Free and forced vibration of porous-FGM sandwich plates with a reentrant auxetic honeycomb core

Abstract

A unified differential quadrature (DQM) model is developed for the free and, for the first time, the forced vibration of sandwich plates with porous functionally graded face sheets and a reentrant auxetic honeycomb core. Face-sheet porosity follows even and uneven cosine distributions, the auxetic core is homogenized by an extended Gibson–Ashby model, and Reddy third-order theory describes the kinematics. The equations are discretized on a Chebyshev–Gauss–Lobatto grid; free vibration is solved as a generalized eigenproblem and the forced responses by modal superposition. The first three frequencies converge to within 0.1% at N=9, and three benchmarks are matched to within 1.28%, 0.84% and 0.62%, the last a three-dimensional elasticity solution. The fundamental frequency peaks at a mildly conventional cell angle (+15° to +30°) rather than at zero. The porosity effect reverses sign at a power-law index n∗, which is not fixed: for the even distribution it moves from 0.620 to 0.878 as the cell becomes conventional. Clamping raises the fundamental frequency by 14.2% (SCSC) and 29.3% (CCCC) over SSSS. Under step loading the dynamic amplification factor rises from 1.68 (SSSS) to 2.07 (CCCC) but is insensitive to grading and porosity.