Nonlinear dynamics of initially imperfect functionally graded circular cylindrical shell under complex loads

The nonlinear vibration of a simply supported FGM cylindrical shell with small initial geometric imperfection under complex loads is studied. The effects of radial harmonic excitation, compressive in-plane force combined with supersonic aerodynamic and thermal loads are considered. The small initial geometric imperfection of the cylindrical shell is characterized in the form of the sine-type trigonometric functions. The effective material properties of this FGM cylindrical shell are graded in the radial direction according to a simple power law in terms of the volume fractions. Based on Reddy's third-order shear deformation theory, von Karman-type nonlinear kinematics and Hamilton's principle, the nonlinear partial differential equation that controls the shell dynamics is derived. Both axial symmetric and driven modes of the cylindrical shell deflection pattern are included. Furthermore, the equations of motion can be reduced into a set of coupled nonlinear ordinary differential equations by applying Galerkin's method. In the study of the nonlinear dynamics responses of small initial geometric imperfect FGM cylindrical shell under complex loads, the 4th order Runge−Kutta method is used to obtain time history, phase portraits, bifurcation diagrams and Poincare maps with different parameters. The effects of external loads, geometric imperfections and volume fractions on the nonlinear dynamics of the system are discussed.