%0 Journal Article
%T Optimal Placement of Piezoelectric Plates to Control Multimode Vibrations of a Beam
%A Fabio Botta
%A Daniele Dini
%A Christoph Schwingshackl
%A Luca di Mare
%A Giovanni Cerri
%J Advances in Acoustics and Vibration
%D 2013
%I Hindawi Publishing Corporation
%R 10.1155/2013/905160
%X Damping of vibrations is often required to improve both the performance and the integrity of engineering structures, for example, gas turbine blades. In this paper, we explore the possibility of using piezoelectric plates to control the multimode vibrations of a cantilever beam. To develop an effective control strategy and optimize the placement of the active piezoelectric elements in terms of vibrations amplitude reduction, a procedure has been developed and a new analytical solution has been proposed. The results obtained have been corroborated by comparison with the results from a multiphysics finite elements package (COMSOL), results available in the literature, and experimental investigations carried out by the authors. 1. Introduction The vibration control is a problem of great interest in many engineering fields since it allows avoiding problems connected with the vibrations. Blade vibrations in aircraft engines, for example, are often induced by interactions between blades and fluid and the associated fatigue phenomena can give rise to catastrophic failures [1¨C3]. Typically, passive damping systems, such as friction damping, are used to increase the blade life. These systems are very effective, but, in contrast to active damping elements, they are not able to change their characteristics depending on the system response. In the last two decades, the adoption of piezoelectric elements has received considerable attention by many researchers for its potential applicability to different areas of mechanical, aerospace, aeronautical, and civil engineering. These elements have an interesting coupling between electrical and mechanical properties: a deformation appears when an electric field is applied and vice versa [4, 5]. Their effectiveness to damp a particular excited mode or a multimode combination strongly depends on their position; in fact the study of their optimal position has received increasing attention. Typically, the aim of these studies is to find the position that minimizes an objective function or maximizes the degree of modal controllability (see [6, 7] for a review). The first study concerned with the optimal position to damp a specified mode has been that of Crawley and de Luis [4]. They found that the actuators should be in regions of higher average strain. Analogous results have been found by other researchers [8, 9]. For a cantilever beam Sunar and Rao [10], Demetriou [11], and Bruant et al. [12] found that the closer the piezoelectric actuators are to the fixed end, the more efficient they are. For a simply supported beam Yang et
%U http://www.hindawi.com/journals/aav/2013/905160/