Free vibration analysis of a cantilever trapezoidal sandwich plate with an auxetic reentrant honeycomb core and laminated nanocomposite polymer/CNT/fiber face sheets
Saeed Rahmani, Hassan Seidi, Farshad Kakavand, Elshan Soltani
Abstract
In the presented work, the free vibration problem is investigated for a cantilever trapezoidal sandwich plate with an auxetic reentrant honeycomb core covered with laminated nanocomposite three-phase face sheets. Each lamina in the face sheets is made of polymer enriched with carbon nanotubes and glass fibers. The plate is modeled based on the first-order shear deformation theory and the mechanical properties of each lamina are estimated using the rule of mixture, the Eshelby–Mori–Tanaka scheme, and Hanh’s homogenization approach. Utilizing Hamilton’s principle, the governing equations and corresponding boundary conditions are derived. These equations are converted from the Cartesian coordinates into dimensionless computational coordinates using a transformation of coordinates. Utilizing the differential quadrature method, an approximate solution is presented to attain the natural frequencies and the corresponding modes shapes. It is observed that there is an optimum ratio of the thickness of the auxetic reentrant honeycomb core to the total thickness of the plate which brings about the highest natural frequencies.