Nonlinear combination resonance of rotating functionally graded circular plates with pores in the temperature field

The nonlinear primary parametric resonance-principal resonance combination vibration of rotating functionally graded circular plates containing pores in temperature field is investigated. The physical parameters of different pore distribution patterns are given using the modified mixed power-law model. Based on geometric nonlinearity, the kinetic energy and potential energy are derived. The nonlinear vibration governing equations with variable speed rotating motion are derived by Hamilton's principle. The influence of transverse static deflection caused by rotation and temperature on transverse vibration is considered. The displacement function of clamped boundary condition is set up, and Galerkin method is carried out to obtain the differential equation. The amplitude-frequency equation is obtained applying the multi-scale method. Based on Lyapunov stability theory, criteria for determining the stability of steady-state solutions are presented. The numerical analysis shows that under the certain gradient index, the change in porosity of A-2 is different to other distributions. Compared with rotating speed, the system is more affected by temperature and transverse harmonic excitation. The thermo-elastic coupling exists between the temperature field and rotating motion, and the system exhibits nonlinear characteristics. The change of parameters induced change of frequency value and amplitude corresponding to bifurcation points.