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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

G. Perla Menzala, Ademir F. Pazoto, Enrique Zuazua (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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...

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

G. Perla Menzala, Ademir F. Pazoto, Enrique Zuazua (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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...

Stabilization of Timoshenko beam by means of pointwise controls

Gen-Qi Xu, Siu Pang Yung (2003)

ESAIM: Control, Optimisation and Calculus of Variations

We intend to conduct a fairly complete study on Timoshenko beams with pointwise feedback controls and seek to obtain information about the eigenvalues, eigenfunctions, Riesz-Basis-Property, spectrum-determined-growth-condition, energy decay rate and various stabilities for the beams. One major difficulty of the present problem is the non-simplicity of the eigenvalues. In fact, we shall indicate in this paper situations where the multiplicity of the eigenvalues is at least two. We build all the above-mentioned...

Stabilization of Timoshenko Beam by Means of Pointwise Controls

Gen-Qi Xu, Siu Pang Yung (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We intend to conduct a fairly complete study on Timoshenko beams with pointwise feedback controls and seek to obtain information about the eigenvalues, eigenfunctions, Riesz-Basis-Property, spectrum-determined-growth-condition, energy decay rate and various stabilities for the beams. One major difficulty of the present problem is the non-simplicity of the eigenvalues. In fact, we shall indicate in this paper situations where the multiplicity of the eigenvalues is at least two. We build all the...

Sul problema di contatto tra piastre

Aldo Maceri (1992)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si studia il problema di contatto tra due piastre sottili linearmente elastiche, incastrate al bordo, poste inizialmente a distanza δ e trasversalmente caricate. Si fa l'ipotesi che il contatto tra le due piastre, a deformazione avvenuta, sia privo di attrito. Il problema dell'equilibrio elastico è formulato per via variazionale in termini di lavori virtuali o, equivalentemente, di minimo del funzionale dell'energia. Il quadro analitico di riferimento è quello della teoria delle disequazioni variazionali...

Sulla flessione elastica delle travi in c.a. in presenza di fessurazione

Mario Como (2003)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Viene formulata una teoria della flessione delle travi in cemento armato in presenza di fessurazione. Si esamina l’effetto del «tension stiffening» e, attraverso un processo di omogeneizzazione, si valuta la curvatura media tra le fessure. Si perviene così all’equazione differenziale della flessione elastica delle travi fessurate. Le applicazioni numeriche svolte vengono confrontate con le risultanze sperimentali.

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