On the stabilization of viscoelastic laminated beams with interfacial slip

Mustafa, Muhammad I.

doi:10.1007/s00033-018-0928-7

Cited by 25 publications

(6 citation statements)

References 19 publications

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“…Recently, Mustafa [35,36] improved the result and established two general and explicit decay results by using (1.14). Li et al [26] extended the result to the case of non-equal speeds and established a general decay of energy to the system.…”

Section: Introductionmentioning

confidence: 98%

Exponential stabilization of laminated beams with history memories

Feng

Júnior

Ramos

2021

Mathematische Nachrichten

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In this paper we consider laminated beams modelled from the well established Timoshenko system, which is a structure given by two identical layers uniform on top of each other, taking into account that an adhesive of small thickness is bonding the two surfaces and produces an interfacial slip. By using semi-group approach, we prove the global well-posedness of the system when a viscoelastic dissipation acts on the three equations. In addition, we prove that the dissipation through memory terms is strong enough to get exponential decay of the system without the condition of equal wave speeds.

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Section: Introductionmentioning

confidence: 98%

Exponential stabilization of laminated beams with history memories

Feng

Júnior

Ramos

2021

Mathematische Nachrichten

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“…and obtained the exponential decay, provided equation (4) holds. Mustafa [15, 16] extended the result to obtain two general decay results under the assumption of equation (4). Li et al [17] and Chen et al [18] extended the result to the case of non-equal speeds.…”

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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“…Lo and Tatar 18 studied () in the presence of a viscoelastic damping, with

\frac{ρ}{G} = \frac{I_{ρ}}{D}

and additional conditions on the coefficients, and established an exponential decay result when the relaxation function decays exponentially. This was improved and extended to more general situations by Chen et al 19 , Liu et al, 20 and Mustafa 21,22 …”

Section: Introductionmentioning

confidence: 99%

Uniform stability for laminated beams with time‐dependent boundary conditions

Mustafa

2022

Math Methods in App Sciences

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In this paper we consider a laminated beam model. This structure is given by two identical uniform layers on top of each other, taking into account that an adhesive of small thickness is bonding the two surfaces and produces an interfacial slip. In the presence of nonlinear boundary controls modulated by time‐dependent coefficients, we use the multiplier method and overcome the difficulty of finding suitable multipliers to establish a uniform stability result. This result provides an explicit formula for the energy decay rates without imposing any conditions on the coefficients of the system which is more meaningful and realistic from the physical point of view. Our result improves the earlier related results in the literature.

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On the stabilization of viscoelastic laminated beams with interfacial slip

Cited by 25 publications

References 19 publications

Exponential stabilization of laminated beams with history memories

Exponential stabilization of laminated beams with history memories

Memory-type boundary control of a laminated Timoshenko beam

Uniform stability for laminated beams with time‐dependent boundary conditions

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