Disturbances in a viscoelastic medium due to impulsive forces on a spherical cavity

Summary The disturbances produced in a visco-elastic medium by impulsive forces on the surface of a spherical cavity inside the medium have been studied.     

Effect of couple-stresses in a semi-infinite elastic medium due to impulsive twist over the surface

Summary Displacement due to impulsive twist in a semi-infinite elastic medium is calculated in the light of Cosserats theory of couple stresses [1, 2]. Numerical results are obtained for a particular     

Transient waves in a rod subjected to impulsive end loading

Herein the propagation of transient waves in a rod due to impulsive end loading is investigated using the method of wavefront expansion. The Mindlin–Herrmann equations which include the Poisson effect are used to model the rod. Since this rod theory is restricted to lower values of Poisson's ratio (< 0.283), the present work also has the same restriction. The impulsive end loading on the rod can be prescribed in the form of stress, strain, velocity or acceleration boundary conditions. The analysis is based on the concept of a wave as a carrier of discontinuities in the field variables and their derivatives. These discontinuities are determined from a set of recurrence relations which are in turn generated by the use of time harmonic asymptotic series solutions to the equations of motion. Transients due to both velocity and strain (or stress) boundary conditions are treated. Numerical examples are presented to illustrate the method of solution. The results indicate the distortion of the transient waves due to the dispersive nature of the governing equations. Transients due to other boundary conditions at the rod end can be treated by using the results presented in the paper.     

Effects of couple-stresses in the semi-infinite viscoelastic medium due to time dependent loading

Summary Effects of couple-stresses on shear stresses in the semi-infinite viscoelastic medium are investigated. Numerical results are obtained.     

Waves and stresses produced in an elastic medium due to impulsive radial forces and twist on the surface of a spherical cavity

Summary Displacements and stresses produced by impulsive radial pressure and by impulsive twists have been determined. In the former case total flow of energy across a spherical boundary has been obtained.     

Wave motion due to impulsive twist on the surface

Summary Wave motion due to two kinds of impulsive twist on the surface has been discussed. The discontinuous nature of solution has been obtained. A function-theoretic approach has been made for solving the problem.     

Three-dimensional elastic wave scattering and diffraction due to a rigid cylinder embedded in an elastic medium by a point source

The formal solutions of displacement field to the problem of elastic wave scattering and diffraction due to an infinitely long rigid cylinder embedded in an infinite elastic medium by an impulsive point source have been obtained in the integral form. The integrals for the reflected and the diffracted waves both in the shadow zone and in the illuminated zone are evaluated asymptotically for the early time motion by the Reisdue-Cagniard method and the Saddle-point-Cagniard method.Numerical results of the diffractedP, S andPS waves at a fixed circum-distance from the surface of the rigid cylinder show noticeably that (1) the energy partition for the diffractedS wave is small in comparison with that for the diffractedP wave, (2) the wave form of the diffractedS wave is broader and more diffused than that of the diffractedP wave, (3) the direction of the radial motions of the diffractedP andS waves varies as a function of the observational point, and (4) the energy partition for the diffractedP wave is much smaller than that for the direct or the reflectedP waves.This paper has been presented at the 46th Annual International Meeting of Society of Exploration Geophysicists in Houston, Texas, Oct. 28, 1976.     

Harmonic wave response of two 3-D rigid surface foundations

A boundary element methodology is developed for studying the response of a system of two rigid, massless or massive, surface foundations of arbitrary plan-forms to various harmonic waves under three-dimensional conditions. The method employs the frequency domain Green's function for the surface of the elastic half-space, thereby restricting the discretization only to the soil-foundation interfaces, and isoparametric quadratic quadrilateral boundary elements for increased accuracy. Extensive comparison studies with other known numerical solutions confirm the high accuracy of the proposed method. Detailed parametric studies are conducted in order to study the harmonic wave response of two square foundations as a function of the kind of incident wave, the angles of wave incidence, the wave frequency, the separation distance between the foundations and the amount of mass in each foundation and compare it against that of a single foundation for assessing the through the soil coupling effect.     

Transient foundation solution of saturated soil to impulsive concentrated loading

The transient dynamic response of saturated soil under suddenly applied normal and horizontal concentrated loading is studied in this paper. The behavior of saturated soil is governed by Biot's consolidation theory. The general solutions for Biot equations of equilibrium are derived in terms of displacements and variations of fluid volume, using Laplace–Hankel integral transforms. The solutions in the time domain can be evaluated by numerical inverse Laplace–Hankel transforms. Selected numerical results for displacements, stresses, and pore pressures are presented. Comparisons with existing closed-form solutions for the elastic half-space are made to confirm the accuracy of the present solutions. The solutions can be used to study a variety of transient wave propagation problems and dynamical interactions between saturated soil and structures.     

Displacement due to impulsive loadings on the surface of elastic half-space

Summary The displacement due to vertical impulsive load has been obtained by function theoretic method. Graphs have been drawn for horizontal as well as for vertical displacement. It has been shown thatPekeris's [12]²) method is easier to apply than that ofCagniard [2] for the same purpose.     

Dynamic response of a flexible pavement submitted by impulsive loading

The present paper introduces results from measurements on site using a falling weight deflectometer (FWD). This apparatus is used for non-destructive testing of damaged pavement in order to estimate the elastic modulus of each layer. The basin of deflection induced by a controlled load can be determined with precision and can reflect the behavior of the pavement structure. The interpretation of data generated by FWD leans on inverse analysis processes. Data from FWD combined with the thickness of layers inform on the evolution of the Young's modulus of each layer of the structure along the studied road profile. This information can be also used to estimate its lifespan and possible repairs to be carried out.     

A fundamental solution of a multilayered half-space due to an impulsive ring source

The fundamental solutions of axisymmetric elastodynamic problem for the multilayered half-space due to an impulsive ring source acting within a layered elastic media are derived in time domain with the aid of Laplace–Hankel mixed transform and transfer matrix techniques. In addition, an effective numerical procedure, which utilizes the fast Hankel transform algorithm, is also proposed to calculate these solutions. Illustrative examples have been given to demonstrate that the fundamental solutions can be readily evaluated and the numerical results are of high accuracy. The present solutions can be directly applied to determine the transient wave fields caused by a seismic source and show the potential application to the elastodynamic problems solved by the boundary element method.     

Waves produced in an infinite elastic medium due to normal forces and twists on the surface of a burried spherical source

Summary In this paper, the waves propagated in an infinite medium has been considered by disturbances on the surface of a burried spherical source. The disturbances are produced by two types of forces viz. i) Transient normal force, ii) Transient twist applied on the surface of the source. The solutions are obtained in a very simple form. Graphical representations of some numerical solutions has been added at the end of each problem.     

Propagation of waves in a visco-elastic half-space due to internal sources

Summary The nature of waves and disturbances generated by a time-periodic concentrated force acting inside a visco-elastic half-space has been studied. Interpretations have been given to the various terms in the expressions for the displacement components.     

Propagation of a fracture in an infinite medium

Summary The displacement produced in an infinite homogeneous, isotropic elastic medium due to a steadily progressing crack has been obtained in a closed form by using Laplace transforms andCagniard's method. Numerical values of the displacement have been obtained and presented graphically.     

OnSH type of motion due to body forces and due to stress-discontinuity in a semi-infinite viscoelastic medium

Summary In this paper, surface displacements of theSH type of motion due to time-dependent body forces and due to sudden introduction of a discontinuity in the shearing stress in a semi-infinite, homogeneous, isotropic, viscoelastic medium have been worked out by the use of Laplace and Fourier transforms. The displacements due to a point force and due to a stress discontinuity over a fixed region have been calculated numerically.     

The Influence of 3-D Structure on the Propagation of Seismic Waves Away from Earthquakes

-- The seismic records from significant earthquakes are profoundly affected by 3-D variations in crustal structure both in the source zone itself and in propagation to some distance. Even in structurally complex zones such as Japan and Mexico relatively coherent arrivals are found associated with different classes of propagation paths. The presence of strong lateral variations can disrupt the arrivals, and impose significant variations in propagation characteristics for different directions from the source as illustrated by observations for the 1995 Kobe and 2000 Tottori-ken Seibu earthquakes in western Japan. Such effects can be modelled in 3 dimensions using a hybrid scheme with a pseudospectral representation for horizontal coordinates and finite differences in depth. This arrangement improves parallel implementation by minimising communication costs. For a realistic 3-D model for the structure in western Japan the 3-D simulations to frequencies close to 1 Hz provide a good representation of the observations from subduction zones events such as the 1946 Nankai earthquake and the 2000 Tottori-ken Seibu earthquake. The model can therefore be used to investigate the pattern of ground motion expected for future events e.g., in current seismic gaps.     

Vibration of three-dimensional rigid raft foundation on viscoelastic medium

Using the coupled model of finite and infinite elements, the compliance of a rigid raft (plate) on a viscoelastic medium is calculated in this paper. Further, the effects of different proportions of radiation damping and material damping in the total damping and the distribution of wave motion in the near field are also investigated. From the numerical results, it can be concluded that: (1) the radiation damping plays an important role in the total damping, compared to the material damping; (2) the material damping has some effect on the compliance of the raft; (3) under the action of harmonic concentrated loads, the displacement amplitudes in the near field gradually decrease with the increase in the distance from the raft and the material damping; (4) the strata characteristics of the soil medium have considerable influence on the compliance of the raft and the distribution of wave motion in the near field.     

On the disturbances in an infinite viscoelastic medium due to transient normal forces and transient twists on the surface of a spherical cavity

Summary In this note the disturbances in an infinite viscoelastic medium ofViogt type with a spherical cavity have been considered. The problem has been solved separately for (1) transient radial forces and (2) transient twist acting on the inner spherical surface of the cavity. Exact solutions have been obtained in both cases.