Mathematical Analysis of Vibration Attenuation in Smart Structures Using Piezoelectric Layers

Abstract

In order to address this issue, a complete mathematical model of the vibration attenuation in smart structures with embedded piezoelectric layers is developed in this study. The Euler–Bernoulli beam theory with linear piezoelectric constitutive relations is used to develop a coupled electromechanical model. Hamilton’s principle is used to find the governing partial differential equations and Galerkin method is used for solving them in (modal) analysis. Harmonic and impulse loading cases of piezoelectric damping are investigated. Results show significant vibration suppression prospects with the optimal piezoelectric placement and the proper control gain. A robust model is proposed for designing next generation adaptive vibration control systems in the areas of aerospace and civil engineering.