Nonlinear Dynamic and Energy Absorption Characteristics of Auxetic Graded Nanotube-Reinforced Polymeric Composite Beams

A mathematical model is developed for nonlinear dynamic analysis in order to study the energy absorption (EA) and dissipation capacities of the functionally graded carbon nanotube-reinforced composites (FG-CNTRC) beam, including negative Poisson’s ratio (NPR). The displacement kinematic relations are derived using higher-order shear deformation theory, and the governing equations of motion are developed using Hamilton’s principle and Galerkin’s technique. The dynamic responses of the FG-CNTRC-NPR beams under transverse excitation are analyzed analytically via time series time responses. The developed mathematical modeling may be useful for the complete analysis of nonlinear dynamics, EA and frequency responses, which relate to the actual behavior of the nonlinear dynamics and EA. Further, the phase diagram, Poincaré maps (PCM), and the routes of chaotic responses have been computed numerically and presented through the bifurcation diagrams. In addition, the presentation of the stiffening and softening feature is accompanied by the jumps phenomena that are related to the dynamics of the FG-CNTRC-NPR shapes. After subjecting the FG-CNTRC-NPR beams to shock loading, their EA capabilities were measured and evaluated. Based on the different outcomes, it is clear that the suggested auxetic structures’ EA and dissipation capabilities are significantly affected by the NPRs and the variation in the proportion of carbon nanotube (CNT) volume fractions through the thickness direction. As compared to non-auxetic beam, the auxetic FG-CNTRC beam has a greater capacity of EA and dissipation, which may also be suitable for use in damping applications.