Approximate analytical solutions of smart composite mindlin beams

In this paper, a refined theory and approximate analytical solutions of laminated composite beams with piezoelectric laminae are developed. The equations of motion of the theory are developed using an energy principle. This formulation is based on linear piezoelectricity and Mindlin lamination theory, and includes the coupling between mechanical deformations and the charge equations of electrostatics. The approximate analytical solutions, using software package MATLAB and MATHEMATICA, are to study the effectiveness of piezoelectric sensors and actuators in actively controlling the transverse response of smart laminated beams. A main feature of this work is that it introduces the displacement potential function to simplify the governing equation. 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 sensor layer and the input voltage acting on the actuator layer is also studied. Graphical results are presented to demonstrate the ability of a closed-loop system to actively control the vibration of laminated beams. The present method has a general application in this field of study.

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