Localization of the limit set of trajectories of the Euler-Bernoulli equation with control. (Russian, English) Zbl 1164.74415

Zuev, A. L.

Ukr. Mat. Zh. 60, No. 2, 173-182 (2008); translation in Ukr. Math. J. 60, No. 2, 199-210 (2008).

Summary: We investigate a differential equation in a Hilbert space that describes vibrations of the Euler-Bernoulli elastic beam with feedback control. The relative compactness of positive semitrajectories of the considered equation is proved. Constructing a Lyapunov functional in explicit form and using the invariance principle, we obtain representations of limit sets.

MSC:

74H10	Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics
74H45	Vibrations in dynamical problems in solid mechanics
93B52	Feedback control

Keywords:

Euler-Bernoulli elastic beam; feedback control; Lyapunov functional