Nonlinear vibrations of carbon fiber reinforced polymer laminated cylindrical shell under non-normal boundary conditions with 1:2 internal resonance

Abstract

In this paper, the nonlinear vibrations of a carbon fiber reinforced polymer (CFRP) laminated cylindrical shell are investigated with 1:2 internal resonance, primary parametric resonance and 1/2 subharmonic resonance. The radial line load and axial excitation are acting on the two free ends of the CFRP laminated cylindrical shell. The partial differential governing equations of motion for the CFRP laminated cylindrical shell are derived by utilizing the von-Karman type nonlinear geometric relationship, the first-order shear deformation theory and Hamilton principle. Galerkin method is used to obtain two-degrees-of-freedom nonlinear ordinary differential governing equations of motion along the radial displacement of the CFRP laminated cylindrical shell under the non-normal boundary conditions. The ordinary differential governing equations are solved as a system of four-dimensional average equations by the second-order approximate multiple scale method. The first two order dimensionless natural frequencies versus the ratio of length to thickness L/h, the frequency-response curves, the force-response curves, the bifurcation diagrams, the three-dimensional bifurcation diagrams, the maximum Lyapunov exponent diagrams, the phase portraits, the time history diagrams and the Poincare maps are obtained by numerical calculations. The influences of the radial line load, the axial excitation as well as the detuning parameter of the CFRP laminated cylindrical shell on the 1:2 internal resonant behaviors are investigated.