Rao–Nakra sandwich beam with second sound

Raposo, Carlos A.; Villagrán, Octavio Paulo Vera; Ferreira, J.; Pışkın, Erhan

doi:10.1016/j.padiff.2021.100053

Cited by 9 publications

(3 citation statements)

References 18 publications

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“…In 2021, 17 Raposo proved the well-posedness and exponential stability for a Rao-Nakra sandwich beam equation with internal damping and time delay. Also, in 2021, 18 the authors proved the well-posedness and exponential stability for a thermoelastic structure given by a Rao-Nakra sandwich beam.…”

Section: Figure 1 Model Describing the Generalised Rao-nakra Beammentioning

confidence: 99%

Stabilization of the generalized Rao‐Nakra beam by partial viscous damping

Akil

Liu

2022

Math Methods in App Sciences

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In this paper, we consider the stabilization of the generalized Rao-Nakra beam equation, which consists of four wave equations for the longitudinal displacements and the shear angle of the top and bottom layers and one Euler-Bernoulli beam equation for the transversal displacement. Dissipative mechanism are provided through viscous damping for two displacements. The location of the viscous damping are divided into two groups, characterized by whether both of the top and bottom layers are directly damped or otherwise. Each group consists of three cases. We obtain the necessary and sufficient conditions for the cases in group 2 to be strongly stable. Furthermore, polynomial stability of certain orders are proved. The cases in group 1 are left for future study.

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Section: Figure 1 Model Describing the Generalised Rao-nakra Beammentioning

confidence: 99%

Stabilization of the generalized Rao‐Nakra beam by partial viscous damping

Akil

Liu

2022

Math Methods in App Sciences

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“…Since then, a great interest has been aroused in different contexts and nowadays there are many results on global and local solutions, stability, and burst behavior of solutions in thermoelasticity theory. We can cite [2][3][4][5][6][7][8][9][10][11] with references therein.…”

Section: Introductionmentioning

confidence: 99%

Global Solution and Blow-up for a Thermoelastic System of $p$-Laplacian Type with Logarithmic Source

Raposo

Cattai

Vera

et al. 2023

Mathematical Sciences and Applications E-Notes

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This manuscript deals with global solution, polynomial stability and blow-up behavior at a finite time for the nonlinear system \begin{align*} \left\{ \begin{array}{rcl} & u'' - \Delta_{p} u + \theta + \alpha u' = \left\vert u\right\vert ^{p-2}u\ln \left\vert u\right\vert \\ &\theta' - \Delta \theta = u' \end{array}% \right. \end{align*} where $\Delta_{p}$ is the nonlinear $p$-Laplacian operator, $ 2 \leq p < \infty$. Taking into account that the initial data is in a suitable stability set created from the Nehari manifold, the global solution is constructed by means of the Faedo-Galerkin approximations. Polynomial decay is proven for a subcritical level of initial energy. The blow-up behavior is shown on an instability set with negative energy values.

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“…The long-time dynamics of a fully damped non-autonomous Rao-Nakra beam with fractional Laplacian dissipation was studied by Aouadi [23]. Stability results of the Rao-Nakra sandwich beam with thermal damping can be found in Mukiawa et al [24] and Raposo et al [25].…”

Section: Introductionmentioning

confidence: 99%

Asymptotic behavior of the Rao–Nakra sandwich beam model with Kelvin–Voigt damping

Méndez

Zannini

Feng

2023

Mathematics and Mechanics of Solids

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The Rao–Nakra sandwich beam is a coupled system consisting of two wave equations for the longitudinal displacements of the top and bottom layers and an Euler–Bernoulli beam equation for the transversal displacement. This paper concerns the system’s stability when the Kelvin–Voigt damping terms act on the first and third equations. Using the semigroup theory of linear operators, we prove the global well-posedness of the associated initial boundary value problem. And then, we prove the lack of exponential stability of the system. Because of this lack of exponential stability, we study the polynomial stability and prove that the system decays with rate [Formula: see text]. We further prove that this decay rate is optimal.

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Rao–Nakra sandwich beam with second sound

Cited by 9 publications

References 18 publications

Stabilization of the generalized Rao‐Nakra beam by partial viscous damping

Stabilization of the generalized Rao‐Nakra beam by partial viscous damping

Global Solution and Blow-up for a Thermoelastic System of $p$-Laplacian Type with Logarithmic Source

Asymptotic behavior of the Rao–Nakra sandwich beam model with Kelvin–Voigt damping

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