A Locking-Free FEM in Active Vibration Control of a Timoshenko Beam

In this paper we analyze the numerical approximation of an active vibration control problem of a Timoshenko beam. In order to avoid locking, we focus on the finite element method used to compute the beam vibration, to minimize it. Optimal order error estimates are obtained for the control variable, which is the amplitude of secondary forces modeled as Dirac’s delta distributions. These estimates are valid with constants that do not depend on the thickness of the beam. In order to assess the performance of the method, numerical tests are reported.