Static Analysis and Damping Capacity (Energy Absorption) of Sandwich Annular Sector Plates with Facesheets Reinforced with GPLs Considering Agglomeration and a Negative Poisson’s Ratio Metallic Lattice Core

This paper investigates the natural frequency and static analysis of a sandwich annular sector plate with a core exhibiting a negative Poisson’s ratio lattice structure, along with facesheets reinforced with agglomerated graphene nanoplatelets (GPL). Both complete and partial agglomeration states are considered using the Eshelby–Mori–Tanaka micromechanical model. The governing equations of motion are derived using Hamilton’s principle, based on First Shear Deformation (FSD) plate theory and the finite element method. The sandwich plates exhibit an ultra-light characteristic, attributable to the auxetic honeycomb core layer, which possesses a negative Poisson’s ratio, and are further reinforced by two laminated skin layers. The study examines the impact of various parameters, including the geometry of the auxetic honeycomb unit cell, the weight fraction of GPL, and the distribution of GPL on the natural frequency, displacement of the center point of the auxetic honeycomb core, and specific absorbed energy of the sandwich plate. The natural frequency decreases with increasing inclination angle, becoming less sensitive as the ratio [Formula: see text] increases. A 57.14% drop occurs for [Formula: see text] when the angle rises from 10[Formula: see text] to 60[Formula: see text], while for [Formula: see text], and 2.5, the reductions are 25.82%, 13.72%, and 9.23%, respectively. Adding 0.1% GPL without agglomeration raises the natural frequency by 237.85%, enhancing stiffness, but full agglomeration cuts this to 12.47%. The X-pattern has the strongest effect, and the O-pattern the least, with distribution patterns becoming more influential as GPL weight fraction rises. In the partial agglomeration state, performance is optimal when [Formula: see text]. For a GPL weight fraction from 0.2% to 1%, displacement drops by 77.94% at [Formula: see text] and by 71.68% at [Formula: see text].