Journal ArticleDOI
Lack of exponential decay for a thermoelastic laminated beam under Cattaneo’s law of heat conduction
Danhua Wang,Wenjun Liu +1 more
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TLDR
In this paper, the authors considered the same system and showed a lack of exponential stability when the stability number of the stability matrix is larger than the stability of the beam, by using the Gearhart-Herbst-Pruss-Huang theorem.Abstract:
Feng (Complexity, Art 5139419, 2020) studied a thermoelastic laminated Timoshenko beam, where the heat conduction is given by Cattaneo’s law, as well as established the exponential and polynomial stabilities depending on the stability number
$$\chi _\tau $$
In this short paper, we consider the same system and show a lack of exponential stability when the stability number
$$\chi _\tau \ne 0$$
, by using Gearhart–Herbst–Pruss–Huang theoremread more
Citations
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Exponential and polynomial decay for a laminated beam with Fourier’s law of heat conduction and possible absence of structural damping
Wenjun Liu,Weifan Zhao +1 more
TL;DR: In this paper, the authors studied the well-posedness and decay properties of a one-dimensional thermoelastic laminated beam system with or without structural damping, of which the heat conduction is given by Fourier's law effective in the rotation angle displacements.
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Lack of Exponential Decay for a Laminated Beam with Structural Damping and Second Sound
Wenjun Liu,Xiangyu Kong,Gang Li +2 more
TL;DR: In this article, the authors studied the same system and showed that the solution of the concerned system lacks of exponential decay result in the case χτ ̸= 0 which solves the open problem proposed by Apalara.
Journal ArticleDOI
Polynomial and exponential decay rates of a laminated beam system with thermodiffusion effects
TL;DR: In this article , the authors considered a laminated beam system with thermodiffusion effects with two kinds of boundary conditions, in which the mass diffusion introduces a new critical thickness in addition to the conventional critical thickness of thermoelastic damping.
Journal ArticleDOI
Exponential stability for a thermoelastic laminated beam with nonlinear weights and time-varying delay
TL;DR: In this paper, the authors studied the well-posedness and asymptotic stability of a thermoelastic laminated beam with nonlinear weights and time-varying delay.
Journal ArticleDOI
Equivalence between internal observability and exponential stabilization for suspension bridge problem
Yasi Zheng,Wenjun Liu,Yadong Liu +2 more
TL;DR: In this paper, the authors study the fourth order semilinear suspension bridge problem with restoring force h(u) and linear damping and show an equivalence between observability and exponential stabilization of this system by using an appropriate decomposition technique and the semigroup method.
References
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Journal ArticleDOI
On the spectrum of ₀-semigroups
Journal ArticleDOI
Structural Damping in Laminated Beams due to Interfacial Slip
Scott W. Hansen,Ruben D. Spies +1 more
TL;DR: In this paper, three closely related models for two-layered beams in which slip can occur at the interface are described, and the optimal damping rates are calculated for these low frequency motions.
Journal ArticleDOI
Exponential Stabilization of Laminated Beams with Structural Damping and Boundary Feedback Controls
TL;DR: It is proved that there is a sequence of generalized eigenfunctions that forms a Riesz basis in the state Hilbert space, and hence the spectrum determined growth condition holds and exponential stability of the closed-loop system can be deduced from the eigenvalue expressions.
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Stabilization of a Thermoelastic Laminated Beam with Past History
Wenjun Liu,Weifan Zhao +1 more
TL;DR: In this paper, the well-posedness and asymptotic stability of a thermoelastic laminated beam with past history was studied. And the authors proved the exponential and polynomial stability of the system with and without structural damping.
Journal ArticleDOI
Easy Test for Stability of Laminated Beams with Structural Damping and Boundary Feedback Controls
TL;DR: In this article, the authors consider the test problem of stability of a closed loop system composed of laminated beams with structural damping and boundary feedback control and give a simple test method of verifying the exponential stability of the closed loop systems.