Approximate analytical solutions of smart composite Mindlin beams

In this paper, a refined theory and approximate analytical solutions of lam inated composite beams with piezoelectric laminae are developed. The equati ons of motion of the theory are developed using an energy principle. This f ormulation is based on linear piezoelectricity and Mindlin lamination theor y, and includes the coupling between mechanical deformations and the charge equations of electrostatics. The approximate analytical solutions, using s oftware package MATLAB and MATHEMATICA, are to study the effectiveness of p iezoelectric sensors and actuators in actively controlling the transverse r esponse of smart laminated beams. A main feature of this work is that it in troduces the displacement potential function to simplify the governing equa tion. A new assumption of harmonic vibration and the transformation method of complex numbers are introduced. It can be used in differential equations that include both items of the functions sin and cosine, and the odd-order differential coefficient. The behaviour of the output voltage from the sen sor layer and the input voltage acting on the actuator layer is also studie d. Graphical results are presented to demonstrate the ability of a closed-l oop system to actively control the vibration of laminated beams. The presen t method has a general application in this field of study. (C) 2001 Academi c Press.