Active damping of the nonstationary flexural vibrations of a bimorph beam

Abstract

A two-layer (metal-piezoceramic) beam with hinged ends under a nonstationary distributed load is considered. A method for solving the problem of active damping of the nonstationary flexural vibrations of this structure is proposed. The shape of the electric signal applied to the electrode of the electroelastic layer to keep the beam almost undeformed is identified. The solution is obtained using the Laplace transform with respect to time. Numerical results are presented and analyzed Keywords: electroelasticity, nonstationary processes, two-layer (metal-piezoceramic) beam, Laplace transformIntroduction. Electroelasticity is an important and intensively developed area of the mechanics of coupled fields. Most publications on the subject dealt with stationary dynamic processes in piezoelectric bodies. There are also relevant monographs [4,7].Nonstationary problems of electroelasticity and hydroelectroelasticity are of current interest. Results on transient processes accompanying the interaction of piezoceramic shells with a fluid are reviewed in [9]. Of the recent publications on nonstationary electroelasticity, [8,11,12,13] are noteworthy.Among many piezoelectric transducers, bimorph plates and beams (consisting of elastic and electroelastic layers) are of wide use. The nonstationary vibrations of such structural elements under mechanical or electric loads were studied in [2,3].It is of interest to find the shape of an electric signal that, depending on the type of external shock load, could be used for controlling the stress-strain state of bimorph piezoelectric transducers, including active damping. This is the subject of the present study.

Active damping of nonstationary vibrations of a rectangular plate under impulse loading

“…The plate will be placed in Cartesian rectangular coordinates Oxyz so that its length will be read along the X axis (-L x L), and its width along the Y axis (-B y B). The origin of the applicate axis is displaced from the plane of layer joining at a distance of (Babaev et al, 2010;Rudnitskii et al, 1990):…”

“…For the case when the temporal and spatial components of the external mechanical load are known, control without feedback is more preferable from the point of view of simple implementation (Lara et al, 2000). In this case, the electric control signal can be computed both by using the optimal control theory (Lara et al, 2000;Karnaukhov and Tkachenko, 2008), assuming minimization of a certain functional, and other control criteria identical to approximation of the mechanical system state to a nonstrained one (Babaev et al, 2010). Among the periodic publications in active control of a strained state are such studies as Chellabi et al (2009), Librescu and Na (1998), Pietrzakowski (2002), Rofooei and Nikkhoo (2009), and Yabuno et al (2003).…”