Free transverse vibrations of smart beams are considered where distributed actuators and sensors are realized by means of piezoelastic layers. Utilizing a variational formulation, the direct piezoelectric effect is incorporated into beam theory via suitable approximations for the axial components of the electric field or the electric displacement, respectively. Influence of shear and rotatory inertia is taken into account in the manner suggested by Timoshenko. It is shown that the correction for electrical coupling leads to effective stiffness parameters. This advantageous behavior is utilized for studying its influence on natural frequencies of smart beams with various boundary conditions.
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Krommer et al. (1999) studied this question.
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