Asymptotic Behavior of a Mindlin-Timoshenko Plate with Viscoelastic Dissipation on the Boundary

Rivera, Jaime E. Muñoz; Oquendo, Higidio Portillo

doi:10.1619/fesi.46.363

Cited by 13 publications

(10 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In that condition, Lagnese proved that the system (1.1)-(1.3) is exponentially stable, without any restrictions on the coefficients of the system. The same result is obtained by Muñoz Rivera and Portillo Oquendo [10], where, in (1.5)-(1.7), they consider boundary dissipations of memory type; that is,…”

supporting

confidence: 72%

On the stability of Mindlin–Timoshenko plates

Sare

2009

Quart. Appl. Math.

View full text Add to dashboard Cite

Abstract. We consider a Mindlin-Timoshenko model with frictional dissipations acting on the equations for the rotation angles. We prove that this system is not exponentially stable independent of any relations between the constants of the system, which is different from the analogous one-dimensional case. Moreover, we show that the solution decays polynomially to zero, with rates that can be improved depending on the regularity of the initial data.

show abstract

supporting

confidence: 72%

On the stability of Mindlin–Timoshenko plates

Sare

2009

Quart. Appl. Math.

View full text Add to dashboard Cite

show abstract

“…, 0 , 1 / is 'star complemented-star shaped' and some additional assumptions on F, even uniform stability has been shown. Similar results were also obtained by Muñoz Rivera and Portillo Oquendo in [14] also for the boundary conditions of memory-type…”

Section: Introductionsupporting

confidence: 89%

On stability of hyperbolic thermoelastic Reissner–Mindlin–Timoshenko plates

Pokojovy

2014

Math Methods in App Sciences

View full text Add to dashboard Cite

In the present article, we consider a thermoelastic plate of Reissner-Mindlin-Timoshenko type with the hyperbolic heat conduction arising from Cattaneo's law. In the absense of any additional mechanical dissipations, the system is often not even strongly stable unless restricted to the rotationally symmetric case, etc. We present a well-posedness result for the linear problem under general mixed boundary conditions for the elastic and thermal parts. For the case of a clamped, thermally isolated plate, we show an exponential energy decay rate under a full damping for all elastic variables. Restricting the problem to the rotationally symmetric case, we further prove that a single frictional damping merely for the bending compoment is sufficient for exponential stability. To this end, we construct a Lyapunov functional incorporating the Bogovskiȋ operator for irrotational vector fields which we discuss in the appendix.MOS subject classification: 35L55; 35Q74; 74D05; 93D15; 93D20

show abstract

“…There is an extensive literature on the well-posedness and stabilization of models based on these theories by, amongst others, Kim and Renardy [19], Lagnese [21], Muñoz Rivera and Racke [28], Muñoz Rivera and Portillo Oquendo [29], Raposo et al [39], Wehbe and Youssef [46], Fernández Sare [10] and Cavalcanti et al [3], by incorporating some sort of dissipative mechanism, e.g. viscous damping, feedback boundary damping, boundary damping of memory type or locally distributed damping into the model.…”

Section: Introductionmentioning

confidence: 99%

Exponential stabilization of magnetoelastic waves in a Mindlin–Timoshenko plate by localized internal damping

Dalsen¹

2015

Z. Angew. Math. Phys.

View full text Add to dashboard Cite

This article is a continuation of our earlier work in Grobbelaar-Van Dalsen (Z Angew Math Phys 63:1047-1065, 2012) on the polynomial stabilization of a linear model for the magnetoelastic interactions in a two-dimensional electrically conducting Mindlin-Timoshenko plate. We introduce nonlinear damping that is effective only in a small portion of the interior of the plate. It turns out that the model is uniformly exponentially stable when the function p(x, U t), that represents the locally distributed damping, behaves linearly near the origin. However, the use of Mindlin-Timoshenko plate theory in the model enforces a restriction on the region occupied by the plate.Mathematics Subject Classification. Primary 74K10 · Secondary 93B15.

show abstract

Asymptotic Behavior of a Mindlin-Timoshenko Plate with Viscoelastic Dissipation on the Boundary

Cited by 13 publications

References 6 publications

On the stability of Mindlin–Timoshenko plates

On the stability of Mindlin–Timoshenko plates

On stability of hyperbolic thermoelastic Reissner–Mindlin–Timoshenko plates

Exponential stabilization of magnetoelastic waves in a Mindlin–Timoshenko plate by localized internal damping

Contact Info

Product

Resources

About