In this paper, we present rapid boundary stabilization of a Timoshenko beam with anti-damping and anti-stiffness at the uncontrolled boundary, by using infinite-dimensional backstepping. We introduce Riemann transformation to map states into set coordinates that verify 1-D hyperbolic PIDE-ODE system. Then backstepping is applied obtain control law guaranteeing closed-loop stability origin in <i...

A method is given by which the response of a rotating or non-rotating Timoshenko beam can be determined, subjected to an accelerating fixed direction distributed surface force. The beam mode1 includes the gyroscopically induced displacement transverse to the direction of the load. The solution for pinned supports is set up using multi-integral transforms, and the inversion is expressed in terms...

We consider the dynamical one-dimensional Mindlin-Timoshenko system for beams. We analyze how its controllability properties depend on the modulus of elasticity in shear k. In particular we prove that the exact boundary controllability property of the Kirchhoff system may be obtained as singular limit, as k → ∞, of the partial controllability of a sharp subspace of low frequency components of t...

In this paper, we introduce a new class of discontinuous Galerkin methods for Timoshenko beams. The main feature of these methods is that they can be implemented in an efficient way through a hybridization procedure which reduces the globally coupled unknowns to approximations to the displacement and bending moment at the element boundaries. After displaying the methods, we obtain conditions un...