Stabilization and observability of a rotating Timoshenko beam model.
Stabilization of a layered piezoelectric 3-D body by boundary dissipation
We consider a linear coupled system of quasi-electrostatic equations which govern the evolution of a 3-D layered piezoelectric body. Assuming that a dissipative effect is effective at the boundary, we study the uniform stabilization problem. We prove that this is indeed the case, provided some geometric conditions on the region and the interfaces hold. We also assume a monotonicity condition on the coefficients. As an application, we deduce exact controllability of the system with boundary control...
Stabilization of Timoshenko beam by means of pointwise controls
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
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...
Stress equations of motion of Ignaczak type for the second axisymmetric problem of micropolar elastodynamics
A second axially-symmetric initial-boundary value problem of linear homogeneous isotropic micropolar elastodynamics in which the displacement and rotation take the forms , ((r,θ,z) are cylindrical coordinates; cf. [17]) is formulated in a pure stress language similar to that of [12]. In particular, it is shown how and can be recovered from a solution of the associated pure stress initial-boundary value problem, and how a singular solution corresponding to harmonic vibrations of a concentrated...
Study of a contact problem with normal compliance and nonlocal friction
We consider a static frictional contact between a nonlinear elastic body and a foundation. The contact is modelled by a normal compliance condition such that the penetration is restricted with unilateral constraint and associated to the nonlocal friction law. We derive a variational formulation and prove its unique weak solvability if the friction coefficient is sufficiently small. Moreover, we prove the continuous dependence of the solution on the contact conditions. Also we study the finite element...
Study of a viscoelastic frictional contact problem with adhesion
We consider a quasistatic frictional contact problem between a viscoelastic body with long memory and a deformable foundation. The contact is modelled with normal compliance in such a way that the penetration is limited and restricted to unilateral constraint. The adhesion between contact surfaces is taken into account and the evolution of the bonding field is described by a first order differential equation. We derive a variational formulation and prove the existence and uniqueness result of the...
Sul principio di indifferenza materiale
Sul problema del rimbalzo in un insieme convesso
In the present paper we seek the bounce trajectories in a convex set which assume assigned positions in two fixed time instants. We find sufficient conditions in order to obtain the existence of infinitely many bounce trajectories.
Sul problema di contatto tra piastre
Si studia il problema di contatto tra due piastre sottili linearmente elastiche, incastrate al bordo, poste inizialmente a distanza 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...
Sull’estensione di un teorema di Menabrea al caso di una microstruttura a deformazioni finite
In the present work an extension of a classical Menabrea’s theorem on a variational principle of the second potential energy is considered. Such extension deals with hyperelastic micropolar media without constraints.
Sullo stress e sulla deformazione di una microstruttura
Sur les fréquences de diffusion (scattering) d'un corps élastique couplé avec l'air