Self-sustained vibrations of functionally graded carbon nanotubes-reinforced composite cylindrical shells in supersonic flow

Abstract

Dynamic model of geometrical nonlinear deformations of functionally graded carbon nanotubes-reinforced composite cylindrical shell is obtained. Reddy higher-order shear deformation theory is used to derive this model. The finite-degree-of-freedom nonlinear system, which describes the structure nonlinear self-sustained vibrations, is obtained using the assumed-mode method. The linear piston theory is used to describe the supersonic flow. The loss of the cylindrical shell dynamic stability owing to the Hopf bifurcations is analyzed. The self-sustained vibrations, which describe the circumferential traveling waves flutter, occur due to this bifurcation. The harmonic balance method is applied to analyze these self-sustained vibrations. The properties of the circumferential traveling waves are analyzed.