Vibrations are a part of our environment and daily life. Many of them are useful and are needed for many purposes, one of the best example being the hearing system. Nevertheless, vibrations are often undesirable and have to be suppressed or reduced, as they may be harmful to structures by generating damages or compromise the comfort of users through noise generation of mechanical wave transmission to the body. Vibration control and limitation is an exciting ?eld in the research community and raises challenging issues in industrial applications. This topic involves multidisciplinary approaches and multi-physic coupling, from mechanical to thermal, and possibly through electrical or magnetic ?elds, the basic idea being the dissipation of the mechanical energy into heat or preventing mechanical energy from entering into the structures. Two strategies are typically used for limiting vibrations. The mechanical energy may be directly dissipated into heat through the use of viscoelastic layers or the use of additional stiffeners can prevent energy from entering in the system, but the performance of such approaches is limited, especially in the case of low-frequency vibrations. In order to dispose of ef?cient systems, the second method consists of using intermediate energy conversion media, such as electromagnets or piezoelectric actuators. When using multiphysic coupling, mechanical energy is ?rst transferred into another form (electrical, magnetic…) before being dissipated. Energy conversion systems may also be used to ensure that the input force spectrum does not overlap the frequency response function of the structure to ensure that no energy goes into the device. To limit the vibrations of a system, many methods have been proposed such as passive control schemes, semi-passive techniques, active control schemes, ect. Active vibration reduction of structures is one of the most important challenges that many of researchers have paid attention to it in recent years. Active vibration control is one of the techniques that is used for decaying structural vibrations. Many materials, such as piezoelectric materials, shape memory alloys, electrostrictive materials, electromagnetotstrictive materials, electro- and magneto rheological fluids, etc, can be used for suppressing vibrations. The application of piezoelectric materials have become popular because of low weight, high strength, high stiffness, high frequency response, and easy implementation. In this study, the active vibration control of a cylindrical shell using piezoelectric sensors and actuators are analyzed. The boundary condition of a cylindrical shell is simply–supported and the piezoelectric patches are attached to its surface locally. Firstly, the continuous model of system is derived by using terms of energy, virtual work and Hamilton's principle. Then, the Rayleigh–Ritz method is used for deriving the dynamic model of a cylindrical shell and piezoelectric sensors and actuators based on Donnel–Mushtari shell theory. In next step, the major goal is to find the optimal location of piezoelectric sensors and actuators on the cylindrical shell. The optimization procedure is designed based on desired controllability and observability of each contributed and undesired mode. Further, to limit spillover reduction, the residual mode is regarded. The optimization variables are positions and orientations of piezoelectric patches. Genetic algorithm is utilized to evaluate the optimal configurations. For active vibration control, a negative velocity feedback control algorithm is used. Finally, the arbitrary locations of patches, dimensions of shell, orientations of paches on the shell, patches sizes and their number, applied voltage and applied mechanical load are discussed. Keyword : active vibration control, Rayleigh–Ritz mothod, cylindrical shell, optimal location, piezoelectric sensor ? actuator, genetic algorithm (GA).
