The present investigation is intended to demonstrate the magnetic field,relaxation time,hydrostatic initial stress,and two temperature on the thermal shock problem.The governing equations are formulated in the context...The present investigation is intended to demonstrate the magnetic field,relaxation time,hydrostatic initial stress,and two temperature on the thermal shock problem.The governing equations are formulated in the context of Lord-Shulman theory with the presence of bodily force,two temperatures,thermal shock,and hydrostatic initial stress.We obtained the exact solution using the normal mode technique with appropriate boundary conditions.The field quantities are calculated analytically and displayed graphically under thermal shock problem with effect of external parameters respect to space coordinates.The results obtained are agreeing with the previous results obtained by others when the new parameters vanish.The results indicate that the effect of magnetic field and initial stress on the conductor temperature,thermodynamic temperature,displacement and stress are quite pronounced.In order to illustrate and verify the analytical development,the numerical results of temperature,displacement and stress are carried out and computer simulated results are presented graphically.This study helpful in the development of piezoelectric devices.展开更多
The present paper paper,we estimate the theory of thermoelasticity a thin slim strip under the variable thermal conductivity in the fractional-order form is solved.Thermal stress theory considering the equation of hea...The present paper paper,we estimate the theory of thermoelasticity a thin slim strip under the variable thermal conductivity in the fractional-order form is solved.Thermal stress theory considering the equation of heat conduction based on the time-fractional derivative of Caputo of orderis applied to obtain a solution.We assumed that the strip surface is to be free from traction and impacted by a thermal shock.The transform of Laplace(LT)and numerical inversion techniques of Laplace were considered for solving the governing basic equations.The inverse of the LT was applied in a numerical manner considering the Fourier expansion technique.The numerical results for the physical variables were calculated numerically and displayed via graphs.The parameter of fractional order effect and variation of thermal conductivity on the displacement,stress,and temperature were investigated and compared with the results of previous studies.The results indicated the strong effect of the external parameters,especially the timefractional derivative parameter on a thermoelastic thin slim strip phenomenon.展开更多
The aim of this paper is to study the effects of rotation and magnetic field on the plane vibrations in a transversely isotropic material of an infinite hollow cylinder.The natural frequency of the plane vibrations in...The aim of this paper is to study the effects of rotation and magnetic field on the plane vibrations in a transversely isotropic material of an infinite hollow cylinder.The natural frequency of the plane vibrations in the case of harmonic vibrations has been obtained.The natural frequencies are calculated numerically and the effects of rotation and magnetic field are discussed.The numerical results obtained have been illustrated graphically to understand the behavior of frequency equation with different values of frequencyωunder effects the rotation and magnetic field.Comparison was made with the results obtained in the presence and absence of the rotation and magnetic field.The results indicate that the effect of rotation and magnetic field are very pronounced.展开更多
The present article deals with the investigation thermal stress of a magnetothermoelastic cylinder subjected to rotation,open or closed circuit,thermal and mechanical boundary conditions.The outer and inner surfaces o...The present article deals with the investigation thermal stress of a magnetothermoelastic cylinder subjected to rotation,open or closed circuit,thermal and mechanical boundary conditions.The outer and inner surfaces of the cylinder are subjected to both mechanical and thermal boundary conditions.A The transient coupled thermoelasticity in an infinite cylinder with its base abruptly exposed to a heat flux of a decaying exponential function of time is devised solve by the finite-difference method.The fundamental equations’system is solved by utilizing an implicit finite-difference method.This current method is a second-order accurate in time and space;it is also unconditionally stable.To illustrate the present model’s efficiency,we consider a suitable material and acquire the numerical solution of temperature,displacement components,and the components of stresses with time t and through the radial of an infinite cylinder.The results indicate that the effect of coupled thermoelasticity,magnetic field,and rotation on the temperature,stresses,and displacement is quite pronounced.In order to illustrate and verify the analytical developments,the numerical solution of partial differential equations,stress components,displacement components and temperature is carried out and computer simulated results are presented graphically.This study is helpful in the development of piezoelectric devices.展开更多
基金Taif University Researchers Supporting Project Number(TURSP-2020/164),Taif University,Taif,Saudi Arabia.
文摘The present investigation is intended to demonstrate the magnetic field,relaxation time,hydrostatic initial stress,and two temperature on the thermal shock problem.The governing equations are formulated in the context of Lord-Shulman theory with the presence of bodily force,two temperatures,thermal shock,and hydrostatic initial stress.We obtained the exact solution using the normal mode technique with appropriate boundary conditions.The field quantities are calculated analytically and displayed graphically under thermal shock problem with effect of external parameters respect to space coordinates.The results obtained are agreeing with the previous results obtained by others when the new parameters vanish.The results indicate that the effect of magnetic field and initial stress on the conductor temperature,thermodynamic temperature,displacement and stress are quite pronounced.In order to illustrate and verify the analytical development,the numerical results of temperature,displacement and stress are carried out and computer simulated results are presented graphically.This study helpful in the development of piezoelectric devices.
文摘The present paper paper,we estimate the theory of thermoelasticity a thin slim strip under the variable thermal conductivity in the fractional-order form is solved.Thermal stress theory considering the equation of heat conduction based on the time-fractional derivative of Caputo of orderis applied to obtain a solution.We assumed that the strip surface is to be free from traction and impacted by a thermal shock.The transform of Laplace(LT)and numerical inversion techniques of Laplace were considered for solving the governing basic equations.The inverse of the LT was applied in a numerical manner considering the Fourier expansion technique.The numerical results for the physical variables were calculated numerically and displayed via graphs.The parameter of fractional order effect and variation of thermal conductivity on the displacement,stress,and temperature were investigated and compared with the results of previous studies.The results indicated the strong effect of the external parameters,especially the timefractional derivative parameter on a thermoelastic thin slim strip phenomenon.
文摘The aim of this paper is to study the effects of rotation and magnetic field on the plane vibrations in a transversely isotropic material of an infinite hollow cylinder.The natural frequency of the plane vibrations in the case of harmonic vibrations has been obtained.The natural frequencies are calculated numerically and the effects of rotation and magnetic field are discussed.The numerical results obtained have been illustrated graphically to understand the behavior of frequency equation with different values of frequencyωunder effects the rotation and magnetic field.Comparison was made with the results obtained in the presence and absence of the rotation and magnetic field.The results indicate that the effect of rotation and magnetic field are very pronounced.
基金Taif University Researchers Supporting Project Number(TURSP-2020/164),Taif University,Taif,Saudi Arabia.
文摘The present article deals with the investigation thermal stress of a magnetothermoelastic cylinder subjected to rotation,open or closed circuit,thermal and mechanical boundary conditions.The outer and inner surfaces of the cylinder are subjected to both mechanical and thermal boundary conditions.A The transient coupled thermoelasticity in an infinite cylinder with its base abruptly exposed to a heat flux of a decaying exponential function of time is devised solve by the finite-difference method.The fundamental equations’system is solved by utilizing an implicit finite-difference method.This current method is a second-order accurate in time and space;it is also unconditionally stable.To illustrate the present model’s efficiency,we consider a suitable material and acquire the numerical solution of temperature,displacement components,and the components of stresses with time t and through the radial of an infinite cylinder.The results indicate that the effect of coupled thermoelasticity,magnetic field,and rotation on the temperature,stresses,and displacement is quite pronounced.In order to illustrate and verify the analytical developments,the numerical solution of partial differential equations,stress components,displacement components and temperature is carried out and computer simulated results are presented graphically.This study is helpful in the development of piezoelectric devices.
