Chaotic vibration analysis of auxetic nanocomposite structures

Abstract

The present work deals with the study of nonlinear vibration behaviours of the carbon nanotube reinforced composite structures having negative Poisson’s ratio (CNTRC-NPR). Such types of flexible auxetic structures have many applications in various engineering fields. Based on classical laminated theory, auxetic structures can be designed by some special stacking sequence of layers in the laminated composites. A mathematical model is formulated for nonlinear vibration analysis of the clamped-clamped CNTRC-NPR beam under the time varying uniformly distributed transverse load. The present formulation is based on the Reddy’s third-order shear deformation theory and the governing equation of motion of such beam is derived by using the Hamilton’s principle. Based on the Galerkin’s method, the obtained governing partial differential equations are converted to an ordinary nonlinear second-order differential equation for the analysis of out plane vibration. The obtained vibrations of such auxetic structures are discussed using time series waveforms, phase portraits and Poincare maps, and the route of chaotic vibration of such structures is found and reported based on the bifurcation diagrams. The jump phenomena associated with the dynamics have also been characterized. Nonlinear vibrations of without and with auxetic nanocomposite structures have also been compared. It is found that the amplitude of transverse force of excitation is the controlling parameter of nonlinear dynamics of such CNTRC-NPR structures.