Nonlinear vibrations of FGM truncated conical shell under aerodynamics and in-plane force along meridian near internal resonances

This paper focuses on the nonlinear dynamics near internal resonance of a truncated FGM conical shell. The FGM conical shell is subjected to the aerodynamic load and the in-plane excitation along the meridian direction. Material properties depend on the temperature and the constituent phases of the truncated FGM conical shell. The volume fractions are modified in the thickness direction based on a power-law function continuously and smoothly. The first-order piston theory is applied for the supersonic aerodynamic pressure. Based on the first order shear deformation theory, von-Karman type nonlinear geometric assumptions, Hamilton principle and Galerkin method, the nonlinear equations of motion for the truncated FGM conical shell are derived. The averaged equations of the truncated FGM conical shell are obtained under the situation of 1:1 internal resonance and 1/2 subharmonic resonance by using the method of multiple scales. The frequency-response curves, the force-response curves, the bifurcation diagrams, the phase portraits, the time history diagrams, and the Poincare maps are obtained by using numerical calculations. The influences of the Mach number, the exponent of volume fraction and the in-plane excitation on the nonlinear resonant behaviors of the truncated FGM conical shell are investigated.