Nonlinear Dynamics and Energy Absorption Analyses of Auxetic Nanocomposite Structures

Abstract

The present work deals with the modelling and analyses in order to study the nonlinear dynamic behaviours as well as energy absorption capacities of the different carbon nanotube (CNT) reinforced polymer composite (CNTRC) structures having negative Poisson’s ratio (NPR). This type of auxetic composite structures have many applications for energy absorption, impact resistance and fracture toughness in the various fields of engineering. Based on the classical lamination theory (CLT), the auxetic laminate has been designed by obtaining the special stacking sequences of layers in the thickness direction. The mathematical models have been formulated for determination of the effective out of plane negative Poisson’s ratios as well as material properties of different auxetic nanocomposite laminates of CNTRC-NPR, functional graded (FG) carbon nanotube reinforced composite having negative Poisson’s ratio (FG- CNTRC-NPR), hybrid nanocomposite having negative Poisson’s ratio (HBD-NC-NPR) and sandwich structures with various auxetic cores. A mathematical model is also developed for nonlinear dynamic analysis of the beams of such different auxetic nanocomposite laminates. The present formulations for nonlinear dynamic analysis are based on the Reddy’s third-order shear deformation theory and von-Karman nonlinear strain-displacement relations. The governing equations of motion of such auxetic structures are derived using the Hamilton’s principle. The obtained governing coupled nonlinear partial differential equations are converted to an ordinary nonlinear differential equation for the analysis of out-plane displacement using the Galerkin’s method. In the present study, three types of boundary conditions (such as clamped-clamped, simply supported and cantilever) of the beam are considered. The dynamic behaviours of the transverse displacements for the different auxetic nanocomposite structures under transverse excitation are analysed in terms of time series waveforms, phase portraits and Poincaré maps, and the routes of chaotic responses of the non-auxetic and auxetic structures have been found and reported based on the bifurcation diagrams. The jumps phenomena associated with the dynamics of the different non-auxetic and auxetic structures have also been presented and analysed. Based on the nonlinear dynamic analyses, the energy absorption (EA) capacities of the various non-auxetic and auxetic nanocomposite structures under shock loading have been determined and analysed. The effects of various important parameters (such as CNT/carbon fiber (CF) volume fractions, types of distributions of CNT volume fractions across the thickness direction of laminate, NPR, damping coefficient, amplitude of transverse excitation, and degree of nonlinearity) on the dynamics, energy absorption capacities and jumps phenomena have also been studied and reported.