Magnetoelastic Principal Parametric Resonance of a Rotating Electroconductive Circular Plate

Abstract

Nonlinear principal parametric resonance and stability are investigated for rotating circular plate subjected to parametric excitation resulting from the time-varying speed in the magnetic field. According to the conductive rotating thin circular plate in magnetic field, the magnetoelastic parametric vibration equations of a conductive rotating thin circular plate are deduced by the use of Hamilton principle with the expressions of kinetic energy and strain energy. The axisymmetric parameter vibration differential equation of the variable-velocity rotating circular plate is obtained through the application of Galerkin integral method. Then, the method of multiple scales is applied to derive the nonlinear principal parametric resonance amplitude-frequency equation. The stability and the critical condition of stability of the plate are discussed. The influences of detuning parameter, rotation rate, and magnetic induction intensity are investigated on the principal parametric resonance behavior. The result shows that stable and unstable solutions exist when detuning parameter is negative, and the resonance amplitude can be weakened by changing the magnetic induction intensity.

Magneto-elastic combined multidimensional resonance of a rotating circular plate in a double-direction magnetic field

“…Meanwhile, bifurcation, chaos and free vibration under static loads were discussed, and the influence of a variable parameter on the resonance characteristics of the system was analyzed. Li et al (2017) studied nonlinear principal parameter vibration and stability of a rotating circular plate with variable speed in a magnetic field and derived the magneto-elastic vibration equation of a rotating circular plate in a magnetic field. The resonance amplitude response equation of the nonlinear principal parameter was obtained by using the multi-scale method, and the effects of parameters on the system stability were discussed.…”

Thermoelastic coupling vibration and stability analysis of rotating circular plate in friction clutch

“…Mottershead and Chan 10 examined the flutter instability of the circular plate under the frictional follower load. Hu and Wang 11 and Li et al 12 established the magnetoelastic vibration equations of a conductive rotating circular plate by Hamilton principle. They investigated the critical condition of stability of the rotating circular plate by the Galerkin method.…”

“…Some research work on a high-order partial differential equation had been carried out by the Galerkin method and finite element method. 1,3,7,8,11,12,22 Yayli 23–27 used the Fourier sine series and Stoke transformation to analyze the high-order partial differential equation of vibration. The computation in these methods is complicated.…”