The dynamical stability of planar networks of non-uniform Timoshenko beams system is considered. Suppose that the displacement and rotational angle is continuous at the common vertex of this network and the bending moment and shear force satisfies Kirchhoff’s laws, respectively. Timedelay terms exist in control inputs at exterior vertices. The feedback control laws are designed to stabilize thi...

In this paper, the dynamic response of a simply supported beam subjected to moving load is reinvestigated. Based on new theory, slope inertia-based Timoshenko (SIBT), governing equations motion are derived. An analytical solution presented by using coupled Fourier and Laplace–Carson integral transformation method. The finite element also developed compared with solution. Then, comparative study...

A Timoshenko beam equation with boundary feedback control is considered. By an abstract result on the Riesz basis generation for the discrete operators in the Hilbert spaces, we show that the closed-loop system is a Riesz system, that is, the sequence of generalized eigenvectors of the closed-loop system forms a Riesz basis in the state Hilbert space. 1. Introduction. The boundary feedback stab...

In this paper we analyze a locking-free numerical scheme for the LQR control of a Timoshenko beam. We consider a non-conforming finite element discretization of the system dynamics and a control law constant in the spatial dimension. To solve the LQR problem we seek a feedback control which depends on the solution of an algebraic Riccati equation. An optimal error estimate for the feedback oper...