Semi-infinite Solid Medium Research Articles

Thermoelastic interaction in the semi-infinite solid medium due to three-phase-lag effect involving memory-dependent derivative

The present study deals with the thermoelastic interaction in a semi-infinite elastic solid with a heat source in the context of three-phase-lag model with memory-dependent derivative. The governing coupled equations, involving time delay and kernel functions are expressed in the vector matrix differential equation form in the Laplace transform domain. The analytical formulations of the problem have been solved by eigenvalue technique. The Honig–Hirdes numerical method is used for the inversion of Laplace transformation. Numerical results are obtained by choosing various types of time delay parameters and kernel functions and graphical representations have been performed accordingly. An extrapolative capability is established by considering the memory-dependent derivative into a three-phase-lag model.

Rayleigh Wave In A Rotating Nonlocal Magnetoelastic Half-Plane*

AbstractThis paper investigates the propagation of Rayleigh surface waves in a rotating semi-infinite solid medium, permeated by an initial magnetic field in the context of linear nonlocal elasticity. Frequency equations are derived and the combined effect of magnetic field and rotation on Rayleigh wave propagation, based on the linear theory of nonlocal elasticity has been studied. Effects of magnetic field, as well as rotation on Rayleigh wave propagation in a nonlocal medium, have also been analyzed in details as special cases. Numerical calculations, graphs and discussions presented in this paper lead us to some important conclusions. Fourier double integral transform technique has been applied to solve the problem.

A Gauss–Newton full-waveform inversion for material profile reconstruction in viscoelastic semi-infinite solid media

An inversion framework employing a Gauss–Newton method is developed to reconstruct material profiles in heterogeneous, viscoelastic, semi-infinite domains. In particular, a full-waveform inversion approach is investigated to image the elastic and attenuating parameters of a layered media. To account for the viscoelasticity of the medium, a Generalized Maxwell Body with one spring and two Maxwell elements in parallel (GMB2) is adopted in the forward and inverse wave propagation problems. Perfectly-matched-layers were introduced as wave absorbing buffers to simulate the semi-infinite extent of the domain. Using transient wave equations endowed with the GMB2 constitutive relation and the PML, a partial-differential-equations-constrained optimization scheme was implemented that lead to classic KKT (Karush–Kuhn–Tucker) conditions including time-dependent state, adjoint, and time-invariant control problems. An optimal solution of the viscoelastic parameters was obtained using a reduced-space approach based on a line search algorithm where the search direction was computed by the Gauss–Newton method. Considerable improvements on the accuracy and convergence rate of solutions were made by the developed Gauss–Newton inversion procedure compared to previous research using the Fletcher–Reeves method.

A Gauss-Newton full-waveform inversion for material profile reconstruction in 1D PML-truncated solid media

This paper discusses a Gauss-Newton full-waveform inversion procedure for material profile reconstruction in semi-infinite solid media. Given surficial measurements of the solid’s response to interrogating waves, the procedure seeks to find an unknown wave velocity profile within a computational domain truncated by Perfectly-Matched-Layer (PML) wave-absorbing boundaries. To this end, the inversion procedure minimizes a Lagrangian functional composed of a cost functional augmented by PML-endowed wave equations via Lagrange multipliers. Enforcing the stationarity of the Lagrangian leads to KKT (Karush-Kuhn-Tucker) conditions comprising time-dependent state, adjoint, and time-invariant control problems. The material parameter is updated by iteratively solving the KKT conditions in the reduced space of the control variable. The update of the control variable is determined by a Gauss-Newton-Krylov optimization algorithms. Super-linear convergence behavior of the Gauss-Newton inversion has been observed in one-dimensional implementations. Regularization and frequency-continuation schemes were used to relieve the ill-posedness of the inverse problem.

TEMPERATURE RATE DEPENDENT GENERALIZED THERMOELASTICITY WITH MODIFIED OHM'S LAW

The present work is concerned with an electro-magneto-thermoelastic coupled problem for a homogeneous, isotropic, thermally and electrically conducting semi-infinite solid medium in two-dimensional space where an initial magnetic field with constant intensity acts parallel to the plane boundary of the half-space. The surface of the half-space taking as traction free which is subjected to a thermal shock. The modified Ohm's law including the temperature gradient and charge density effect to the governing equations of the generalized thermoelasticity under the temperature rate dependent thermoelasticity (TRDTE) proposed by Green and Lindsay (GL model) has been introduced. Normal mode analysis together with eigenvalue approach technique is used to obtain the general solutions for the physical quantities. Numerical results for the physical quantities are illustrated graphically and analyzed. The graphical results indicate that the effect of the coefficient connecting the temperature gradient and the electric current density of the modified Ohm's law on the plane waves is very pronounced. Comparison are made with the results obtained in the absence of the above coefficient.

On body shapes providing maximum depth of penetration

The problem of maximization of the depth of penetration of rigid impactor into semi-infinite solid media (concrete shield) is investigated analytically and numerically using two-stage model and experimental data of Forrestal and Tzou (Int J Solids Struct 34(31–32):4127–4146, 1997). The shape of the axisymmetric rigid impactor has been taken as an unknown design variable. To solve the formulated optimization problem for nonadditive functional, we expressed the depth of penetration (DOP) under some isoperimetric constraints. We apply approaches based on analytical and qualitative variational methods and numerical optimization algorithm of global search. Basic attention for considered optimization problem was given to constraints on the mass of penetrated bodies, expressed by the volume in the case of penetrated solid body and by the surface area in the case of penetrated thin-walled rigid shell. As a result of performed investigation, based on two-term and three-term two stage models proposed by Forrestal et al. (Int J Impact Eng 15(4):396–405, 1994), Forrestal and Tzou (Int J Solids Struct 34(31–32):4127–4146, 1997) and effectively developed by Ben-Dor et al. (Comp Struct 56:243–248, 2002, Comput Struct 81(1):9–14, 2003a, Int J Solids Struct 40(17):4487–4500, 2003b, Mech Des Struct Mach 34(2): 139–156, 2006), we found analytical and numerical solutions and analyzed singularities of optimal forms.

Wave Propagation in a Piezoelectric Coupled Solid Medium

Shear horizontal (SH) wave propagation in a semi-infinite solid medium surface bonded by a layer of piezoelectric material abutting the vacuum is investigated in this paper. The dispersive characteristics and the mode shapes of the deflection, the electric potential, and the electric displacements in the thickness direction of the piezoelectric layer are obtained theoretically. Numerical simulations show that the asymptotic phase velocities for different modes are the Bleustein surface wave velocity or the shear horizontal wave velocity of the pure piezoelectric medium. Besides, the mode shapes of the deflection, electric potential, and electric displacement show different distributions for different modes and different wave number. These results can be served as a benchmark for further analyses and are significant in the modeling of wave propagation in the piezoelectric coupled structures.

Probing confined interfacial excitations in buried layers by Brillouin light scattering

Brillouin light scattering from silicon oxynitride films grown on GaAs reveals an excitation at frequencies lying below that of the Rayleigh surface wave. The mode, identified as a localized interfacial excitation, arises from the presence of a soft, thin transition layer between the film and substrate. The results are discussed in the framework of a Green’s function formalism that reproduces the experimental features and illustrates the nature of the mode and its difference from Stoneley excitations that exist in special cases for an abrupt interface separating two semi-infinite solid media. Observations of this low-frequency excitation offer a previously unexplored approach to characterize, nondestructively, the elastic properties of buried interfaces.

Love waves in piezoelectric coupled solid media

The propagation of Love waves in a piezoelectric lamina bonded ontoa semi-infinite solid medium is investigated in this paper. The dispersivecharacteristics and the mode shapes of the deflection and the electricpotential in the thickness direction of the piezoelectric layer aretheoretically derived. Numerical simulations show that the phase velocitiesinitiate at the shear wave velocity of the host medium and tend towards theBleustein-Gulyayev surface wave velocity for the piezoelectric layer at highwavenumbers for the first mode. The first two mode shapes of the electricpotential correspond to a half-cosine and a full-cycle sinusoidaldistribution, respectively, and become distorted as the wavenumber increases.These findings are significant in the application of inter-digital transducersfor surface wave excitation in structural health monitoring.

Semi-analytical solution for heat transfer from a buried pipe with convection on the exposed surface

The problem of heat transfer from a constant-wall-temperature pipe buried in a semi-infinite solid medium with a plane surface exposed to a fluid flow is solved semi-analytically. Using a conformal mapping, the original semi-infinite physical domain is transformed into a finite rectangular domain. A singular Fredholm integral equation of the second kind is derived and solved numerically to find the temperature distribution for the solid. The total heat flux Q from the exposed surface is expressed by modifying the conventional expression Q=kSΔ T to Q=ηkSΔ T, where S is the conduction shape factor, k is the thermal conductivity of the solid, and Δ T represents the temperature difference between the pipe wall and the surrounding fluid. The panel efficiency η and maximum surface temperature are presented in terms of the Biot number and a geometric parameter, L/ D.

Thermal Traces of a Buried Heat Source

An exact solution in series form is presented for the steady temperature distribution in a semi-infinite solid medium bounded internally by a spherical inclusion of uniform temperature. Heat transfer at the interface is via convection. The solution is obtained by means of a transformation to a bispherical coordinate system. Surface temperatures, which are of engineering interest for monitoring purposes, are also calculated.

Elastic Wave Propagation in a Semi-Infinite Solid Medium

A simple physical picture is given of plane waves possessing complex angles of propagation, which play an important role in the theory of elastic wave radiation. Their utility is illustrated by studying continuous sinusoidal wave propagation parallel to the unstressed, plane boundary of a semi-infinite, homogeneous and isotropic solid medium, the Rayleigh and head waves being particular features of the investigation. A novel study of the field due to an impulsive force acting at a line in the surface of a semi-infinite medium indicates a general method of solving important transient propagation problems encountered in seismology. The equivalent problem of an impulsive force acting at the edge and in the plane of a semi-infinite thin sheet has been simulated experimentally by detonating small explosive charges at the edge of an aluminium sheet. The displacements detected by a condenser microphone technique are in excellent agreement with the theoretical determinations.

Elastic Wave Propagation in a Semi-Infinite Solid Medium

Plane waves possessing complex angles of propagation play an important role in the theory of elastic wave radiation. A simple physical picture is given of these waves and their utility illustrated by employing them in the study of continuous sinusoidal wave propagation in the neighborhood of an unstressed, plane boundary in a semi-infinite, homogeneous, and isotropic solid medium. The Rayleigh wave and the von Schmidt, or Head wave are particular features of the study. A simpler solution than Sauter's [Z. angew Math. Mech. (1950)] has been found for the displacement field radiated by an impulsive force acting at a line in the surface. By reciprocity this gives the surface displacement due to an internal line force. An equivalent problem is provided by an impulsive force acting at the edge and in the plane of a semi-infinite thin sheet, provided that the bulk dilatation wave velocity is replaced by the thin sheet dilatation wave velocity. This has been simulated experimentally by detonating small explosive charges at the edge of an aluminum sheet, 0.5 mm thick. Displacements detected by a novel condenser microphone technique are in excellent agreement with those determined theoretically.

Boussinesq's problem for a rigid cone

1. The problem of determining the distribution of stress in a semi-infinite solid medium when its plane boundary is deformed by the pressure against it of a perfectly rigid cone is of considerable importance in various branches of applied mechanics. It arises in soil mechanics where the cone is the base of a conical-headed cylindrical pillar and the semi-infinite medium is the soil upon which it rests (1). In this instance the distribution of stress in the soil is known to be more or less similar to that calculated on the assumption that the soil is a perfectly elastic, isotropic and homogeneous medium, at least if the factor of safety of a mass of soil with respect to failure by plastic flow exceeds a value of about three (2). The same problem occurs in the theory of indentation tests in which a ductile material is indected by cylindrical punches with conical heads (3).