An analytical method for the three-dimensional vibration analysis of a functionally graded cylindrical shell integrated by two thin functionally graded piezoelectric (FGP) layers is presented. The first-order shear deformation theory is used to model the electromechanical system. Nonlinear equations of motion are derived by considering the von Karman nonlinear strain-displacement relations using Hamilton's principle. The piezoelectric layers on the inner and outer surfaces of the core can be considered as a sensor and an actuator for controlling characteristic vibration of the system. The equations of motion are derived as partial differential equations and then discretized by the Navier method. Numerical simulation is performed to investigate the effect of different parameters of material and geometry on characteristic vibration of the cylinder. The results of this study show that the natural frequency of the system decreases by increasing the non-homogeneous index of FGP layers and decreases by increasing the non-homogeneous index of the functionally graded core. Furthermore, it is concluded that by increasing the ratio of core thickness to cylinder length, the natural frequencies of the cylinder increase considerably.

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This paper studies free vibration analysis of cylindrical micro/nano shell made from a mixture of ceramic/metal, reinforced with some carbon-nanotube-reinforced (CNTRC) patches, based on shear deformation theory and nonlocal elasticity theory. Extended rule of mixture and power law model are utilized to find effective properties of composite patches and the ceramic/metal core, respectively. The main aim of this work is to investigate the effect of characteristics of attached CNTRC patches on the free vibration responses. It is concluded that some important parameters such as number and angle of composite patches as well as their volume fraction, and some geometric parameters have significant influence on the free vibration responses.

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