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Shear horizontal waves have several applications in diverse scientific and engineering fields such as seismology, sensors, non-destructive evaluation techniques and structural health monitoring. Interior of earth is a complex layered structure which exhibits inhomogeneity, have internal microstructures, possesses initial stresses, and have imperfect bonding among the layers. Thus, to explore the impacts of inhomogeneity, internal microstructures, initial stresses, and imperfectness parameters on the propagation of shear horizontal waves, a geometrical model containing a thin microstructural layer sandwiched between a pre-stressed half-space and an inhomogeneous half-space has been considered. The layer has been modeled using consistent couple stress theory, which includes a length parameter into its mathematical formulations that capture internal microstructures of the material. The problem has been solved analytically and dispersion relations have been generated by employing two different set of boundary conditions, one referring to perfect and the other to imperfect bonding at the interfacial surfaces between different materials involved in the problem. Some special cases have also been generated and influence of different parameters is presented graphically on the phase velocity of waves. [ABSTRACT FROM AUTHOR]

This article concerns with the study of propagation of torsional surface waves in dry sandy layer sandwiched between upper inhomogeneous half space and lower pre-stressed viscoelastic half space with non-planer boundaries. Exponential variation of inhomogeneity is taken in upper half space. Displacement components in the dry sandy layer, upper inhomogeneous half space and lower pre-stressed viscoelastic half space are found in closed form and used to derive the complex velocity equation under the suitable boundary condition using the separation of variable technique. The real part of complex velocity equation gives the dispersion relation in terms of implicit function of relevant parameters that affect the resultant torsional velocity. Four particular cases have been deduced to compare the dispersion relation obtained for the present work for validation purpose. The significant effect of inhomogeneity, corrugated boundaries, initial stress, sandiness and viscoelasticity on the phase velocity of considered torsional surface waves has been numerically simulated for a specific model and demonstrated through different graphs. [ABSTRACT FROM AUTHOR]

The problem of determining the characteristics of the sensitivity of inhomogeneous isotropic elastic solids with respect to three functions characterizing the inhomogeneity – Lame coefficients and density – is considered. The corresponding boundary value problems are formulated, equations for determining the sensitivity are obtained. An example is presented for a cylindrical rod in the analysis of longitudinal and bending oscillations, the sensitivity to changes in Young's modulus and density is analyzed. Using the iterative algorithm and the A.N. Tikhonov's regularization method, a number of inverse problems were solved to determine these characteristics for monotone and non-monotone laws of their change, and the results of computational experiments are presented. The norm of the difference between the exact and reconstructed solutions is analyzed. Recommendations are given for choosing the most efficient frequency range for sounding from the point of view of reconstruction. [ABSTRACT FROM AUTHOR]

The generalized Prandtl boundary value problem is considered, which simulates a quasistatic technological compression process in one direction and rapid spreading in another for a thin incompressible perfectly rigid plastic layer (a plane strain state) corresponding to the Mises–Hencky plasticity criterion with a yield stress variable in thickness. Stratification can be either continuous or piecewise constant. In the latter case, the problem simulates the pressing of layered plastic composites (laminates, "sandwiches") and precisely bringing them to the desired thickness. On the basis of thin-layer singular asymptotics for a small geometric parameter, an approximate solution for kinematic and force quantities is found using the asymptotic integration method developed in this study. The applicability of the quasistatic approach to various time ranges of the compression process is discussed. [ABSTRACT FROM AUTHOR]

In this article, the torsion of rods made of an anisotropically hardening rigid-plastic material under a linearized plasticity condition is studied. It is assumed that the rod is under the action of an external pressure that varies linearly along the generatrix. The stress and strain states of the rod are determined. Stress break lines are found. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We present an asymptotic derivation of the two-dimensional equations of equilibrium of a thin elastic inhomogeneous plate manufactured of an anisotropic material of general form with 21 moduli of elasticity. We also consider simplified models obtained under special assumptions on the moduli. We use test examples to illustrate the error estimate of the proposed model and discuss its scope. The model is compared with the classical Kirchhoff-Love and Timoshenko-Reissner models. [ABSTRACT FROM AUTHOR]

Some general laws concerning the structure of dispersion relations for solid inhomogeneous waveguides with attenuation are studied. An approach based on the analysis of a first-order matrix differential equation is presented in the framework of the concept of complex moduli. Some laws concerning the structure of components of the dispersion set for a viscoelastic inhomogeneous cylindrical waveguide are studied analytically and numerically, and the asymptotics of components of the dispersion set are constructed for arbitrary inhomogeneity laws in the low-frequency region. [ABSTRACT FROM AUTHOR]

The growing bodies are considered as bodies with induced inhomogeneity caused by junction of inconsistently deformed parts. The body is formalized as an abstract smooth manifold, and all possible affine connections on it are classified. A method is shown for introducing a special connection—material connection—for which neighborhoods of all material points of a growing body pass into a stress-free state. A method for constructing a global stress-free reference configuration of a growing body as an embedding in a space with absolute parallelism is proposed. It is shown that in the case of layered accretion, the material connection corresponding to the stress-free embedding is determined by three independent functions and is in general non-Euclidean. The property of being non-Euclidean is determined by the fact that the torsion of the material connection is nonzero. We suggest to formalize the growing body as a fibration of a three-dimensional smooth manifold over a one-dimensional base, and this formalization characterizes the structure of the material connection. [ABSTRACT FROM AUTHOR]

We consider a problem on an ellipsoidal inhomogeneity in an infinitely extended homogeneous isotropic elastic medium. The inhomogeneity differs from the ambient body in the elastic moduli (Poisson's ratio ν and shear modulus µ) and in that it has intrinsic strains. We use the equivalent inclusion method to write out expressions for the Helmholtz and Gibbs free energy of the inhomogeneity as quadratic forms in the intrinsic strains and strains at infinity. The general expressions for the coefficients of these quadratic forms are written out as three rank four tensors characterizing the contribution to the energy by the plastic strain ( ɛ), by the strain at infinity ( ɛ), and (only for the Gibbs energy) by the cross term ɛ ɛ. The solutions for some important particular cases are written out by asymptotically expanding the general solution in small parameters. The parameters determining the type of the asymptotic behavior are the inclusion semiaxis ratio and the inclusion-to-matrix elastic modulus ratio. We consider various physical situations arising when studying needle- and disk-shaped inclusions and characterized by various order of passage to the limit. We analyze the applicability domains of the asymptotics by reduction to a single small parameter. For the case in which the parameters considerably differ from unity simultaneously, we single out seven domains corresponding to various relations between these parameters. We construct the diagrams of relative error isolines for the resulting tensors corresponding to the energy contribution from various strain tensor components. [ABSTRACT FROM AUTHOR]

By passing to the limit in the general solution, we obtain several exact asymptotic formulas for the energy of an inhomogeneity in a body located in an external stress field. The parameters determining the type of the asymptotic behavior are the inclusion semiaxis ratio and the inclusion-matrix elastic modulus ratio. In the case of a large simultaneous deviation of the parameters from unity, we distinguish seven regions corresponding to various successive passages to the limit as these parameters approach zero (or infinity). [ABSTRACT FROM AUTHOR]