Love waves in a nonlocal elastic media with voids

2019 ◽  
Vol 25 (8) ◽  
pp. 1470-1483 ◽  
Author(s):  
Gurwinderpal Kaur ◽  
Dilbag Singh ◽  
SK Tomar
Keyword(s):  
Boundary Conditions ◽  
Elastic Layer ◽  
Love Wave ◽  
Critical Frequency ◽  
Elastic Solid ◽  
Specific Model ◽  
Elastic Media ◽  
Present Formulation ◽  
Classical Elasticity ◽  
Coefficient Versus

The propagation of Love-type waves in a nonlocal elastic layer with voids resting over a nonlocal elastic solid half-space with voids has been studied. Dispersion relations are derived using appropriate boundary conditions of the model. It is found that there exist two fronts of Love-type surface waves that may travel with distinct speeds. The appearance of the second front is purely due to the presence of voids in layered media. Both fronts are found to be dispersive in nature and affected by the presence of the nonlocality parameter. The first front is found to be nonattenuating, independent of void parameters and analogous to the Love wave of classical elasticity, while the second front is attenuating and depends on the presence of void parameters. Each of the fronts is found to face a critical frequency above which it ceases to propagate. For a specific model, the variation of the phase speeds of both the fronts with frequency, nonlocality, voids and thickness parameters is shown graphically. Attenuation coefficient versus frequency for the second front has also been depicted separately. Some particular cases are deduced from the present formulation.

Wave Propagation in a Micropolar Elastic Plate with Voids

2005 ◽  
Vol 11 (6) ◽  
pp. 849-863 ◽  
Author(s):  
S. K. Tomar
Keyword(s):  
Wave Propagation ◽  
Attenuation Coefficient ◽  
Elastic Material ◽  
Elastic Plate ◽  
Lamb Wave ◽  
Specific Model ◽  
Present Formulation ◽  
Numerical Computations ◽  
Lamb Wave Propagation ◽  
Symmetric And Antisymmetric Modes

Frequency equations are obtained for Rayleigh–Lamb wave propagation in a plate of micropolar elastic material with voids. The thickness of the plate is taken to be finite and the faces of the plate are assumed to be free from stresses. The frequency equations are obtained corresponding to symmetric and antisymmetric modes of vibrations of the plate, and some limiting cases of these equations are discussed. Numerical computations are made for a specific model to solve the frequency equations for symmetric and antisymmetric modes of propagation. It is found that both modes of vibrations are dispersive and the presence of voids has a negligible effect on these dispersion curves. However, the attenuation coefficient is found to be influenced by the presence of voids. The results of some earlier works are also deduced from the present formulation.

Comments on “Lamb's problem for fluid-saturated porous media”

1992 ◽  
Vol 82 (5) ◽  
pp. 2263-2273
Author(s):  
M. D. Sharma
Keyword(s):  
Porous Media ◽  
Boundary Conditions ◽  
Solid Phase ◽  
Elastic Solid ◽  
Porous Solid ◽  
Surface Boundary ◽  
Vertical Force ◽  
Saturated Porous Media ◽  
Concentrated Load ◽  
Lamb’S Problem

Abstract Philippacopoulos (1988) discusses axisymmetric wave propagation in a fluid-saturated porous solid half-space. The disturbance is considered to be produced by the concentrated load P0exp(iωt) acting vertically at the surface. Boundary conditions chosen imply that a vertical force acting on the surface of fluid-saturated porous solid exerts no pressure on the interstitial liquid. These boundary conditions do not seem appropriate. In the present study, the boundary conditions have been changed in order to satisfy the concept of porosity. These are also in accordance with those discussed by Deresiewicz and Skalak (1963) for the special case of interface between liquid and liquid-saturated porous media. Analytic expressions have been derived for the displacements at the surface. The limiting case of a dry elastic solid is also deduced. Effects of intergranular energy losses due to solid phase and of dissipation due to flow of pore fluid are exhibited on the displacements at the surface. Contrary to Philippacopoulos (1988), the displacements in saturated poroelastic solids are found to be larger than those in a dry elastic solid with same Lamb's moduli.

On the existence of type-6 transonic states in linear elastic media of cubic symmetry

1987 ◽  
Vol 411 (1840) ◽  
pp. 251-263 ◽  
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Elastic Solid ◽  
Mechanics Of Solids ◽  
Elastic Media ◽  
Slowness Surface ◽  
Cubic Symmetry ◽  
Linear Elastic ◽  
Surface Wave Propagation ◽  
Anisotropic Elastic

Crucial to the understanding of surface-wave propagation in an anisotropic elastic solid is the notion of transonic states, which are defined by sets of parallel tangents to a centred section of the slowness surface. This study points out the previously unrecognized fact that first transonic states of type 6 (tangency at three distinct points on the outer slowness branch S 1 ) indeed exist and are the rule, rather than the exception, in so-called C 3 cubic media (satisfying the inequalities c 12 + c 44 > c 11 - c 44 > 0); simple numerical analysis is used to predict orientations of slowness sections in which type-6 states occur for 21 of the 25 C 3 cubic media studied previously by Chadwick & Smith (In Mechanics of solids , pp. 47-100 (1982)). Limiting waves and the composite exceptional limiting wave associated with such type-6 states are discussed.

A Variational Approach to the Dynamics of Structures Having Mixed or Discontinuous Boundary Conditions

1984 ◽  
Vol 51 (4) ◽  
pp. 831-836 ◽  
Author(s):  
P. J. Torvik
Keyword(s):  
Boundary Conditions ◽  
Variational Approach ◽  
Natural Frequencies ◽  
Elastic Solid ◽  
Approximate Solutions ◽  
Forced Response ◽  
Field Equations ◽  
Elastic Circular Plate ◽  
Discontinuous Boundary ◽  
Elastic Systems

A procedure is developed whereby the steady-state forced response and the modes of free vibration for elastic systems having mixed or discontinuous boundary conditions can be determined. Approximate solutions are obtained as a superposition of a set of functions, each of which satisfies the field equations but not the boundary conditions. The coefficients of this expansion are obtained through applying a variational principle developed from Hamilton’s principle which for simple harmonic motion, is equivalent to Reissner’s principle. The reduction from the general elastic solid to the elastic plate is given, as are some results obtained for the first several natural frequencies of an elastic circular plate, free on a portion of the boundary and clamped on the remainder.

Surface waves in homogenous visco-elastic media of higher order under the influence of surface stresses

2013 ◽  
Vol 22 (5-6) ◽  
pp. 185-191 ◽  
Author(s):  
Munish Sethi ◽  
K.C. Gupta ◽  
Monika Rani ◽  
A. Vasudeva
Keyword(s):  
Surface Waves ◽  
Solid Medium ◽  
Elastic Solid ◽  
Higher Order ◽  
Love Waves ◽  
Elastic Media ◽  
Time Rate ◽  
Surface Stresses ◽  
Rayleigh And Love Waves

AbstractThe aim of the present paper is to investigate the surface waves in a homogeneous, isotropic, visco-elastic solid medium of nth order, including time rate of strain under the influence of surface stresses. The theory of generalized surface waves is developed to investigate particular cases of waves such as the Stoneley, Rayleigh, and Love waves. Corresponding equations have been obtained for different cases. These are reduced to classical results, when the effects of surface stresses and viscosity are ignored.

Arbitrarily Oriented Cracks in a Reinforced Sheet

1985 ◽  
Vol 52 (1) ◽  
pp. 13-18 ◽  
Author(s):  
C.-C. Chu
Keyword(s):  
Boundary Conditions ◽  
Failure Mode ◽  
Fiber Orientation ◽  
Loading Condition ◽  
Elastic Interaction ◽  
Fundamental Solutions ◽  
Relative Orientation ◽  
Loading Conditions ◽  
Present Formulation ◽  
Critical Loading

The elastic interaction between a crack and a fiber is studied for various loading conditions. Generalized from earlier work by Greif and Sanders, the present formulation is valid for arbitrary relative orientation between the crack and the fiber. Helpful design information, such as the critical loading condition and the critical fiber orientation to trigger a certain failure mode, is therefore attainable. The fundamental solutions, each associated with proper parameters and proper boundary conditions, can also be superposed to model more realistic problems.

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