283 research outputs found

    A mathematical model of shear wave propagation in the incompressible transversely isotropic thermoelastic half-spaces

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    This article deals with the problem of reflection and transmission of shear waves at a plane interface between two dissimilar incompressible transversely isotropic thermoelastic half-spaces. Two coupled quasi-shear waves are found to propagate due to the incompressibility of such materials. Applying appropriate boundary conditions at the plane interface, amplitude ratios of the reflected and transmitted quasi-shear waves are obtained. It has been observed that these ratios are functions of the angle of incidence, elastic and thermal parameters of the materials. These ratios are computed numerically for a particular model to see the effects of specific heat and thermal expansion on quasi-shear waves in incompressible transversely isotropic thermoelastic materials. The results are also presented graphically

    Plane wave propagation in a 3D anisotropic half-space under Green-Naghdi theory II

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    In this paper, the theory of coupled thermoelasticity in three dimension is employed for triclinic half-space, subjected to time dependent heat source on the boundary of the space which is traction free and is considered in the context of Green-Naghdi model of type II (thermoelasticity without energy dissipation) of generalized thermoelasticity. Normal mode analysis is used to the non-dimensional coupled equations. Finally, the resulting equations are written in the form of a vector-matrix differential equation which is then solved by eigenvalue approach. Numerical results for the temperature, thermal stresses, and displacements are presented graphically and analyzed. Mathematical results shown in thermoelastic curves were supplemented by tectonic movements of elastic lithospheric plates

    The Effect of Hydrostatic Initial Stress on the Plane Waves in a Fiber-Reinforced Magneto-Thermoelastic Medium with Fractional Derivative Heat Transfer

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    An effect of three factors - the order of fractional derivative, the hydrostatic initial stress, and parameter of magnetic field – on the plane waves in the half-space made of fiber-reinforced material, that is described by the theory of generalized magnetothermoelasticity, is studied. The problem is solved numerically using the normal mode analysis. The results correspond to the Lord-Shulman model and the model, that uses the fractional derivatives and are presented in the form of graphs. The findings show pronounced effect of mentioned three factors. The results are compared with the case, when the initial stress and magnetic field are absent.Вивчено вплив трьох факторів – порядку дробових похідних, початкового гідростатичного напруження, параметру магнітного поля – на плоскі хвилі в півпросторі з армованого волокнами матеріалу, який описується теорією узагальненої магнітотермопружності. Задача розв’язана чисельно за допомогою аналізу нормальних мод. Результати аналізу відповідають моделі Лорда – Шульмана і моделі, що описується за допомогою дробових похідних, і представлені у вигляді графіків. Отримані результати показують добре виражений вплив вказаних трьох факторів. Також ці результати порівнюються з результатами, що отримані для випадку відсутності початкового гідростатичного напруження і магнітного поля

    State-space approach to 3D generalized thermoviscoelasticity under Green and Naghdi theory II

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    The present paper is aimed at studying the effects of viscosity on thermoelastic interactions in a three-dimensional homogeneous isotropic half-space solid medium whose surface is subjected to a thermal shock and is assumed to be stress free. The formulation is applied to the generalized thermoelasticity based on the GN model without energy dissipation (GN II model). The normal mode analysis together with state-space approach is used to obtain the exact analytical expressions for the field variables considered. Numerical computations are performed for a specific material and the results obtained are represented graphically. Comparisons are made within the theory in the presence and absence of viscosity effects

    Fractional Thermoelasticity Model of a 2D Problem of Mode-I Crack in a Fibre-Reinforced Thermal Environment

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    A model of fractional-order of thermoelasticity is applied to study a 2D problem of mode-I crack in a fibre-reinforced thermal environment. The crack is under prescribed distributions of heat and pressure. The normal mode analysis is applied to deduce exact formulae for displacements, stresses, and temperature. Variations of field quantities with the axial direction are illustrated graphically. The results regarding the presence and absence of fiber reinforcement and fractional parameters are compared. Some particular cases are also investigated via the generalized thermoelastic theory. The presented results can be applied to design different fibre-reinforced isotropic thermoelastic elements subjected to the thermal load in order to meet special technical requirements

    Effects of Rotation and Gravity Field on Surface Waves in Fibre-Reinforced Thermoelastic Media under Four Theories

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    Estimation is done to investigate the gravitational and rotational parameters effects on surface waves in fibre-reinforced thermoelastic media. The theory of generalized surface waves has been firstly developed and then it has been employed to investigate particular cases of waves, namely, Stoneley waves, Rayleigh waves, and Love waves. The analytical expressions for surface waves velocity and attenuation coefficient are obtained in the physical domain by using the harmonic vibrations and four thermoelastic theories. The wave velocity equations have been obtained in different cases. The numerical results are given for equation of coupled thermoelastic theory (C-T), Lord-Shulman theory (L-S), Green-Lindsay theory (G-L), and the linearized (G-N) theory of type II. Comparison was made with the results obtained in the presence and absence of gravity, rotation, and parameters for fibre-reinforced of the material media. The results obtained are displayed by graphs to clear the phenomena physical meaning. The results indicate that the effect of gravity, rotation, relaxation times, and parameters of fibre-reinforced of the material medium is very pronounced

    Photothermal excitation in non-local semiconductor materials with variable moisture thermal conductivity according to moisture diffusivity

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    In this work, a new model is described for the case of interference between thermal, plasma and elastic waves in a non-local excited semiconductor medium. The governing equations have been put under the influence of moisture diffusion in one dimension (1D) when the moisture thermal conductivity of the non-local medium is taken in variable form. Linear transformations were used to describe the dimensionless model. The photo-thermoelasticity theory according to moisture diffusivity was applied to describe the governing equations using Laplace transforms to obtain analytical solutions. In the time domain, complete solutions are obtained linearly when the conditions are applied (thermal ramp type and non-Gaussian plasma shock) to the surface through numerical methods of inverse Laplace transforms. Numerical simulation is used to display the basic physical quantities under study graphically. The current research has yielded several specific examples of great significance. Many comparisons are made under the influence of fundamental physical variables such as relaxation times, variable thermal conductivity, non-local parameters, and reference moisture parameters through graphing and describing them theoretically

    On the dissipation of seismic energy from source to surface

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    Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Geology, 1958.Vita.Includes bibliographical references (leaves [157]-162).by Sven Treitel.Ph.D
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