Nonlinear transient dynamics of polymer matrix nanocomposite straight beams strengthened with functionally graded graphene oxide powders

Abstract

This paper reports on a comprehensive nonlinear transient dynamic analysis of nanocomposite beams reinforced with graphene oxide powders (GOPs) dispersed in a functionally graded (FG) manner within the polymer matrix (PM). The Bernoulli–Euler beam structural model, incorporating von Kármán-type geometric nonlinearities, is adopted for modeling composite beams. The nanocomposite beams’ effective mechanical properties are determined using the modified Halpin–Tsai micromechanical model and the rule of mixture. The nonlinear governing equations of motion are derived using Hamilton’s principle and solved within a numerical framework that combines the finite element method for spatial discretization, the Newton–Raphson method for nonlinear resolution, and the Newmark time integration scheme for temporal discretization. After validating the results by ABAQUS software, parametric investigations are conducted to examine the influence of the GOPs diameter-to-thickness ratio, GOPs weight fraction, and various functionally graded distribution patterns on the nonlinear transient dynamic response of composite beams. The results reveal that an increase in the nanofillers’ geometric dimensions and content significantly enhances stiffness, leading to reduced deflection amplitudes and shorter oscillation periods of the beams. Additionally, among the distribution patterns, the FG-X configuration demonstrates the most favorable dynamic performance, followed by UD, FG-V, and FG-O. These findings offer valuable insights into the nonlinear dynamic characteristics of advanced nanocomposite beams and highlight the potential of FG-GOPs-reinforced PM nanocomposite structures for vibration-critical applications, such as aerospace and mechatronics. This work makes a substantial contribution to the ongoing development of smart materials and nonlinear structural dynamics in engineered systems.