Intelligent beam structures: Timoshenko theory vs. Euler-Bernoulli theory

In this paper, the derivation of the governing equations and boundary conditions of laminated beam smart structures are developed. Sensor and actuator layers are included in the beam so as to facilitate vibration suppression. Two mathematical models, namely the shear-deformable (Timoshenko) model and the shear-indeformable (Euler-Bernoulli) model, are presented. The global asymptotic stability of the continuous beam models is proven via the Mukherjee and Chen theorem. The differential equations for the continuous system are approximated by utilizing finite element techniques. A cantilever laminated beam is investigated to assess the validity and the accuracy of the proposed models. Comparison between the two models is presented to show the advantages and the limitations of the proposed models. Since the Timoshenko beam theory is higher order than the Euler-Bernoulli theory, it is known to be superior in predicting the transient response of the beam.