On the Set of Reachable States in the Problem of Controllability of Rotating Timishenko Beams

Abstract

This work continues the authors' previous investigation on the controllability problem of a slowly rotating Timoshenko beam. We obtain conditions of exact controllability under the assumption that the parameter γ appearing in the model equation is rational. Our result rests on a generalization of the theorem by Ullrich on the Riesz basis property of exponential divided differences.

Optimal damping coefficient of a slowly rotating Timoshenko beam

“…One of the most interesting DPS is a Timoshenko beam, slowly rotating in a horizontal plane. It has intriguing spectral properties [6,7,8,9], which makes the analysis of the system both thought-provoking, and important for applications. Stability of such a hyperbolic system means elimination of unwanted vibrations of the arm.…”

Solutions Stability of Initial Boundary Problem, Modeling of Dynamics of Some Discrete Continuum Mechanical System

“…Исследованию динами-ки механических систем, содержащих твердые тела и упругие стержни, посвящено большое количество работ. Упругие стержни рассматриваются как в рамках модели Эйлера-Бернулли [6][7][8][9], так и в рамках модели балки Тимошенко [10][11][12][13][14][15][16]. Изучают-ся задачи стабилизации и управления поведением таких механических систем.…”

Spectral properties of non-homogeneous Timoshenko beam and its rest to rest controllability

“…Full analysis of the controllability of the above mentioned model was described by W. Krabs and G.M. Sklyar first in [5] and then in monograph [6] and in series of papers (for example, [3,7]). The research presented there is based on spectral model analysis and on non-Fourier trigonometric moment problem methods.…”