Nonclassical approach to nonlinear vibration problem of fluid-immersed axially moving sandwich auxetic microplates with functionally graded carbon nanotube-reinforced composite face sheets under thermal loading

Abstract

This study develops a unified size-dependent nonlinear framework for the coupled vibrational behavior of axially moving sandwich microplates with functionally graded carbon nanotube-reinforced composite (FG-CNTRC) face sheets and auxetic re-entrant aluminum cores immersed in an ideal fluid. The framework simultaneously addresses fluid-structure interaction, geometric nonlinearity, and microscale effects, a combination absent from the existing literature. The dynamic model integrates linear potential flow theory and first-order shear deformation theory (FSDT) with modified couple stress theory (MCST) to capture size-dependent stiffening and hydrodynamic added mass, while von Kármán strain–displacement relations account for geometric nonlinearity. Five thermal loading patterns, four carbon nanotube (CNT) distribution profiles (FG-X, FG-O, FG-V, and UD, corresponding to X-shaped, O-shaped, V-shaped, and uniformly distributed patterns, respectively), and three auxetic core configurations with negative, zero, and positive Poisson's ratios are examined under simply supported and clamped boundary conditions. Hamilton’s principle yields the nonlinear equations of motion, which are discretized via the Galerkin technique and solved using the harmonic balance method to extract frequency-amplitude relationships under forced vibration. The results reveal amplitude-dependent resonance shifts and hardening/softening behavior governed by CNT distribution, core topology, axial velocity, and thermal loading, providing quantitative design guidelines for micro-electromechanical systems resonators, aerospace microstructures, and biomedical microdevices operating in fluid-thermal environments.

Graphical abstract

Keywords

auxetic re-entrant core / axially moving sandwich microplate / FG-CNTRC / modified couple stress theory / nonlinear vibration

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