On the Internal and Boundary Stabilization of Timoshenko Beams

Messaoudi, Salim A.; Mustafa, Muhammad I.

doi:10.1007/s00030-008-7075-3

Cited by 65 publications

(32 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In 1921, Timoshenko [21] gave, as model for a thick beam, the following system of coupled hyperbolic equations ρu tt = K (u x − ϕ) x , in (0, L) × (0, +∞), (1.1) by Messaoudi and Mustafa [13], where the decay rate has been discussed for several systems and without imposing any growth condition on the damping functions.…”

Section: Introductionmentioning

confidence: 99%

Uniform decay in a Timoshenko-type system with past history

Messaoudi

Said‐Houari

2009

Journal of Mathematical Analysis and Applications

Self Cite

View full text Add to dashboard Cite

of Timoshenko systems with past history, J. Math. Anal. Appl. 339 (1) (2008) 482-502] considered the following Timoshenko-type systemwhere g is a positive differentiable exponentially decaying function. They established an exponential decay result in the case of equal wave-speed propagation and a polynomial decay result in the case of nonequal wave-speed propagation. In this paper, we study the same system, for g decaying polynomially, and prove polynomial stability results for the equal and nonequal wave-speed propagation. Our results are established under conditions on the relaxation function weaker than those in [H.D. Fernández Sare, J.E. Muñoz Rivera, Stability of Timoshenko systems with past history, J. Math. Anal. Appl. 339 (1) (2008) 482-502].

show abstract

Section: Introductionmentioning

confidence: 99%

Uniform decay in a Timoshenko-type system with past history

Messaoudi

Said‐Houari

2009

Journal of Mathematical Analysis and Applications

Self Cite

View full text Add to dashboard Cite

show abstract

“…See, for example, the literature. () For laminated Timoshenko beams without time delay, there are just a few published works. Wang et al considered the boundary with one end fixed:

(ω (0) = ψ (0) = s (0) = 0)

and

ψ (1) - ω_{x} (1) = k_{1} ω_{t} (1), s_{x} (1) = 0, (3 s_{x} - ψ_{x}) (1) = - k_{2} (3 s_{t} - ψ_{t}) (1)

at the other end and established the exponential stability by assuming

\frac{G}{ρ} \neq \frac{D}{I_{ρ}}

and k i ≠ r i ,( i =1,2).…”

Section: Introductionmentioning

confidence: 99%

Well‐posedness and exponential decay for laminated Timoshenko beams with time delays and boundary feedbacks

Feng

2017

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…He also obtained the rate of decay of the energy, which is exactly the rate of decay of the relaxation functions. This last result has been improved and generalized by Messaoudi and Soufyane [13] and Messaoudi and Mustafa [15] (see also [17][18][19]22,26]). …”

mentioning

confidence: 66%