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 estimate...

Brinson’s one-dimensional constitutive modeling for shape memory alloy (SMA) is extended to consider the asymmetric tensile and compressive behavior as well as the torsional behavior. The incremental finite element method using linear Timoshenko beam elements is formulated by the total Lagrangian approach for the superelastic, large deformation analysis of SMA helical springs. The NiTi helical ...

The nonlinear free vibration for viscoelastic cross-ply moderately thick laminated composite plates under considering transverse shear deformation and damage effect is investigated. Based on the Timoshenko-Mindlin theory, strain-equivalence hypothesis, and Boltzmann superposition principle, the nonlinear free vibration governing equations for viscoelastic moderately thick laminated plates with ...

A Mindlin-Timoshenko model with non constant and non smooth coefficients set in a bounded domain of R, d ≥ 1 with some internal dissipations is proposed. It corresponds to the coupling between the wave equation and the dynamical elastic system. If the dissipation acts on both equations, we show an exponential decay rate. On the contrary if the dissipation is only active on the elasticity equati...

In this investigation we develop a mathematical model to simulate the actuation of a multilayer metallic strip. In the first step of the model development, we employ the theory of Judy [4] and Timoshenko [5] to quantify the radius of curvature in the unimorph due to differing thermal coefficients in the constituent materials. The resulting radius of curvature is subsequently used to compute the...

Plates and shells represent principal elements of aerospace structures, including fuselages of planes and missiles, control surfaces, bulkheads, helicopter blades, and others. The multiple applications, shapes, and materials found in plate and shell structures dictate the necessity of a comprehensive approach to their analysis reflected in relevant theories and methodologies. Various aspects of...

In this work we analyze the numerical approximation of an optimal control problem of a Timoshenko beam, by considering two kinds of distributed control. The discretization of the control variables is performed by using piecewise constant functions. The states and the adjoint states are approximated by a locking free scheme of linear finite elements. An interpolation postprocessing technique is ...