Bucking and free vibration characteristics of smart hybrid sandwich plate via spatial state-space approach

Abstract

While carbon nanotubes (CNT)- and graphene nanoplatelets (GNPs)-reinforced composites have been widely studied, hybrid nanocomposites are less explored. Polyurethane (PU) foams, valued for their low density and cost-effectiveness, face mechanical limitations, prompting nanoparticle reinforcement. This study investigates, for the first time, the buckling and vibration properties of PU matrices reinforced with multi-walled carbon nanotubes (MWCNTs), GNPs, and their hybrid combinations. This hybrid composite plate integrates two layers of piezoelectric sensors and actuators. The dynamics behavior of the system is modeled using linear three-dimensional piezo-elasticity theory. Through dual transformation pairs, the equations are converted into two decoupled, lower-order spatial state-space systems that describe both the plate's planar and transverse mechanical behaviors. Additionally, various parametric studies are conducted for the first time to explore the impacts of different ratios of MWCNT:GNP, different flake sizes of GNP, MWCNT aspect ratios, weight fractions of nanofillers, reinforced patterns, dimension ratios of the plate, electrical boundary conditions, and various boundary conditions for the edge of the plate on the natural frequency and buckling properties of hybrid smart composites. The results show that natural frequency and buckling load in PU nanocomposites rise with nanofiller weight fraction, peaking with FG-GNP24 at 1.0 wt% featuring 3.5 % and 6.2 % gains for frequency and buckling, respectively. Hybrid MWCNT-GNP systems excel at specific ratios: 5:1 (MWCNT-GNP1.5) surpasses single fillers, while 1:1 (MWCNT-GNP5) performs best at 0.25–0.5 wt%. Open-circuit piezoelectric configurations outperform closed-circuit. X-O nanofiller patterns optimize frequency in MWCNT-GNP24 composites (8:2, 5:1 ratios), while uniform distributions maximize buckling resistance.