward bouncing I model for the case when a free surface is located at any position along lattice links and thus term it the backward bouncing II model. It uses the reflection coefficient at the free surface to calculate the reflected number densities during PLSI simulations. Hence, the free surface is handled in the same way as an interface within a model. Numerical examples and comparisons with exact solutions show that these four methods used at the microscopic scale are all appropriate for modelling macroscopic waves reflected from free surfaces.

Recent advances in multicomponent processing

The evolution of 3-D multicomponent processing and collection methods has increased our information about reservoirs. Processing techniques now exist to generate a time or depth image of P-to-S converted waves (or C-waves) using ocean‐bottom sensors. These images can enhance reservoir characterization, especially when shallow gas clouds may inhibit compressional wave propagation.

Theory of compressional and transverse wave propagation in consolidated porous media

A theory of compressional and shear wave propagation in consolidated porous media (rocks) is developed by extending ideas already introduced in connection with unconsolidated marine sediments. The consolidated material is treated as an elastic medium which exhibits a specific form of stress relaxation associated with grain boundaries and microcracks. The stress relaxation, which is linear in the sense that it obeys superposition, shows hysteresis, as characterized by a material response function. Two linear wave equations are derived, one for compressional and the second for shear waves, from which expressions for the wave speeds and attenuations are established. In both cases, the attenuation is found to scale with the first power of frequency, consistent with many observations of attenuation in sandstones, limestones, and shales; the wave speeds show weak logarithmic dispersion. These expressions for the wave speeds and attenuations satisfy the Kronig–Kramers dispersion relationships, as they must if the response of the medium to disturbances is to be causal. Some comments are offered on the nature of the material response, notably that it appears to be primarily associated with grain-boundary interactions occurring at a molecular level, rather than being related to the macroscopic properties of the material, such as density or porosity.

Compressional MHD waves in the magnetosphere: A new approach

Dynamics of compressional MHD wave propagation is theoretically studied in the dayside and nightside magnetosphere. In order to analytically examine the MHD wave equation, we adopt the quantum mechanical approach which is often used in the problem of the Schrödinger's equation. The wave solutions are obtained for dayside and nightside Alfven speed profiles, respectively, without any arbitrary boundary condition at the magnetopause or the bow shock. The result shows that the previous cavity/waveguide models are found to be inappropriate for studying compressional wave properties in the magnetosphere. We discuss the role of virtual resonances which generally represent any possible compressional modes in the magnetosphere.

On the Formation of Discontinuities of Wave Fronts in a Saturated Granular Body

The paper deals with propagation of plane wave fronts in a solid with a non-linear relation between stress and deformation. The objective is to calculate the distance that a wave front covers before it loses continuity. The formulae derived for a general quasi-linear system of two equations are applied to the propagation of plane compression waves in dry and partially saturated granular bodies. In the case of a saturated body with gas bubbles, the influence of gas and capillary pressure on the stiffness of the body is taken into account. Numerical calculations relevant to soil mechanics are presented. For the numerical calculations a constitutive equation of the hypoplasticity theory for granular materials has been used.

Propagation of solitary compression waves in heterogeneous materials under high-speed loading

Based on the method of molecular dynamics, we investigated the special features of the passage of soliton-like waves, initiated by high-speed loading, through regions with a low atomic density. It is shown that the shape of these waves is mainly determined by the structure of a material region in which they propagate. The decrease in the amplitude of solitary waves is shown to be determined by the defect concentration. This effect is of interest from the viewpoint of developing the methods of monitoring the microdamage build-up in materials.

Use of ultrasonics to follow crack growth

Cubes made of steel fiber reinforced concrete (SFRC) were progressively sawed, while recording the ultrasonic parameters between the saw-cuts. The waves were analyzed in terms of ultrasonic wave velocity, peak amplitude and wave energy. Different relative positions between transducers and notch were considered. It was found that a relation between the ultrasonic parameters and the notch length could be drawn according to the layout of the transducers: the energy and amplitude drop once the portion of material between both transducers is diminished by sawing, whilst the velocity only changes once this whole portion of material has been cut out. The findings were then used to follow the crack growth of a SFRC beam during a bending test. The propagation of ultrasonic compression waves through the samples was recorded at regular time intervals during the tests. The interpretation of the signals was in this case complicated due to the facts that micro-cracking occurred, that the macro-crack was much thinner than a sawcut and that it was moreover bridged by fibres. It appeared that in this case both peak amplitude and energy dropped before the onset of a visible macro-crack, because of extensive micro-cracking, while the velocity only changed after considerable crack growth.

Dynamical aspects of various solitary waves and double layers in dusty plasmas

Employing quasipotential analysis, the Sagdeev potential equation has been derived in a multicomponent plasma consisting of free and trapped electrons and contaminated by the dust charged grains forming therein by the attachment of electrons to finite-size dust particles. Because of the free and trapped electrons in the dusty plasma, the plasma-acoustic wave exhibits the different features of various solitary waves. The Sagdeev potential equation, at a small-amplitude approximation, leads to the evaluation, by a proposed new formalism of a simple wave solution technique, of the new scenario of solitary wave propagation in a dusty plasma. It has been shown that the ordering of the nonisothermality in the dusty plasma also plays a unique role. In the case of a plasma with first-order nonisothermality, the Sagdeev potential equation derives the compressive solitary wave propagation, while for plasma with higher-order nonisothermality the method might fail to solve the Sagdeev potential equation and, thus, an alternate method is used to reveal the coexistence of compressive and rarefactive solitary waves. In addition, for certain plasma parameters, the solitary waves disappear and a double layer is expected. Again, with the better approximation in the Sagdeev potential, more features of solitary waves, known as spiky and explosive, along with the double layers, are also highlighted. The observations made of the solitary waves could be of further interest in the understanding of laboratory and space plasmas.