Primary and Secondary Instability Region Analysis of Rotating Carbon Nanotube–Reinforced Non-uniform Hybrid Composite Plates

In this work, the primary and secondary instability region analysis of rotating multi-walled carbon nanotube (MWCNT) reinforced non-uniform hybrid composite plates (CNT-FRP) under uniaxial periodic loads is performed. First-order shear deformation theory has been used to derive the kinetic and potential energy equations of the various configurations of non-uniform composite plates by including the effect of rotary inertia, shear deformation, varying centrifugal stiffness and non-uniformity along the transverse direction of the plate. The governing differential equations of motion are derived in the form of Mathieu–Hill equations using the Hamilton’s principle. The efficacy of the developed finite-element formulation has been verified by comparing the natural frequencies of the rotating composite plates evaluated using the numerical simulation with the experimental results and available literature. This study also investigates the influence of the CNT vol%, CNT aspect ratio, angular rotation of plate and static load on the primary and secondary instability region of various non-uniform configurations of CNT-FRP hybrid composite plates. It was noticed that the primary and secondary regions of parametric instability of CNT-FRP hybrid composite plates shift upward when CNT vol% increases from 0 to 2%. It was further noticed that primary and secondary instability regions of various non-uniform configurations shift to the lower excitation frequency when MWCNT vol% increases beyond the saturation limit. It was observed that the effect of angular rotation and static load is significant on the primary and secondary regions of instability.