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Love waves in fiber-reinforced layer imperfectly bonded to microstructural couple stress substrate

Sharma Vishal, Sharma Vikas

Journal of Theoretical and Applied Mechanics

2020

Vol. 58 nr 1

221--232

Interior of the Earth is quite complex and it shows many heterogeneities in the form of microstructures. It is difficult to model the Earth in mathematical formulation of a problem, yet it is always desirable that the proposed model should be the nearest approximation of the Earth. In this paper, Love waves are investigated, using a new geometrical configuration which consists of a finite thicker fiber-reinforced layer lying over a couple stress half-space having internal microstructures. The two media are assumed to be imperfectly bonded to each other at the interface. Dispersion and damping equations are derived for the propagation of Love waves in the considered model. The impact of various parameters like imperfectness at the interfacial surface, thickness of the layer, characteristic length parameter of the halfspace, direction of reinforcement are studied on the phase and damping velocities of Love waves.

Dispersion of Rayleigh Waves in a Microstructural Couple Stress Substrate Loaded with Liquid Layer Under the Effects of Gravity

Sharma V., Kumar S.

Archives of Acoustics

2018

Vol. 43, No. 1

11--20

Bone loss is one of the serious health issues in bedridden patients or young generation due to lack of physical activities. Mechanical forces are exerted on the bones through ground reaction forces, liquid loadings and by other contraction activities of the muscles. We are assuming an isotropic half-space with mechanical properties equivalent to that of bone exhibiting microstructures. Consistent couple stress theory introduces an additional material parameter called characteristic length which accounts for inner microstructure of the material. Dispersion relations for leaky Rayleigh waves are derived by considering a model consisting of couple stress half space under the effects of gravity and loaded with inviscid liquid layer of finite thickness or a liquid half space. Impact of the gravity, liquid loadings and microstructures of the material are investigated on propagation of leaky Rayleigh type waves. Phase velocity of leaky Rayleigh waves is studied for five different values of characteristic length parameter which are of the order of internal cell size of the considered material. Variations in phase velocity of leaky Rayleigh waves are also studied under the effect of gravity parameter and thickness of liquid loadings.

Dispersion of SH waves in a viscoelastic layer imperfectly bonded with a couple stress substrate

Sharma V., Kumar S.

Journal of Theoretical and Applied Mechanics

2017

Vol. 55 nr 2

535--546

The paper deals with propagation of SH waves in a viscoelastic layer over a couple stress substrate with imperfect bonding at the interface. A dispersion equation of SH waves in a viscoelastic layer overlying the couple stress substrate with an imperfect interface between them has been obtained. Dispersion equations for propagation of SH waves with perfectly bonded interface and slippage interface between two media are also obtained as particular cases. Effects of the degree of imperfectness of the interface are studied on the phase velocity of SH waves. The dispersion curves are plotted and the effects of material properties of both couple stress substrate and viscoelastic layer are studied. The effects of internal microstructures of the couple stress substrate in terms of characteristic length of the material are presented. The effects of heterogeneity, friction parameter and thickness of the viscoelastic layer are also studied on the propagation of SH waves.