scholarly journals On the Stabilization for Laminated Beam with Infinite Memory and Different Speeds of Wave Propagation

2017 ◽  
Author(s):  
Gang Li ◽  
Xiangyu Kong
Keyword(s):  
Wave Propagation ◽  
Differential Equations ◽  
Boundary Control ◽  
Rotation Angle ◽  
General Decay ◽  
Laminated Beam ◽  
Wave Speeds ◽  
Infinite Memory ◽  
One Dimensional ◽  
Order Energy

In this work, we consider a one-dimensional laminated beam in the case of non-equal wave speeds with only one infinite memory on the effective rotation angle. In this case, we establish the general decay result for the energy of solution without any kind of internal or boundary control. The main result is obtained by applying the method used in Guesmia et al. (Electron. J. Differential Equations 193: 1-45, 2012) and the second-order energy.

Asymptotic stability for a laminated beam with structural damping and infinite memory

2020 ◽  
Vol 25 (10) ◽  
pp. 1979-2004 ◽  
Author(s):  
Wenjun Liu ◽  
Xiangyu Kong ◽  
Gang Li
Keyword(s):  
Wave Propagation ◽  
Relaxation Function ◽  
Rotation Angle ◽  
Structural Damping ◽  
Laminated Beam ◽  
Infinite Memory ◽  
One Dimensional ◽  
Special Cases ◽  
Lack Of Exponential Stability ◽  
Well Posed

In this paper, we consider a one-dimensional laminated beam with structural damping and an infinite memory acting on the effective rotation angle. Under appropriate assumptions imposed on the relaxation function, we show that the system is well-posed by using the Hille–Yosida theorem, and then we establish general decay results, from which exponential and polynomial decays are only special cases, in the case of equal speeds of wave propagation as well as that of nonequal speeds. In the particular case when the wave propagation speeds are different and the relaxation function decays exponentially, we show the lack of exponential stability.

scholarly journals Exponential and Polynomial Decay for a Laminated Beam with Fourier's Type Heat Conduction

2019 ◽  
Author(s):  
Wenjun Liu ◽  
Weifan Zhao
Keyword(s):  
Heat Conduction ◽  
Energy Method ◽  
Rotation Angle ◽  
Polynomial Decay ◽  
Structural Damping ◽  
Laminated Beam ◽  
Wave Speeds ◽  
One Dimensional ◽  
Exponentially Stable ◽  
Well Posed

In this paper, we study the well-posedness and asymptotics of a one-dimensional thermoelastic laminated beam system either with or without structural damping, where the heat conduction is given by Fourier's law effective in the rotation angle displacements. We show that the system is well-posed by using Lumer-Philips theorem, and prove that the system is exponentially stable if and only if the wave speeds are equal, by using the perturbed energy method and Gearhart-Herbst-Prüss-Huang theorem. Furthermore, we show that the system with structural damping is polynomially stable provided that the wave speeds are not equal, by using the second-order energy method.

scholarly journals Exponential and Polynomial Decay for a Laminated Beam with Fourier's Type Heat Conduction

2017 ◽  
Author(s):  
Wenjun Liu ◽  
Weifan Zhao
Keyword(s):  
Heat Conduction ◽  
Rotation Angle ◽  
Polynomial Decay ◽  
Well Posedness ◽  
Laminated Beam ◽  
Wave Speeds ◽  
One Dimensional ◽  
Beam System ◽  
Exponentially Stable ◽  
Well Posed

In this paper, we study the well-posedness and the asymptotic behavior of a one-dimensional laminated beam system, where the heat conduction is given by Fourier's law effective in the rotation angle displacements. We show that the system is well-posed by using the Hille-Yosida theorem and prove that the system is exponentially stable if and only if the wave speeds are equal. Furthermore, we show that the system is polynomially stable provided that the wave speeds are not equal.

Elastic-Plastic Boundaries in Combined Longitudinal and Torsional Plastic Wave Propagation

1968 ◽  
Vol 35 (4) ◽  
pp. 782-786 ◽  
Author(s):  
R. J. Clifton
Keyword(s):  
Wave Propagation ◽  
Time Derivative ◽  
Plastic Wave ◽  
Wave Speeds ◽  
One Dimensional ◽  
Elastic Plastic ◽  
Simple Waves ◽  
Thin Walled Tube ◽  
Loading And Unloading ◽  
All Speeds

Assuming a one-dimensional rate independent theory of combined longitudinal and torsional plastic wave propagation in a thin-walled tube, restrictions are obtained on the possible speeds of elastic-plastic boundaries. These restrictions are shown to depend on the type of discontinuity at the boundary and on whether loading or unloading is occurring. The range of unloading (loading) wave speeds for the case when the nth time derivative of the solution is the first derivative that is discontinuous across the boundary is the complement of the range of unloading (loading) wave speeds for the case when the first discontinuity is in the (n + 1)th time derivative. Thus all speeds are possible for elastic-plastic boundaries corresponding to either loading or unloading. The general features of the discontinuities associated with loading and unloading boundaries are established, and examples are presented of unloading boundaries overtaking simple waves.

Characteristic Forms of Differential Equations for Wave Propagation in Nonlinear Media

1981 ◽  
Vol 48 (4) ◽  
pp. 743-748 ◽  
Author(s):  
T. C. T. Ting
Keyword(s):  
Wave Propagation ◽  
Differential Equations ◽  
Constitutive Equations ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Compressible Fluids ◽  
Elastic Solids ◽  
Nonlinear Media ◽  
Nonlinear Materials ◽  
One Dimensional

Characteristic forms of differential equations for wave propagation in nonlinear media are derived directly from equations of motion and equations which combine the constitutive equations and the equations of continuity. Both Lagrangian coordinates and Eulerian coordinates are considered. The constitutive equations considered here apply to a large class of nonlinear materials. The characteristic forms derived here clearly show which components of the stress and velocity are involved in the differentiation along the bicharacteristics. Moreover, the reduction to one-dimensional cases from three-dimensional problems is obvious for the characteristic forms obtained here. Examples are given and compared with the known solution in the literature for wave propagation in linear isotropic elastic solids and isentropic compressible fluids.

Decay of solutions for a one-dimensional porous elasticity system with memory: the case of non-equal wave speeds

2018 ◽  
Vol 24 (8) ◽  
pp. 2361-2373 ◽  
Author(s):  
Baowei Feng ◽  
Mingyang Yin
Keyword(s):  
Point Of View ◽  
General Decay ◽  
Wave Speeds ◽  
One Dimensional ◽  
Elasticity System ◽  
Decay Of Solutions ◽  
With Memory

In previous work, Apalara considered a one-dimensional porous elasticity system with memory and established a general decay of energy for the system in the case of equal-speed wave propagations. In this paper, we extend the result to the case of non-equal wave speeds, which is more realistic from the physics point of view.

Nonlinear dynamics of pulsating detonation wave with two-stage chemical kinetics in the shock-attached frame

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Yaroslava E. Poroshyna ◽  
Aleksander I. Lopato ◽  
Pavel S. Utkin
Keyword(s):  
Wave Propagation ◽  
Detonation Wave ◽  
Model Comparison ◽  
Approximation Order ◽  
Transition Regime ◽  
Stage Model ◽  
Two Stage ◽  
One Dimensional ◽  
Kinetics Of ◽  
Detonation Wave Propagation

Abstract The paper contributes to the clarification of the mechanism of one-dimensional pulsating detonation wave propagation for the transition regime with two-scale pulsations. For this purpose, a novel numerical algorithm has been developed for the numerical investigation of the gaseous pulsating detonation wave using the two-stage model of kinetics of chemical reactions in the shock-attached frame. The influence of grid resolution, approximation order and the type of rear boundary conditions on the solution has been studied for four main regimes of detonation wave propagation for this model. Comparison of dynamics of pulsations with results of other authors has been carried out.

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