A general stability result in a memory-type Timoshenko system

Messaoudi, Salim A.; Mustafa, Muhammad I.

doi:10.3934/cpaa.2013.12.957

Cited by 48 publications

(43 citation statements)

References 21 publications

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“…Notice that in case s ≡ 0 we find the usual Timoshenko system studied by many authors (see [1,8,11,16,17,[20][21][22][23][24][25][29][30][31]33,34] to cite but a few).…”

Section: Introductionmentioning

confidence: 98%

Uniform Stability of a Laminated Beam with Structural Memory

Tatar

2015

Qual. Theory Dyn. Syst.

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Of concern is a structure consisting of two identical beams of uniform thickness. The beams are fastened tightly but still allowing an interfacial slip between the two components. This means that we are in presence of a longitudinal displacement and at the same time keeping a continuous contact of the layers. These beams are also subject to rotatory inertia and shear forces. We prove uniform stability of the system when a viscoelastic damping acts on the effective rotation and in the slip. This extends previous works where boundary controls were used in addition to a frictional damping in the dynamic of the slip.

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“…Notice that in case s ≡ 0 we find the usual Timoshenko system studied by many authors (see [1,8,11,16,17,[20][21][22][23][24][25][29][30][31]33,34] to cite but a few).…”

Section: Introductionmentioning

confidence: 98%

Uniform Stability of a Laminated Beam with Structural Memory

Tatar

2015

Qual. Theory Dyn. Syst.

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“…Guesmia and Messaoudi [6] obtained the same uniform decay results without imposing those extra technical conditions on g and g . Recently, Messaoudi and Mustafa [13] improved the results of [2,6] by allowing more general relaxation functions. They established a more general decay result, from which the exponential and the polynomial decay results are only special cases, later, Fernández Sare and Muñoz Rivera [4] considered a similar Timoshenko-type system with a past history of the form…”

Section: Introductionmentioning

confidence: 95%

Exponential stability for a Timoshenko-type system with history

Ma¹,

Zhang²,

Yang³

2011

Journal of Mathematical Analysis and Applications

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“…This result has been later improved by Guesmia and Messaoudi [10] and [11], where the technical conditions on g have been removed and those on g have been weakened. Messaoudi and Mustafa [20] improved the result further by allowing the relaxation function to be of more general decay, from which the usual exponential and polynomial decays are only special cases. Recently, Fernández Sare and Muñoz Rivera [6], considered a Timoshenko-type system with a past history of the form…”

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confidence: 93%