Frequency analysis of smart sandwich cylindrical panels with nanocomposite core and piezoelectric face sheets

An analysis is performed in this research to investigate the vibration response of sandwich cylindrical panels with piezoelectric layers. Core of the sandwich panel is made from a composite laminated media which is reinforced with graphene platelets. The amount of graphene in the layers may be different which results in a piecewise functionally graded media. Elasticity modulus of the core media is estimated via the Halpin–Tsai rule, while the mass density and Poisson’s ratio are obtained via the simple rule of mixtures approach. By means of the first-order shear deformation panel theory and linear variation of electric field for the smart layers as the basic assumptions, the expressions of the energies of the panel are obtained. With the general idea of the Ritz method whose shape functions are constructed via the Legendre polynomials, the matrix representation of motion equations is obtained. The obtained form of equations may be used for both closed and open circuit conditions of piezoelectric layers. Results of this study are first compared with the available data in the open literature for simple cases, and after that novel numerical results are given to explore the effects of graded patterns of GPLs, weight fraction of GPLs, mechanical and electrical boundary conditions, number of layers, and also geometrical parameters. It is highlighted that frequencies may be controlled via proper graded pattern and weight fraction of GPLs. Also open circuit type of electrical boundary conditions results in higher natural frequencies in comparison to closed circuit type.