The paper discusses the role of entropy in the open systems, following Prigogine's theory of... more The paper discusses the role of entropy in the open systems, following Prigogine's theory of nonlinear thermodynamics. The apparent contradiction between the biological order and the second principle of thermodynamics is examined, noting the relationship between the thermodynamics equilibrium and minimum entropy production. Finally it is shown that the dissipative structures in hydrodynamics, optics, chemistry and biology are a general phenomenon of nature.
International Journal of Engineering Science, 1979
Al&&-We consider Saint-Venant's problem in the case when the cross-section of the cylinder is occ... more Al&&-We consider Saint-Venant's problem in the case when the cross-section of the cylinder is occupied by different inhomogeneous and isotropic micropolar elastic solids. The results are used to study the deformation of a circular composite cylinder.
A PRINCIPLE OF SAINT-VENANT-TYPE is established for a right cylinder composed of an anisotropic, ... more A PRINCIPLE OF SAINT-VENANT-TYPE is established for a right cylinder composed of an anisotropic, linear, homogeneous micropolar elastic solid and subjected to harmonic loading on one of its ends. The amplitude of the harmonic vibrations of this cylinder is also shown to depend continuously on the prescribed data.
This paper is dedicated to propagation of waves with assigned length in a model describing the ev... more This paper is dedicated to propagation of waves with assigned length in a model describing the evolutionary behavior of materials with double porosity. Basic equations are considered for an isotropic and homogeneous material which occupies the entire three dimensional space. Wave solutions with assigned wavelength are sought. It is shown that there exist two shear waves that are undamped in time, non-dispersive and that are unaltered by the presence of pore system. There also exist other three longitudinal wave solutions that are dispersive and damped in time: one longitudinal quasi-elastic wave and two quasi-pore modes due to presence of pore system. The dispersion relation is explicitly established like a quartic equation and it is shown that it could allow negative real roots, thus explaining the existence of standing waves. A numerical analysis indicates that the speed of propagation of the longitudinal quasi-elastic wave is larger than the wave speed for its counterpart from the classical elasticity theory. The propagation of the Rayleigh surface waves is addressed and the corresponding secular equation is explicitly established.
International Journal of Engineering Science, 1996
Venant type are established within the context of dynamic generalized thermoelasticity. A thermoe... more Venant type are established within the context of dynamic generalized thermoelasticity. A thermoelastic body is deformed under null body loads and initial conditions and subject to non-zero boundary data only on a plane end. The behaviour is studied for the total energy stored in that part of the body beyond a distance z from the basis. An estimate is established that describes the spatial decay of end effects. When the harmonically vibrations of a right cylinder are considered, it is shown that an exponential decay of activity holds away from the excited end provided that the exciting frequency is less than a certain critical frequency.
International Journal of Engineering Science, Feb 1, 1996
Venant type are established within the context of dynamic generalized thermoelasticity. A thermoe... more Venant type are established within the context of dynamic generalized thermoelasticity. A thermoelastic body is deformed under null body loads and initial conditions and subject to non-zero boundary data only on a plane end. The behaviour is studied for the total energy stored in that part of the body beyond a distance z from the basis. An estimate is established that describes the spatial decay of end effects. When the harmonically vibrations of a right cylinder are considered, it is shown that an exponential decay of activity holds away from the excited end provided that the exciting frequency is less than a certain critical frequency.
On etudie l'unicite et la dependance continue des solutions en fonction de l'etat initial... more On etudie l'unicite et la dependance continue des solutions en fonction de l'etat initial et on fournit des termes pour les problemes de valeurs initiales et aux limites en theorie tridimensionnelle des materiaux a variables d'etat interne. La methode est basee sur une inegalite de type Gronwall
ABSTRACT Recently it has been shown that chemical oscillations are a general phenomenon, that app... more ABSTRACT Recently it has been shown that chemical oscillations are a general phenomenon, that appears both in biological or nonbiological systems. Using nonlinear thermodynamics and nonlinear differential equations the stability of the steady state solutions for these chemical oscillations is analyzed. A set of reactions produced between molecular species with self-catalytic properties is analyzed, noting a fidelity factor, introduced in the process.
Abstract This work aims to highlight, by a series of spatial estimates, the effect of the presenc... more Abstract This work aims to highlight, by a series of spatial estimates, the effect of the presence of pore system and local thermal non-equilibrium properties in a triple porosity material matrix on the transmission depth of a thermo-mechanical signal. Two kind of spatial behaviors are established, for which the spatial response obeys a linear first-order differential inequality with two kind different coefficients: one is time independent and the other is time dependent. The first differential inequality furnishes some exponential decaying spatial estimates with uniform in time exponent and such estimates are recommended to be used for appropriately large values of the time variable. While the second first-order differential inequality furnishes some exponential decaying spatial estimates with time dependent exponent, thus showing a rapid spatial decrease of the solution for appropriate short values of time. These results are compared with their counterparts without mechanical effects, that is for purely pore system or local thermal non-equilibrium effects theories: this is done for appropriate short and large values of the time variable.
A PRINCIPLE OF SAINT-VENANT-TYPE is established for a right cylinder composed of an anisotropic, ... more A PRINCIPLE OF SAINT-VENANT-TYPE is established for a right cylinder composed of an anisotropic, linear, homogeneous micropolar elastic solid and subjected to harmonic loading on one of its ends. The amplitude of the harmonic vibrations of this cylinder is also shown to depend continuously on the prescribed data.
International Journal of Engineering Science, 1979
Al&&-We consider Saint-Venant's problem in the case when the cross-section of the cylinder is occ... more Al&&-We consider Saint-Venant's problem in the case when the cross-section of the cylinder is occupied by different inhomogeneous and isotropic micropolar elastic solids. The results are used to study the deformation of a circular composite cylinder.
The present paper studies the propagation of plane time harmonic waves in an infinite space fille... more The present paper studies the propagation of plane time harmonic waves in an infinite space filled by a thermoelastic material with microtemperatures. It is found that there are seven basic waves traveling with distinct speeds: (a) two transverse elastic waves uncoupled, undamped in time and traveling independently with the speed that is unaffected by the thermal effects; (b) two transverse thermal standing waves decaying exponentially to zero when time tends to infinity and they are unaffected by the elastic deformations; (c) three dilatational waves that are coupled due to the presence of thermal properties of the material. The set of dilatational waves consists of a quasi-elastic longitudinal wave and two quasithermal standing waves. The two transverse elastic waves are not subjected to the dispersion, while the other two transverse thermal standing waves and the dilatational waves present the dispersive character. Explicit expressions for all these seven waves are presented. The Rayleigh surface wave propagation problem is addressed and the secular equation is obtained in an explicit form. Numerical computations are performed for a specific model, and the results obtained are depicted graphically.
The paper discusses the role of entropy in the open systems, following Prigogine's theory of... more The paper discusses the role of entropy in the open systems, following Prigogine's theory of nonlinear thermodynamics. The apparent contradiction between the biological order and the second principle of thermodynamics is examined, noting the relationship between the thermodynamics equilibrium and minimum entropy production. Finally it is shown that the dissipative structures in hydrodynamics, optics, chemistry and biology are a general phenomenon of nature.
We study a thermal model associated with a heat-conducting material based on a three-phase-lag co... more We study a thermal model associated with a heat-conducting material based on a three-phase-lag constitutive equation for the heat flux, a model that leads to a Moore–Gibson–Thompson type equation for the thermal displacement. We are researching the compatibility of the three-phase-lag constitutive equation in concern with the second law of thermodynamics, thus discovering restrictions to be imposed on the involved thermal coefficients. On this basis, we manage to obtain the well-posedness problem of the model as the uniqueness of the solutions and their continuous dependence on the given data. Finally, we show that such a model not only allows the propagation of damped in time waves but also exponentially decaying in time thermal standing mode waves. We also show that if the thermodynamic restrictions are not fulfilled, then we can be led to instability. Through the present treatment of the thermal model in question, we obtain important information on the associated Moore–Gibson–Thompson type equation for the thermal displacement.
In this article we analyze the behavior of plane harmonic waves in the entire space lled by a lin... more In this article we analyze the behavior of plane harmonic waves in the entire space lled by a linear thermoviscoelastic material with voids. We take into account the e ect of the thermal and viscous dissipation energies upon the corresponding waves and, consequently, we study the damped in time wave solutions. There are ve basic waves in an isotropic and homogeneous thermoviscoelastic porous space. Two of them are shear waves, while the remaining three are dilatational waves. The shear waves are uncoupled, damped in time with decay rate depending only on the viscosity coe cients. The three dilatational waves are coupled and consist of a predominantly dilatational damped wave of Kelvin-Voigt viscoelasticity, other is predominantly a wave carrying a change in the void volume fraction and the third takes the form of a standing thermal wave whose amplitude decays exponentially with time. The explicit form of the dispersion equation is obtained in terms of the wave speed and the thermoviscoelastic homogeneous pro le. Furthermore, we use numerical methods and computations to solve the secular equation for some special classes of thermoviscoelastic materials considered in literature.
The paper discusses the role of entropy in the open systems, following Prigogine's theory of... more The paper discusses the role of entropy in the open systems, following Prigogine's theory of nonlinear thermodynamics. The apparent contradiction between the biological order and the second principle of thermodynamics is examined, noting the relationship between the thermodynamics equilibrium and minimum entropy production. Finally it is shown that the dissipative structures in hydrodynamics, optics, chemistry and biology are a general phenomenon of nature.
International Journal of Engineering Science, 1979
Al&&-We consider Saint-Venant's problem in the case when the cross-section of the cylinder is occ... more Al&&-We consider Saint-Venant's problem in the case when the cross-section of the cylinder is occupied by different inhomogeneous and isotropic micropolar elastic solids. The results are used to study the deformation of a circular composite cylinder.
A PRINCIPLE OF SAINT-VENANT-TYPE is established for a right cylinder composed of an anisotropic, ... more A PRINCIPLE OF SAINT-VENANT-TYPE is established for a right cylinder composed of an anisotropic, linear, homogeneous micropolar elastic solid and subjected to harmonic loading on one of its ends. The amplitude of the harmonic vibrations of this cylinder is also shown to depend continuously on the prescribed data.
This paper is dedicated to propagation of waves with assigned length in a model describing the ev... more This paper is dedicated to propagation of waves with assigned length in a model describing the evolutionary behavior of materials with double porosity. Basic equations are considered for an isotropic and homogeneous material which occupies the entire three dimensional space. Wave solutions with assigned wavelength are sought. It is shown that there exist two shear waves that are undamped in time, non-dispersive and that are unaltered by the presence of pore system. There also exist other three longitudinal wave solutions that are dispersive and damped in time: one longitudinal quasi-elastic wave and two quasi-pore modes due to presence of pore system. The dispersion relation is explicitly established like a quartic equation and it is shown that it could allow negative real roots, thus explaining the existence of standing waves. A numerical analysis indicates that the speed of propagation of the longitudinal quasi-elastic wave is larger than the wave speed for its counterpart from the classical elasticity theory. The propagation of the Rayleigh surface waves is addressed and the corresponding secular equation is explicitly established.
International Journal of Engineering Science, 1996
Venant type are established within the context of dynamic generalized thermoelasticity. A thermoe... more Venant type are established within the context of dynamic generalized thermoelasticity. A thermoelastic body is deformed under null body loads and initial conditions and subject to non-zero boundary data only on a plane end. The behaviour is studied for the total energy stored in that part of the body beyond a distance z from the basis. An estimate is established that describes the spatial decay of end effects. When the harmonically vibrations of a right cylinder are considered, it is shown that an exponential decay of activity holds away from the excited end provided that the exciting frequency is less than a certain critical frequency.
International Journal of Engineering Science, Feb 1, 1996
Venant type are established within the context of dynamic generalized thermoelasticity. A thermoe... more Venant type are established within the context of dynamic generalized thermoelasticity. A thermoelastic body is deformed under null body loads and initial conditions and subject to non-zero boundary data only on a plane end. The behaviour is studied for the total energy stored in that part of the body beyond a distance z from the basis. An estimate is established that describes the spatial decay of end effects. When the harmonically vibrations of a right cylinder are considered, it is shown that an exponential decay of activity holds away from the excited end provided that the exciting frequency is less than a certain critical frequency.
On etudie l'unicite et la dependance continue des solutions en fonction de l'etat initial... more On etudie l'unicite et la dependance continue des solutions en fonction de l'etat initial et on fournit des termes pour les problemes de valeurs initiales et aux limites en theorie tridimensionnelle des materiaux a variables d'etat interne. La methode est basee sur une inegalite de type Gronwall
ABSTRACT Recently it has been shown that chemical oscillations are a general phenomenon, that app... more ABSTRACT Recently it has been shown that chemical oscillations are a general phenomenon, that appears both in biological or nonbiological systems. Using nonlinear thermodynamics and nonlinear differential equations the stability of the steady state solutions for these chemical oscillations is analyzed. A set of reactions produced between molecular species with self-catalytic properties is analyzed, noting a fidelity factor, introduced in the process.
Abstract This work aims to highlight, by a series of spatial estimates, the effect of the presenc... more Abstract This work aims to highlight, by a series of spatial estimates, the effect of the presence of pore system and local thermal non-equilibrium properties in a triple porosity material matrix on the transmission depth of a thermo-mechanical signal. Two kind of spatial behaviors are established, for which the spatial response obeys a linear first-order differential inequality with two kind different coefficients: one is time independent and the other is time dependent. The first differential inequality furnishes some exponential decaying spatial estimates with uniform in time exponent and such estimates are recommended to be used for appropriately large values of the time variable. While the second first-order differential inequality furnishes some exponential decaying spatial estimates with time dependent exponent, thus showing a rapid spatial decrease of the solution for appropriate short values of time. These results are compared with their counterparts without mechanical effects, that is for purely pore system or local thermal non-equilibrium effects theories: this is done for appropriate short and large values of the time variable.
A PRINCIPLE OF SAINT-VENANT-TYPE is established for a right cylinder composed of an anisotropic, ... more A PRINCIPLE OF SAINT-VENANT-TYPE is established for a right cylinder composed of an anisotropic, linear, homogeneous micropolar elastic solid and subjected to harmonic loading on one of its ends. The amplitude of the harmonic vibrations of this cylinder is also shown to depend continuously on the prescribed data.
International Journal of Engineering Science, 1979
Al&&-We consider Saint-Venant's problem in the case when the cross-section of the cylinder is occ... more Al&&-We consider Saint-Venant's problem in the case when the cross-section of the cylinder is occupied by different inhomogeneous and isotropic micropolar elastic solids. The results are used to study the deformation of a circular composite cylinder.
The present paper studies the propagation of plane time harmonic waves in an infinite space fille... more The present paper studies the propagation of plane time harmonic waves in an infinite space filled by a thermoelastic material with microtemperatures. It is found that there are seven basic waves traveling with distinct speeds: (a) two transverse elastic waves uncoupled, undamped in time and traveling independently with the speed that is unaffected by the thermal effects; (b) two transverse thermal standing waves decaying exponentially to zero when time tends to infinity and they are unaffected by the elastic deformations; (c) three dilatational waves that are coupled due to the presence of thermal properties of the material. The set of dilatational waves consists of a quasi-elastic longitudinal wave and two quasithermal standing waves. The two transverse elastic waves are not subjected to the dispersion, while the other two transverse thermal standing waves and the dilatational waves present the dispersive character. Explicit expressions for all these seven waves are presented. The Rayleigh surface wave propagation problem is addressed and the secular equation is obtained in an explicit form. Numerical computations are performed for a specific model, and the results obtained are depicted graphically.
The paper discusses the role of entropy in the open systems, following Prigogine's theory of... more The paper discusses the role of entropy in the open systems, following Prigogine's theory of nonlinear thermodynamics. The apparent contradiction between the biological order and the second principle of thermodynamics is examined, noting the relationship between the thermodynamics equilibrium and minimum entropy production. Finally it is shown that the dissipative structures in hydrodynamics, optics, chemistry and biology are a general phenomenon of nature.
We study a thermal model associated with a heat-conducting material based on a three-phase-lag co... more We study a thermal model associated with a heat-conducting material based on a three-phase-lag constitutive equation for the heat flux, a model that leads to a Moore–Gibson–Thompson type equation for the thermal displacement. We are researching the compatibility of the three-phase-lag constitutive equation in concern with the second law of thermodynamics, thus discovering restrictions to be imposed on the involved thermal coefficients. On this basis, we manage to obtain the well-posedness problem of the model as the uniqueness of the solutions and their continuous dependence on the given data. Finally, we show that such a model not only allows the propagation of damped in time waves but also exponentially decaying in time thermal standing mode waves. We also show that if the thermodynamic restrictions are not fulfilled, then we can be led to instability. Through the present treatment of the thermal model in question, we obtain important information on the associated Moore–Gibson–Thompson type equation for the thermal displacement.
In this article we analyze the behavior of plane harmonic waves in the entire space lled by a lin... more In this article we analyze the behavior of plane harmonic waves in the entire space lled by a linear thermoviscoelastic material with voids. We take into account the e ect of the thermal and viscous dissipation energies upon the corresponding waves and, consequently, we study the damped in time wave solutions. There are ve basic waves in an isotropic and homogeneous thermoviscoelastic porous space. Two of them are shear waves, while the remaining three are dilatational waves. The shear waves are uncoupled, damped in time with decay rate depending only on the viscosity coe cients. The three dilatational waves are coupled and consist of a predominantly dilatational damped wave of Kelvin-Voigt viscoelasticity, other is predominantly a wave carrying a change in the void volume fraction and the third takes the form of a standing thermal wave whose amplitude decays exponentially with time. The explicit form of the dispersion equation is obtained in terms of the wave speed and the thermoviscoelastic homogeneous pro le. Furthermore, we use numerical methods and computations to solve the secular equation for some special classes of thermoviscoelastic materials considered in literature.
Cinematica punctului material studiazȃ mişcarea unui sistem material format dintr-un singur punct... more Cinematica punctului material studiazȃ mişcarea unui sistem material format dintr-un singur punct P . Un astfel de sistem reprezintȃ un bun model pentru studiul mişcȃrii corpurilor a cȃror dimensiuni sunt suficient de miciîncât sȃ poatȃ fi neglijate,în raport cu celelalte dimensiuni cuprinseîn mediul ambiantîn care se produce mişcarea.
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