Hybrid laminated Timoshenko beam

Raposo, Carlos A.; Villagrán, Octavio Vera; Rivera, Jaime E. Muñoz; Alves, Margareth S.

doi:10.1063/1.4998945

Cited by 40 publications

(20 citation statements)

References 23 publications

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“…Raposo [7] investigated a laminated Timoshenko beam with frictional damping, as modelled by the three equations, and proved that the system decays exponentially without the equal wave-speed condition (equation (4)). Recently, Raposo et al [8] considered a hybrid laminated Timoshenko beam. The authors proved that the solution is polynomially stable using the semigroup approach and a result of Borichev and Tomilov [9].…”

Section: Introductionmentioning

confidence: 99%

Memory-type boundary control of a laminated Timoshenko beam

Feng

Soufyane

2020

Mathematics and Mechanics of Solids

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In this paper, we consider a laminated Timoshenko beam with boundary conditions of a memory type. This structure is given by two identical uniform layers, one on top of the other, taking into account that an adhesive of small thickness bonds the two surfaces and produces an interfacial slip. Under the assumptions of wider classes of kernel functions, we establish an optimal explicit energy decay result. The stability result is more general than previous works and hence improves earlier results in the literature.

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Section: Introductionmentioning

confidence: 99%

Memory-type boundary control of a laminated Timoshenko beam

Feng

Soufyane

2020

Mathematics and Mechanics of Solids

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“…Raposo (2016) proved that the exponential stability holds without any restriction on the parameters if the first two equations in (1.1) are also damped via frictional dampings. Recently, Raposo et al (2017) proved that, without any restriction on the parameters, the polynomial stability of (1.1) holds under additional three dynamic boundary conditions at l, where l is the length of the beam. For the stability of laminated beams with Cattaneo's or Fourier's type heat conduction, we refer the readers to Alves et al (2016) and Liu & Zhao (2017).…”

Section: Introductionmentioning

confidence: 99%

Well-posedness and stability results for laminated Timoshenko beams with interfacial slip and infinite memory

Guesmia

2019

IMA Journal of Mathematical Control and Information

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The model under consideration in this paper describes a vibrating structure of an interfacial slip and consists of three coupled hyperbolic equations in one-dimensional bounded interval under mixed homogeneous Dirichlet-Neumann boundary conditions. The first two equations are related to Timoshenko-type systems and the third one is subject to the dynamics of the slip. The main problem we discuss here is stabilizing the system by a viscoelastic damping generated by an infinite memory and acting only on one equation. First, we prove the existence, uniqueness and regularity of solutions using the semigroup theory. After that, we combine the energy method and the frequency domain approach to show that the infinite memory is capable alone to guarantee the strong and polynomial stability of the model, that is bringing it back to its equilibrium state with a decay rate of type t −d , where d is a positive constant depending on the regularity of initial data. Moreover, we prove that, when the infinite memory is effective on the first equation, the model is not exponentially stable independently of the values of the parameters. However, when the infinite memory is effective on the second or the third equation, we prove that the exponential stability is equivalent to the equality between the three speeds of wave propagations. An extension of our results to the frictional damping case is also given. Our results improve and extend some existing results in the literature subject to other types of controls.

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“…By adding suitable damping effects, such as internal damping, (boundary) frictional damping, and viscoelastic damping, it was shown that if the linear damping terms are added in two of the three equations, system (4) is exponentially stable under the "equal wave speeds" assumption (ρ/I ρ ) � (G/D). But if the damping terms are added in the three equations, then the system decays exponentially without the equal wave speeds assumption, see, for example, [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. For thermoelastic laminated Timoshenko beam, there are few published works, we can mention the results due to Liu and Zhao [18] and Apalara [19].…”

Section: Introductionmentioning

confidence: 99%