The equations of generalized thermoelasticity with one relaxation time with variable modulus of elasticity and the thermal conductivity were used to solve a problem of an infinite material with a spherical cavity.The ...The equations of generalized thermoelasticity with one relaxation time with variable modulus of elasticity and the thermal conductivity were used to solve a problem of an infinite material with a spherical cavity.The inner surface of the cavity was taken to be traction free and acted upon by a thermal shock to the surface. Laplace transforms techniques were used to obtain the solution by a direct approach.The inverse Laplace transforms was obtained numerically.The temperature,displacement and stress distributions are represented graphically.展开更多
In the nanoscale beam,two effects become domineering.One is the non-Fourier effect in heat conduction and the other is the coupling effect between temperature and strain rate.In the present study,a generalized solutio...In the nanoscale beam,two effects become domineering.One is the non-Fourier effect in heat conduction and the other is the coupling effect between temperature and strain rate.In the present study,a generalized solution for the generalized thermoelastic vibration of gold nano-beam resonator induced by ramp type heating is developed.The solution takes into account the above two effects.State-space and Laplace transform methods are used to determine the lateral vibration,the temperature,the displacement,the stress and the strain energy of the beam.The effects of the relaxation time and the ramping time parameters have been studied.展开更多
A mathematical model is elaborated for a thermoelastic infinite body with a spherical cavity.A generalized set of governing equations is formulated in the context of three different models of thermoelasticity:the Biot...A mathematical model is elaborated for a thermoelastic infinite body with a spherical cavity.A generalized set of governing equations is formulated in the context of three different models of thermoelasticity:the Biot model,also known as“coupled thermoelasticity”model;the Lord-Shulman model,also referred to as“generalized thermoelasticity with one-relaxation time”approach;and the Green-Lindsay model,also called“generalized thermoelasticity with two-relaxation times”approach.The Adomian’s decomposition method is used to solve the related mathematical problem.The bounding plane of the cavity is subjected to harmonic thermal loading with zero heat flux and strain.Numerical results for the temperature,radial stress,strain,and displacement are represented graphically.It is shown that the angular thermal load and the relaxation times have significant effects on all the studied fields.展开更多
文摘The equations of generalized thermoelasticity with one relaxation time with variable modulus of elasticity and the thermal conductivity were used to solve a problem of an infinite material with a spherical cavity.The inner surface of the cavity was taken to be traction free and acted upon by a thermal shock to the surface. Laplace transforms techniques were used to obtain the solution by a direct approach.The inverse Laplace transforms was obtained numerically.The temperature,displacement and stress distributions are represented graphically.
文摘In the nanoscale beam,two effects become domineering.One is the non-Fourier effect in heat conduction and the other is the coupling effect between temperature and strain rate.In the present study,a generalized solution for the generalized thermoelastic vibration of gold nano-beam resonator induced by ramp type heating is developed.The solution takes into account the above two effects.State-space and Laplace transform methods are used to determine the lateral vibration,the temperature,the displacement,the stress and the strain energy of the beam.The effects of the relaxation time and the ramping time parameters have been studied.
文摘A mathematical model is elaborated for a thermoelastic infinite body with a spherical cavity.A generalized set of governing equations is formulated in the context of three different models of thermoelasticity:the Biot model,also known as“coupled thermoelasticity”model;the Lord-Shulman model,also referred to as“generalized thermoelasticity with one-relaxation time”approach;and the Green-Lindsay model,also called“generalized thermoelasticity with two-relaxation times”approach.The Adomian’s decomposition method is used to solve the related mathematical problem.The bounding plane of the cavity is subjected to harmonic thermal loading with zero heat flux and strain.Numerical results for the temperature,radial stress,strain,and displacement are represented graphically.It is shown that the angular thermal load and the relaxation times have significant effects on all the studied fields.
