The paper deals with the existence of time-periodic solutions to the beam equation, in which terms expressing torsion and damping are also considered. The existence of periodic solutions is proved in the cas of time-periodic outer forces by means of an apriori estimate and the Fourier method.
In questo lavoro viene studiato il comportamento dinamico di una piastra vincolata monolateralmente su una fondazione elastica alla Winkler. Si presentano alcuni risultati numerici ottenuti mediante discretizzazione agli elementi finiti. Tali risultati mettono in luce l'influenza di alcuni fattori tipici come le funzioni di forma, il parametro di mesh e l'ampiezza dell'intervallo con cui si realizza l'integrazione nel tempo delle equazioni del moto. Si istituiscono infine dei confronti con risultati...
A linearized formulation of the elastic theory of suspension bridges is confronted with early investigations in the field. For decades, the structure was schematized as a beam (deck or girder) relieved by a one parameter distribution of forces exerted by the cable, disregarding the influence of beam deflection on that distribution as given by the linearized approach. An anonymous note presented the essential conclusions of this theory anticipating results of investigations following the methods...
A mechanical one-dimensional model which describes the dynamical behaviour of laminated curved beams is formulated. It is assumed that each lamina can be regarded as a Timoshenko's beam and that the rotations of the cross sections can differ from one lamina to another. The relative displacements at the interfaces of adjacent laminae are assumed to be zero. Consequently the model includes a shear deformability, due to the warping of the cross beam section consequent to the variability of the laminae...
It is proved that any weak solution to a nonlinear beam equation is eventually globally oscillatory, i.e., there is a uniform oscillatory interval for large times.
We consider the problem of controlling pointwise (by means of a time dependent Dirac measure supported by a given point) the motion of a vibrating plate Ω. Under general boundary conditions, including the special cases of simply supported or clamped plates, but of course excluding the cases where multiple eigenvalues exist for the biharmonic operator, we show the controlability of finite linear combinations of the eigenfunctions at any point of Ω where no eigenfunction vanishes at any time greater...
We show that the set of nonnegative equilibrium-like states, namely, like of the semilinear vibrating string that can be reached from any non-zero initial state , by varying its axial load and the gain of damping, is dense in the “nonnegative” part of the subspace of . Our main results deal with nonlinear terms which admit at most the linear growth at infinity in and satisfy certain restriction on their total impact on (0,∞) with respect to the time-variable.