Resolution composite shell with a layer of piezoelectric vibration analysis

In this paper, the vibration of composite cylindrical shell with piezoelectric layers in the interior and exterior surfaces is investigated. The composite shell without piezoelectric layers can be studied and compared the results with the results of other researchers, the cylindrical shell laminated with layers of piezoelectric vibration checked. The result is a three-dimensional elasticity equations relationships because they do not apply any approximate gain are quite analytical. Shells intended, is closed and has restricted the mainstays in the end it was simple, and the results for the ratio of the radius and the radius of the different thickness are obtained