The beam equation as a limit of a 1-D nonlinear von Kármán model

Menzala, G. Perla; Zuazua, Enrique

doi:10.1016/s0893-9659(98)00125-6

Cited by 22 publications

(25 citation statements)

References 6 publications

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“…Indeed, the analysis in [17,18] allows to get the convergence of solutions in bounded intervals of time. However, the decay properties we have in mind require the analysis of convergence as time goes to infinity as well.…”

Section: It Is Then Natural To Raise the Following Question: Can One mentioning

confidence: 99%

“…The connections between the various available models for a given mechanical problem may be often described precisely in mathematical terms by means of the analysis of the underlying singular perturbation problem. At this respect, in addition to the works [17,18] discussed above on the beam models, we also refer to the monograph by Ciarlet [2] in which various plate models are derived as singular limits from the equations of 3 − d elasticity in thin domains, and to [3] and [22] for the asymptotic analysis of beam models.…”

Section: It Is Then Natural To Raise the Following Question: Can One mentioning

confidence: 99%

“…In order to make more precise the problem we have in mind let us recall the essentials of [17,18]. In these works the following von Kármán system for the vibrations of a beam occupying the inverval (0, L) was considered subject to various boundary conditions.…”

Section: It Is Then Natural To Raise the Following Question: Can One mentioning

confidence: 99%

“…Recently, it was proved that the Berger-Timoshenko beam model may be derived as a singular limit of the von Kármán beam model. This was done in [17,18] in the conservative case and under various boundary conditions. Here the same analysis is developed for the corresponding damped systems.…”

Section: Introductionmentioning

confidence: 99%

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Stabilization of Berger–Timoshenko's equation as limit of the uniform stabilization of the von Kármán system of beams and plates

2002

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Abstract.We consider a dynamical one-dimensional nonlinear von Kármán model for beams depending on a parameter ε > 0 and study its asymptotic behavior for t large, as ε → 0. Introducing appropriate damping mechanisms we show that the energy of solutions of the corresponding damped models decay exponentially uniformly with respect to the parameter ε. In order for this to be true the damping mechanism has to have the appropriate scale with respect to ε. In the limit as ε → 0 we obtain damped Berger-Timoshenko beam models for which the energy tends to zero exponentially as well. This is done both in the case of internal and boundary damping. We address the same problem for plates with internal damping.Mathematics Subject Classification. 35B40, 35Q72, 74B20.

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Section: It Is Then Natural To Raise the Following Question: Can One mentioning

confidence: 99%

Section: It Is Then Natural To Raise the Following Question: Can One mentioning

confidence: 99%

Section: It Is Then Natural To Raise the Following Question: Can One mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stabilization of Berger–Timoshenko's equation as limit of the uniform stabilization of the von Kármán system of beams and plates

2002

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“…In agreement with many authors that have analysed large deformation in Timoshenko`s beams [7,8,24,25], only nonlinear terms product of the variation in the longitudinal direction of transverse displacements will be considered in this work (Von Karman strains), leading to the following simplification of the Almansi strain tensor for any generic C point on the contour:…”

Section: Strains Stress Resultants and Constituve Relationshipsmentioning

confidence: 85%

Linear and non-linear finite element analysis of shear-corrected composites box beams

López

Patiño

2013

Lat. Am. j. solids struct.

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The Updated Lagrangian formulation for non-linear finite element analysis is applied to the problem of thin-walled composites box beams undergoing large displacements. A shear correction factor for thinclosed rectangular sections is introduced into some terms of the variational formulation and its influence in the results is analyzed, in both linear and non-linear problems. The Vlasov's theory describing the coupled flexural-torsional phenomenon and the implementation of the FSDT theory in thin-walled beams is discussed, as well as the strains, stress resultants and constitutive relationships for composites box beams. The application of the Mechanic of Laminated Beam theory (MLB) to the calculation of the shear correction factors considering more constitutive terms for computing the shear flow in flanges and webs than those ones used in the original theory is also debated. The Updated Lagrangian finite element model applied in this work for nonlinear analysis of box beams is described. A comparison of the numerical results with those obtained experimentally, analytically and by the numerical models proposed by other authors is done for both linear and non-linear problems. The assumptions made in this work and the formulation developed only applies to thin-walled beams that undergo large displacements, but small to moderate twist rotations.

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On the Accuracy of the Galerkin Method for a Nonlinear Dynamic Beam Equation

Peradze

2011

Math. Meth. Appl. Sci.

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The beam equation as a limit of a 1-D nonlinear von Kármán model

Cited by 22 publications

References 6 publications

Stabilization of Berger–Timoshenko's equation as limit of the uniform stabilization of the von Kármán system of beams and plates

Stabilization of Berger–Timoshenko's equation as limit of the uniform stabilization of the von Kármán system of beams and plates

Linear and non-linear finite element analysis of shear-corrected composites box beams

On the Accuracy of the Galerkin Method for a Nonlinear Dynamic Beam Equation

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