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
To thoroughly examine the complex relationships between tire and pavement vibrations,a sophisticated vehicle-pavement coupled system is proposed,incorporating a non-uniform dynamic friction force between the tire and ...To thoroughly examine the complex relationships between tire and pavement vibrations,a sophisticated vehicle-pavement coupled system is proposed,incorporating a non-uniform dynamic friction force between the tire and the pavement.According to the Timoshenko beam theory,a dynamic model of pavement structure with a finite length beam was formulated on a nonlinear Pasternak foundation.To more accurately describe the coupling relationship between the tire and the pavement,and to take into account the vibration state under vehicle-pavement interaction,the load distribution between the tire and the pavement is modeled as a dynamic non-uniform contact.Combined with the classic LuGre tire model,the adhesion between the tire and the pavement is calculated.The Galerkin truncation method is employed to transform the pavement vibration partial differential equation into a finite ordinary differential equation,and the integral expression of the nonlinear foundation beam term is derived using the product to sum formula.By using the Runge-Kutta method,the tire-road coupled system can be numerically calculated,thus determining tire adhesion.This research demonstrates that compared with tire force under the traditional static load distribution,load distribution has a significant influence on adhesion.This study offers valuable insights for pavement structure design and vehicle performance control.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
The dynamics of beams subjected to moving loads are of practical importance since the responses caused by these loads can be greater than those under equivalent static loads in some cases.In this work,a novel inertial...The dynamics of beams subjected to moving loads are of practical importance since the responses caused by these loads can be greater than those under equivalent static loads in some cases.In this work,a novel inertial nonlinear energy sink(NES)is applied for the first time to achieve vibration suppression in beams under moving loads.Based on the Timoshenko beam theory,the nonlinear motion equations of a beam with an inertial NES are derived using the energy method and Lagrange equations.The Newmark-βmethod combined with the Heaviside step function is adopted to calculate the responses of the beam under moving loads of constant amplitude and harmonic excitation.The accuracy of the modelling derivation and solution methodology are validated through comparisons with results from other studies.The results demonstrate that the velocity and excitation frequency of the moving load significantly affect the response of the beam as well as the performance of the inertial NES.To enhance its effectiveness under various moving load conditions,parametric optimization is numerically performed.The optimized inertial NES can achieve good performance by efficiently reducing the maximum deflection of the beam.The findings of this study contribute to advancing the understanding and application of NESs in mitigating structural vibrations caused by moving loads.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financially supported by the National Natural Science Foundation of China(Grant No.12072204).
文摘To thoroughly examine the complex relationships between tire and pavement vibrations,a sophisticated vehicle-pavement coupled system is proposed,incorporating a non-uniform dynamic friction force between the tire and the pavement.According to the Timoshenko beam theory,a dynamic model of pavement structure with a finite length beam was formulated on a nonlinear Pasternak foundation.To more accurately describe the coupling relationship between the tire and the pavement,and to take into account the vibration state under vehicle-pavement interaction,the load distribution between the tire and the pavement is modeled as a dynamic non-uniform contact.Combined with the classic LuGre tire model,the adhesion between the tire and the pavement is calculated.The Galerkin truncation method is employed to transform the pavement vibration partial differential equation into a finite ordinary differential equation,and the integral expression of the nonlinear foundation beam term is derived using the product to sum formula.By using the Runge-Kutta method,the tire-road coupled system can be numerically calculated,thus determining tire adhesion.This research demonstrates that compared with tire force under the traditional static load distribution,load distribution has a significant influence on adhesion.This study offers valuable insights for pavement structure design and vehicle performance control.
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supported by the National Natural Science Foundation of China(Grant Nos.12102015 and 12472003)the General Program of Science and Technology Development Project of the Beijing Municipal Education Commission(Grant No.KM202110005030)the Key Research Project of Zhejiang Market Supervision Administration(Grant No.ZD2024013).
文摘The dynamics of beams subjected to moving loads are of practical importance since the responses caused by these loads can be greater than those under equivalent static loads in some cases.In this work,a novel inertial nonlinear energy sink(NES)is applied for the first time to achieve vibration suppression in beams under moving loads.Based on the Timoshenko beam theory,the nonlinear motion equations of a beam with an inertial NES are derived using the energy method and Lagrange equations.The Newmark-βmethod combined with the Heaviside step function is adopted to calculate the responses of the beam under moving loads of constant amplitude and harmonic excitation.The accuracy of the modelling derivation and solution methodology are validated through comparisons with results from other studies.The results demonstrate that the velocity and excitation frequency of the moving load significantly affect the response of the beam as well as the performance of the inertial NES.To enhance its effectiveness under various moving load conditions,parametric optimization is numerically performed.The optimized inertial NES can achieve good performance by efficiently reducing the maximum deflection of the beam.The findings of this study contribute to advancing the understanding and application of NESs in mitigating structural vibrations caused by moving loads.
