This paper presents a new four-variable refined plate theory for free vibration analysis of laminated piezoelectric functionally graded carbon nanotube-reinforced composite plates (PFG-CNTRC). The present theory includes a parabolic distribution of transverse shear strain through the thickness and satisfies zero traction boundary conditions at both free surfaces of the plates. Thus, no shear correction factor is required. The distribution of carbon nanotubes across the thickness of each FG-CNT layer can be functionally graded or uniformly distributed. Additionally, the electric potential in piezoelectric layers is assumed to be quadratically distributed across the thickness. Equations of motion for PFG-CNTRC rectangular plates are derived using both Maxwell’s equation and Hamilton’s principle. Using the Navier technique, natural frequencies of the simply supported hybrid plate with closed circuit and open circuit of electrical boundary conditions are calculated. New parametric studies regarding the effect of the volume fraction, the CNTs distribution, the number of layers, CNT fiber orientation and thickness of the piezoelectric layer on the free vibration response of hybrid plates are performed.

In this paper a new eight-unknown higher order shear deformation theory is proposed to study the buckling and free vibration of functionally graded (FG) material plates. The theory bases on full twelve-unknown higher order shear deformation theory, simultaneously satisfies zero transverse shear stress at the top and bottom surfaces of FG plates. Equations of motion are derived from Hamilton's principle. The critical buckling load and the vibration natural frequency are analyzed. The accuracy of present analytical solution is confirmed by comparing the present results with those available in existing literature. The effect of power law index of functionally graded material, side-to-thickness ratio on buckling and free vibration responses of FG plates is investigated.

In this paper, a new four-variable refined shell theory is developed for free vibration analysis of multi-layered functionally graded carbon nanotube-reinforced composite (FG-CNTRC) doubly curved shallow shell panels. The theory has only four unknowns and satisfies zero stress conditions at the free surfaces without correction factor. Five different types of carbon nanotube (CNTs) distribution through the thickness of each FG-CNT layer are considered. Governing equations of simply supported doubly curved FG-CNTRC panels are derived from Hamilton’s principle. The resultant eigenvalue system is solved to obtain the frequencies and mode shapes of the anti-symmetric cross-ply laminated panels by using the Navier solution. The numerical results in the comparison examples have proved the accuracy and efficiency of the developed model. Detailed parametric studies have been carried out to reveal the influences of CNTs volume fraction, CNTs distribution, CNTs orientation, dimension ratios and curvature on the free vibration responses of the doubly curved laminated FG-CNTRC panels.

The purpose of the paper is to develop an analytical investigation on free vibration of a simply supported functionally graded (FG) doubly curved shell panels resting on elastic foundation in thermal environment. Heat conduction and temperature-dependent material properties are both taken into account. The temperature field considered is assumed to be a uniform distribution over the shell surface and varied in the thickness direction only. Material properties are assumed to be temperature dependent and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. Based on the first-order shear deformation theory and applying the Hamilton’s principle, governing equations of motion are derived. The results of the study are compared with the available published literature. The numerical results obtained reveal that the material volume fraction index, geometrical parameters and temperature change have significant effects on natural frequencies of the FG doubly curved shell panels.

In this paper, a new eight-unknown shear deformation theory is developed for bending and free vibration analysis of functionally graded plates by finite-element method. The theory based on full 12-unknown higher order shear deformation theory simultaneously satisfies zeros transverse stresses at top and bottom surfaces of FG plates. A four-node rectangular element with 16 degrees of freedom per node is used. Poisson’s ratios, Young’s moduli, and material densities vary continuously in thickness direction according to the volume fraction of constituents which is modeled as power-law functions. Results are verified with available results in the literature. Parametric studies are performed for different power-law indices, side-to-thickness ratios.

In this paper, authors use a finite element model based on higher-order displacement plate theory for analysis of stiffened laminated composite plates. Transverse shear deformation is included in the formulation making the model applicable for both moderately thick and thin composite plates. The plate element used is a nine-noded isoparametric one with nine degrees of freedom at each node. The stiffness of stiffener is reflected at all nine nodes of plate element in which it is placed. Accordingly, the stiffeners can be positioned anywhere within the place element. Free vibration and deflection of stiffened laminated composite plates are carried out, and results are compared with existing analytical and other solutions.