Geometrically nonlinear free vibration of shear deformable piezoelectric carbon nanotube/fiber/polymer multiscale laminated composite plates

The nonlinear free vibration of carbon nanotubes/fiber/polymer composite (CNTFPC) multi-scale plates with surface-bonded piezoelectric actuators is studied in this paper. The governing equations of the piezoelectric nanotubes/fiber/polymer multiscale laminated composite plates are derived based on first-order shear deformation plate theory (FSDT) and von Kármán geometrical nonlinearity. Halpin-Tsai equations and fiber micromechanics are used in hierarchy to predict the bulk material properties of the multiscale composite. The carbon nanotubes are assumed to be uniformly distributed and randomly oriented through the epoxy resin matrix. A perturbation scheme of multiple time scales is employed to determine the nonlinear vibration response and the nonlinear natural frequencies of the plates with immovable simply supported boundary conditions. The effects of the applied constant voltage, plate geometry, volume fraction of fibers and weight percentage of single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs) on the linear and nonlinear natural frequencies of the piezoelectric nanotubes/fiber/polymer multiscale composite plate are investigated through a detailed parametric study.