In this paper we consider one-dimensional Timoshenko system with linear fric- tional damping and a distributed delay acting on the displacement equation. Under suitable assumptions on the weight of the delay and the w...In this paper we consider one-dimensional Timoshenko system with linear fric- tional damping and a distributed delay acting on the displacement equation. Under suitable assumptions on the weight of the delay and the wave speeds, we establish the well-posedness of the system and show that the dissipation through the frictional damping is strong enough to uniformly stabilize the system even in the presence of delay.展开更多
In this paper,we first establish the global existence and asymptotic behavior of solutions by using the semigroup method and multiplicative techniques,then further prove the existence of a uniform attractor for Timosh...In this paper,we first establish the global existence and asymptotic behavior of solutions by using the semigroup method and multiplicative techniques,then further prove the existence of a uniform attractor for Timoshenko systems with Gurtin-Pipkin thermal law by using the method of uniform contractive functions.The main advantages of this method is that we need only to verify compactness condition with the same type of energy estimates as that for establishing absorbing sets.Moreover,we also investigate an alternative result of solutions to the semilinear Timoshenko systems by virtue of the semigroup method.展开更多
In this paper, we consider the Timoshenko system as an initial-boundary value problem in a one-dimensional bounded domain. And then we establish the global existence and asymptotic behavior of solution by using the se...In this paper, we consider the Timoshenko system as an initial-boundary value problem in a one-dimensional bounded domain. And then we establish the global existence and asymptotic behavior of solution by using the semigroup method and multiplicative techniques, then further prove the existence of a uniform attractor by using the method of uniform contractive function. The main advantage of this method is that we need only to verify compactness condition with the same type of energy estimate as that for establishing absorbing sets.展开更多
Considering Timoshenko systems under the Cattaneo thermal law, the purpose of the article is to obtain the global existence of linear Timoshenko system and semilinear Timoshenko system for the solutions of non-autonom...Considering Timoshenko systems under the Cattaneo thermal law, the purpose of the article is to obtain the global existence of linear Timoshenko system and semilinear Timoshenko system for the solutions of non-autonomous situations. The main method is converting the systems into abstract ODE, constructing proper spaces and proving the global existence by using semigroup methods. For asymptotic behavior, there will be a remark to describe the results.展开更多
In this paper,we study the well-posedness for the thermoelastic Timoshenko system with a constant delay and mass diffusion effects.Heat and mass exchange with the environment during thermodiffusion in Timoshenko beam....In this paper,we study the well-posedness for the thermoelastic Timoshenko system with a constant delay and mass diffusion effects.Heat and mass exchange with the environment during thermodiffusion in Timoshenko beam.The C_(0)-semigroup theory will be used to prove the well-posedness of the considered problem.展开更多
In this paper, we study a semilinear Timoshenko system with heat conduction having two damping effects. The observation that two damping effects might lead to smaller decay rates for solutions in comparison to one dam...In this paper, we study a semilinear Timoshenko system with heat conduction having two damping effects. The observation that two damping effects might lead to smaller decay rates for solutions in comparison to one damping effect is rigorously proved here in providing optimality results. Moreover, the global well-posedness for small data is presented.展开更多
In this paper, we consider a vibrating system of Timoshenko-type in a one- dimensional bounded domain with complementary frictional damping and infinite memory acting on the transversal displacement. We show that the ...In this paper, we consider a vibrating system of Timoshenko-type in a one- dimensional bounded domain with complementary frictional damping and infinite memory acting on the transversal displacement. We show that the dissipation generated by these two complementary controls guarantees the stability of the system in case of the equal-speed propagation as well as in the opposite case. We establish in each case a general decay estimate of the solutions. In the particular case when the wave propagation speeds are different and the frictional damping is linear, we give a relationship between the smoothness of the initiM data and the decay rate of the solutions. By the end of the paper, we discuss some applications to other Timoshenko-type systems.展开更多
In this work,a Timoshenko system of type Ⅲ of thermoelasticity with frictional versus viscoelastic under Dirichlet-Dirichlet-Neumann boundary conditions was considered.By exploiting energy method to produce a suitabl...In this work,a Timoshenko system of type Ⅲ of thermoelasticity with frictional versus viscoelastic under Dirichlet-Dirichlet-Neumann boundary conditions was considered.By exploiting energy method to produce a suitable Lyapunov functional,we establish the global existence and exponential decay of type-Ⅲ case.展开更多
Based on the Timoshenko beam theory,this paper proposes a nonlocal bi-gyroscopic model for spinning functionally graded(FG)nanotubes conveying fluid,and the thermal–mechanical vibration and stability of such composit...Based on the Timoshenko beam theory,this paper proposes a nonlocal bi-gyroscopic model for spinning functionally graded(FG)nanotubes conveying fluid,and the thermal–mechanical vibration and stability of such composite nanostructures under small scale,rotor,and temperature coupling effects are investigated.The nanotube is composed of functionally graded materials(FGMs),and different volume fraction functions are utilized to control the distribution of material properties.Eringen’s nonlocal elasticity theory and Hamilton’s principle are applied for dynamical modeling,and the forward and backward precession frequencies as well as 3D mode configurations of the nanotube are obtained.By conducting dimensionless analysis,it is found that compared to the Timoshenko nano-beam model,the conventional Euler–Bernoulli(E-B)model holds the same flutter frequency in the supercritical region,while it usually overestimates the higher-order precession frequencies.The nonlocal,thermal,and flowing effects all can lead to buckling or different kinds of coupled flutter in the system.The material distribution of the P-type FGM nanotube can also induce coupled flutter,while that of the S-type FGM nanotube has no impact on the stability of the system.This paper is expected to provide a theoretical foundation for the design of motional composite nanodevices.展开更多
文摘In this paper we consider one-dimensional Timoshenko system with linear fric- tional damping and a distributed delay acting on the displacement equation. Under suitable assumptions on the weight of the delay and the wave speeds, we establish the well-posedness of the system and show that the dissipation through the frictional damping is strong enough to uniformly stabilize the system even in the presence of delay.
基金Supported by the National Natural Science Foundation of China(11271066)Supported by the Shanghai Education Commission(13ZZ048)
文摘In this paper,we first establish the global existence and asymptotic behavior of solutions by using the semigroup method and multiplicative techniques,then further prove the existence of a uniform attractor for Timoshenko systems with Gurtin-Pipkin thermal law by using the method of uniform contractive functions.The main advantages of this method is that we need only to verify compactness condition with the same type of energy estimates as that for establishing absorbing sets.Moreover,we also investigate an alternative result of solutions to the semilinear Timoshenko systems by virtue of the semigroup method.
基金Supported by the National Natural Science Foundation of China（l1671075）
文摘In this paper, we consider the Timoshenko system as an initial-boundary value problem in a one-dimensional bounded domain. And then we establish the global existence and asymptotic behavior of solution by using the semigroup method and multiplicative techniques, then further prove the existence of a uniform attractor by using the method of uniform contractive function. The main advantage of this method is that we need only to verify compactness condition with the same type of energy estimate as that for establishing absorbing sets.
基金Supported by the National Natural Science Foundation of China（11671075）
文摘Considering Timoshenko systems under the Cattaneo thermal law, the purpose of the article is to obtain the global existence of linear Timoshenko system and semilinear Timoshenko system for the solutions of non-autonomous situations. The main method is converting the systems into abstract ODE, constructing proper spaces and proving the global existence by using semigroup methods. For asymptotic behavior, there will be a remark to describe the results.
基金Supported by the NNSF of China(Grant No.12171082)Fundamental Funds for the Central Universities(Grant No.2232021G-13).
文摘In this paper,we study the well-posedness for the thermoelastic Timoshenko system with a constant delay and mass diffusion effects.Heat and mass exchange with the environment during thermodiffusion in Timoshenko beam.The C_(0)-semigroup theory will be used to prove the well-posedness of the considered problem.
基金supported by National Natural Science Foundation of China(11771284)
文摘In this paper, we study a semilinear Timoshenko system with heat conduction having two damping effects. The observation that two damping effects might lead to smaller decay rates for solutions in comparison to one damping effect is rigorously proved here in providing optimality results. Moreover, the global well-posedness for small data is presented.
基金funded by KFUPM under the scientific project IN141015
文摘In this paper, we consider a vibrating system of Timoshenko-type in a one- dimensional bounded domain with complementary frictional damping and infinite memory acting on the transversal displacement. We show that the dissipation generated by these two complementary controls guarantees the stability of the system in case of the equal-speed propagation as well as in the opposite case. We establish in each case a general decay estimate of the solutions. In the particular case when the wave propagation speeds are different and the frictional damping is linear, we give a relationship between the smoothness of the initiM data and the decay rate of the solutions. By the end of the paper, we discuss some applications to other Timoshenko-type systems.
基金Supported by the NNSF of China with contract numbers 11671075
文摘In this work,a Timoshenko system of type Ⅲ of thermoelasticity with frictional versus viscoelastic under Dirichlet-Dirichlet-Neumann boundary conditions was considered.By exploiting energy method to produce a suitable Lyapunov functional,we establish the global existence and exponential decay of type-Ⅲ case.
基金National Natural Science Foundation of China,12372025,Feng Liang,12072311,Feng Liang.
文摘Based on the Timoshenko beam theory,this paper proposes a nonlocal bi-gyroscopic model for spinning functionally graded(FG)nanotubes conveying fluid,and the thermal–mechanical vibration and stability of such composite nanostructures under small scale,rotor,and temperature coupling effects are investigated.The nanotube is composed of functionally graded materials(FGMs),and different volume fraction functions are utilized to control the distribution of material properties.Eringen’s nonlocal elasticity theory and Hamilton’s principle are applied for dynamical modeling,and the forward and backward precession frequencies as well as 3D mode configurations of the nanotube are obtained.By conducting dimensionless analysis,it is found that compared to the Timoshenko nano-beam model,the conventional Euler–Bernoulli(E-B)model holds the same flutter frequency in the supercritical region,while it usually overestimates the higher-order precession frequencies.The nonlocal,thermal,and flowing effects all can lead to buckling or different kinds of coupled flutter in the system.The material distribution of the P-type FGM nanotube can also induce coupled flutter,while that of the S-type FGM nanotube has no impact on the stability of the system.This paper is expected to provide a theoretical foundation for the design of motional composite nanodevices.
