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Abstract: Analytical investigation of the free vibration behavior of thin circular functionally graded (FG) plates integrated with two uniformly distributed actuator layers made of piezoelectric (PZT4) material based on the classical plate theory (CPT) is presented in this paper. The material properties of the FG substrate plate are assumed to be graded in the thickness direction according to the power-law distribution in terms of the volume fractions of the constituents and the distribution of electric potential field along the thickness direction of piezoelectric layers is simulated by a quadratic function. The differential equations of motion are solved analytically for clamped edge boundary condition of the plate. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of varying the gradient index of FG plate on the free vibration characteristics of the structure. The results are verified by those obtained from three-dimensional finite element analyses. [Copyright &y& Elsevier]

Present manuscript is mainly arranged to take into consider the influences of nanofillers' aggregation, beam's shear deformation and various boundary conditions on the vibration frequency of multi-scale hybrid nanocomposites in the framework of finite element based Rayleigh-Ritz method. The constituent material is made from three phases, namely polymer matrix, macro-scale carbon fibers and nano-scale carbon nanotubes. Homogenization procedure is procured based on Eshelby-Mori-Tanaka approach incorporated with a micromechanical scheme to obtain the effective material properties via a two-step method. In addition, a new refined higher-order beam theory is introduced to govern shear stress and strain through the thickness direction. Furthermore, influences of different boundary conditions are included, too. The accuracy of the presented finite element formulations is examined by setting a comparison between the dimensionless frequency of multi-scale hybrid nanocomposite beams via both analytical and finite element solutions. Afterwards, parametric studies are adopted to put emphasize on the influence of various terms on the vibrational behaviors of nanocomposite beams. It is reported that influence of different parameters deeply depends on the magnitude of volume fraction of nanofillers inside the inclusions. • Vibration frequency of multi-scale hybrid nanocomposites in the framework of finite element based Rayleigh-Ritz method is investigated. • A new refined higher-order beam theory is introduced to govern shear stress and strain through the thickness direction. • The influences of nanofillers' aggregation, beam's shear deformation and various boundary conditions are considered. • Homogenization procedure is procured based on Eshelby-Mori-Tanaka approach incorporated with a micromechanical scheme. • Comparison of the finite element responses with those achieved from the analytical solution guarantees the accuracy of the presented model. [ABSTRACT FROM AUTHOR]