M. Rafiee

Nonlinear analysis of piezoelectric nanocomposite energy harvesting plates

This paper investigates the nonlinear analysis of energy harvesting from piezoelectric functionally graded carbon nanotube reinforced composite plates under combined thermal and mechanical loadings. The excitation, which derives from harmonically varying mechanical in-plane loading, results in parametric excitation. The governing equations of the piezoelectric functionally graded carbon nanotube reinforced composite plates are derived based on classical plate theory and von K?rm?n geometric nonlinearity. The material properties of the nanocomposite plate are assumed to be graded in the thickness direction. The single-walled carbon nanotubes (SWCNTs) are assumed to be aligned, straight and have a uniform layout. The linear buckling and vibration behavior of the nanocomposite plates is obtained in the first step. Then, Galerkin?s method is employed to derive the nonlinear governing equations of the problem with cubic nonlinearities associated with mid-plane stretching. Periodic solutions are determined by using the Poincar??Lindstedt perturbation scheme with movable simply supported boundary conditions. The effects of temperature change, the volume fraction and the distribution pattern of the SWCNTs on the parametric resonance, in particular the amplitude of vibration and the average harvested power of the smart functionally graded carbon nanotube reinforced composite plates, are investigated through a detailed parametric study.

An Analytical Study on Thermally Induced Vibration Analysis of FG Beams Using Different HSDTs

Thermo-mechanical vibrations of functionally graded (FG) beams are developed. Governing equations of functionally graded beams are obtained based on higher-order variation of transverse shear strain through the depth of the beam. The material properties of the functionally graded beam are assumed to vary according to power law distribution of the volume fraction of the constituents. Equations of motion and boundary condition are derived from Hamilton’s principle. Beam is assumed under uniform thermal loading and simply supported boundary condition. Analytical solution is presented, and the obtained results are compared with the existing solutions to verify the validity of the developed theories. Numerical computations are performed for a functionally graded simply supported beam with a gradient index obeying power law and the results are displayed graphically and tabular to show the effects of the gradient index, temperature rise, and geometrical parameters on the fundamental natural frequency of FG beams, indicating that natural frequency is sensitive to the gradient variation of material properties, geometrical parameters, shear deformations and temperature rise.