Title :
Approximate controllability of a rotating Kirchhoff plate model
Author :
Zuyev, Alexander
Author_Institution :
Inst. of Appl. Math. & Mech., Nat. Acad. of Sci. of Ukraine, Donetsk, Ukraine
Abstract :
In this paper, we consider a mechanical system consisting of a rigid body with a thin elastic plate. The plate vibration is governed by the Kirchhoff plate theory. We derive the equations of motion as a system of ordinary and partial differential equations and consider the angular acceleration as a control parameter. The dynamical equations are transformed into an infinite set of ordinary differential equations with respect to modal coordinates. It is shown that such a system is not controllable in general. Hence, the approximate controllability problem is set out for the dynamics restricted to an invariant manifold. Then sufficient conditions for the approximate controllability are proposed. Simulation results are presented to illustrate the spillover effect.
Keywords :
controllability; elasticity; manifolds; partial differential equations; plates (structures); shear modulus; structural engineering; vibrations; angular acceleration; approximate controllability; dynamical equation; invariant manifold; mechanical system; ordinary differential equation; partial differential equation; plate vibration; rigid body; rotating Kirchhoff plate model; thin elastic plate; Approximation methods; Controllability; Differential equations; Eigenvalues and eigenfunctions; Equations; Mathematical model;
Conference_Titel :
Decision and Control (CDC), 2010 49th IEEE Conference on
Conference_Location :
Atlanta, GA
Print_ISBN :
978-1-4244-7745-6
DOI :
10.1109/CDC.2010.5717555