Abstract:
The study investigates the primary parameter resonance of a functionally graded circular plate with variable-speed rotational motion under the influence of temperature. Developed are the heat conduction equation and physical parameter expressions depend on the spatial position and on temperature variation. Based on the thin plate theory and considering the geometric nonlinearity, the expressions of kinetic and potential energies for the circular plate are obtained. The nonlinear dynamic governing equations are derived by applying the Hamiltonian principle. The Galerkin method is employed to discretize time and space, the nonlinear vibration differential equation is derived, and the control equations of radial and lateral static deflections generated by temperature field and rotational motion are obtained. The amplitude-frequency response equations are derived by solving the differential equation upon the multi-scale method, and the stability of steady-state motion is discriminated. Through example analyses, obtained are the amplitude-frequency curves, parameter-amplitude diagrams, dynamic phase plane trajectory diagrams and time-history diagrams, revealing nonlinear dynamic characteristics of the primary parameter resonance. The analysis results indicate that: when the dimensionless natural frequency is close to 1 and 2, respectively, two forms of primary parameter resonance can be activated, and the temperature rises and speed improves, the response amplitude increases, and resonance region narrows.