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 تفاصيل المقالة

In this paper, the vibration characteristics of multi-layer shell that internal and external surfaces with a layer of piezoelectric sensor and actuator is investigated. The backrest shell laminated with simple analytical method to evaluate and the results were compared with results obtained by other researchers. The numerical solution methods (GDQ) for shells with piezoelectric layers and plain bearings, compared with analytical solution and then a variety of boundary conditions is studied. Using the equations of motion, the fundamental equations and relations Krnsh- displacement, State-space equations derived the equations using approximate separate layer, State-space equations with constant coefficients will become. These equations can be solved using natural frequencies in the backrest shell simple to obtain. If the abutments are not simple, solving equations differentials State-space analysis is not possible and should be used numerical methods. A fourth difference method numerical method common with the small number of sample points can be exact to achieve. By dq, State-space differential equations are solved and the non-traction conditions by applying high and low levels, can be found at the natural frequency. The direct and inverse piezoelectric effect, piezoelectric layer and composite layer thickness ratio of the radius of the middle of a thick crust on the vibrational behavior is studied تفاصيل المقالة