In this work, a theory of thermoelasticity with diffusion is taken into consideration by using the methodology of fractional calculus. The governing equations for particle motion in a homogeneous anisotropic fractiona...In this work, a theory of thermoelasticity with diffusion is taken into consideration by using the methodology of fractional calculus. The governing equations for particle motion in a homogeneous anisotropic fractional order generalized thermoelastic diffusive medium are presented. Uniqueness and reciprocity theorems are proved. The plane wave propagation in the homogeneous transversely isotropic thermoelastic diffusive medium with fractional order derivative is studied. For the two-dimensional problem, there exist a quasi-longitudinal wave, a quasi-transverse wave, a quasi-mass diffusion wave, and a quasi-thermal wave. From the obtained results, the different characteristics of waves, like phase velocity, attenuation coefficient, specific loss, and penetration depth, are computed numerically and presented graphically. Some special cases are also discussed.展开更多
The present paper is devoted to the study of Rayleigh wave propagation in a homogeneous, transversely isotropic, thermoelastic diffusive half-space, subject to stress free, thermally insulated/isothermal, and chemical...The present paper is devoted to the study of Rayleigh wave propagation in a homogeneous, transversely isotropic, thermoelastic diffusive half-space, subject to stress free, thermally insulated/isothermal, and chemical potential boundary conditions in the context of the generalized thermoelastic diffusion theory. The Green-Lindsay（GL） theory is used in the study. In this theory, thermodiffusion and thermodiffusion mechanical relaxations are governed by four different time constants. Secular equations for surface wave propagation in the considered media are derived. Anisotropy and diffusion effects on the phase velocity, attenuation coefficient are graphically presented in order to present the analytical results and make comparison. Some special cases of frequency equations are derived from the present investigation.展开更多
The present paper is concerned with the investigation of disturbances in＇a homogeneous, isotropic elastic medium with generalized thermoelastic diffusion, when a moving source is acting along one of the co-ordinate a...The present paper is concerned with the investigation of disturbances in＇a homogeneous, isotropic elastic medium with generalized thermoelastic diffusion, when a moving source is acting along one of the co-ordinate axis on the boundary of the medium. Eigen value approach is applied to study the disturbance in Laplace-Fourier transform domain for a two dimensional problem. The analytical expressions for displacement components, stresses, temperature field, concentration and chemical potential are obtained in the physical domain by using a numerical technique for the inversion of Laplace transform based on Fourier expansion techniques. These expressions are calculated numerically for a copper like material and depicted graphically. As special cases, the results in generalized thermoelastic and elastic media are obtained. Effect of presence of diffusion is analyzed theoretically and numerically.展开更多
The two-dimensional problem of generalized thermoelastic diffusion material with thermal and diffusion relaxation times is investigated in the context of the Lord-Shulman theory. As an application of the problem, a pa...The two-dimensional problem of generalized thermoelastic diffusion material with thermal and diffusion relaxation times is investigated in the context of the Lord-Shulman theory. As an application of the problem, a particular type of thermal source is considered and the problem is solved numerically by using a finite element method. The components of displacement, stress, temperature distribution chemical potential and mass concentration are obtained. The resulting quantities are depicted graphically for a special model. An appreciable effect of relaxation times is observed on various resulting quantities.展开更多
The propagation of circularly crested thermoelastic diffusive waves in an infinite homogeneous transversely isotropic plate subjected to stress free, isothermal/insulated and chemical potential conditions is investiga...The propagation of circularly crested thermoelastic diffusive waves in an infinite homogeneous transversely isotropic plate subjected to stress free, isothermal/insulated and chemical potential conditions is investigated in the framework of different thermo- elastic diffusion theories. The dispersion equations of thermoelastic diffusive Lamb type waves are derived. Some special cases of the dispersion equations are also deduced.展开更多
This paper concentrates on the wave motion at the interface of viscous compressible fluid half-space and homogeneous isotropic,generalized thermoelastic diffusive half-space.The wave solutions in both the fluid and t...This paper concentrates on the wave motion at the interface of viscous compressible fluid half-space and homogeneous isotropic,generalized thermoelastic diffusive half-space.The wave solutions in both the fluid and thermoelastic diffusive half-spaces have been investigated;and the complex dispersion equation of leaky Rayleigh wave motion have been derived.The phase velocity and attenuation coefficient of leaky Rayleigh waves have been computed from the complex dispersion equation by using the Muller’s method.The amplitudes of displacements,temperature change and concentration have been obtained.The effects of viscosity and diffusion on phase velocity and attenuation coefficient of leaky Rayleigh waves motion for different theories of thermoelastic diffusion have been depicted graphically.The magnitude of heat and mass diffusion flux vectors for different theories of thermoelastic diffusion have also been computed and represented graphically.展开更多
基金the Council of Scientific and Industrial Research(CSIR),India
文摘In this work, a theory of thermoelasticity with diffusion is taken into consideration by using the methodology of fractional calculus. The governing equations for particle motion in a homogeneous anisotropic fractional order generalized thermoelastic diffusive medium are presented. Uniqueness and reciprocity theorems are proved. The plane wave propagation in the homogeneous transversely isotropic thermoelastic diffusive medium with fractional order derivative is studied. For the two-dimensional problem, there exist a quasi-longitudinal wave, a quasi-transverse wave, a quasi-mass diffusion wave, and a quasi-thermal wave. From the obtained results, the different characteristics of waves, like phase velocity, attenuation coefficient, specific loss, and penetration depth, are computed numerically and presented graphically. Some special cases are also discussed.
基金Council of Scientific and Industrial Research(CSIR)
文摘The present paper is devoted to the study of Rayleigh wave propagation in a homogeneous, transversely isotropic, thermoelastic diffusive half-space, subject to stress free, thermally insulated/isothermal, and chemical potential boundary conditions in the context of the generalized thermoelastic diffusion theory. The Green-Lindsay（GL） theory is used in the study. In this theory, thermodiffusion and thermodiffusion mechanical relaxations are governed by four different time constants. Secular equations for surface wave propagation in the considered media are derived. Anisotropy and diffusion effects on the phase velocity, attenuation coefficient are graphically presented in order to present the analytical results and make comparison. Some special cases of frequency equations are derived from the present investigation.
文摘The present paper is concerned with the investigation of disturbances in＇a homogeneous, isotropic elastic medium with generalized thermoelastic diffusion, when a moving source is acting along one of the co-ordinate axis on the boundary of the medium. Eigen value approach is applied to study the disturbance in Laplace-Fourier transform domain for a two dimensional problem. The analytical expressions for displacement components, stresses, temperature field, concentration and chemical potential are obtained in the physical domain by using a numerical technique for the inversion of Laplace transform based on Fourier expansion techniques. These expressions are calculated numerically for a copper like material and depicted graphically. As special cases, the results in generalized thermoelastic and elastic media are obtained. Effect of presence of diffusion is analyzed theoretically and numerically.
文摘The two-dimensional problem of generalized thermoelastic diffusion material with thermal and diffusion relaxation times is investigated in the context of the Lord-Shulman theory. As an application of the problem, a particular type of thermal source is considered and the problem is solved numerically by using a finite element method. The components of displacement, stress, temperature distribution chemical potential and mass concentration are obtained. The resulting quantities are depicted graphically for a special model. An appreciable effect of relaxation times is observed on various resulting quantities.
文摘The propagation of circularly crested thermoelastic diffusive waves in an infinite homogeneous transversely isotropic plate subjected to stress free, isothermal/insulated and chemical potential conditions is investigated in the framework of different thermo- elastic diffusion theories. The dispersion equations of thermoelastic diffusive Lamb type waves are derived. Some special cases of the dispersion equations are also deduced.
文摘This paper concentrates on the wave motion at the interface of viscous compressible fluid half-space and homogeneous isotropic,generalized thermoelastic diffusive half-space.The wave solutions in both the fluid and thermoelastic diffusive half-spaces have been investigated;and the complex dispersion equation of leaky Rayleigh wave motion have been derived.The phase velocity and attenuation coefficient of leaky Rayleigh waves have been computed from the complex dispersion equation by using the Muller’s method.The amplitudes of displacements,temperature change and concentration have been obtained.The effects of viscosity and diffusion on phase velocity and attenuation coefficient of leaky Rayleigh waves motion for different theories of thermoelastic diffusion have been depicted graphically.The magnitude of heat and mass diffusion flux vectors for different theories of thermoelastic diffusion have also been computed and represented graphically.
