Nonlinear vibrations of auxetic honeycomb thin plates based on the modified Gibson functions.

• A novel model for auxetic honeycomb thin plates, utilizing modified Gibson functions, is developed. • The tensile and compressive deformation are considered in the equivalent elastic formulas. • Nonlinear primary/super-/sub- harmonic resonances of auxetic honeycomb plates are analyzed. • The geometric parameters of auxetic honeycomb unit cells exhibit a significant influence on nonlinear dynamic behaviors. Auxetic honeycombs possess many excellent properties, making them ideal cores for sandwich structures that can absorb energy effectively. This paper investigates the nonlinear vibrations of auxetic honeycomb composite plates, focusing on the primary resonance, super-/sub-harmonic resonances of the composite plates. Two pure panels sandwich an auxetic honeycomb core to form the honeycomb composite plate. The proposed modified Gibson function enables the derivation of effective material properties. By considering geometric nonlinearity, the nonlinear motion equations are derived through the implementation of the Hamilton principle, and then nonlinear ordinary differential equations are given by introducing stress functions and the Galerkin method. The nonlinear response curves are then determined by the multiple scale method. The impact of important parameters on the nonlinear vibration of auxetic honeycomb composite plates is evaluated in this study. [ABSTRACT FROM AUTHOR]