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2 Journal of Theoretical and Applied Mechanics

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Thermoelastic strongly nonlinear vibration of rotating functionally graded ring plate

Hu Yu Da, Bao Hai Jun, XU Hao Ran

Journal of Theoretical and Applied Mechanics

2021

Vol. 59 nr 1

157--171

For a metal ceramic functionally graded (FGM) ring plate, considering variations in physical properties with temperature and a power-law distribution of material components along the thickness direction, thermoelastic coupled nonlinear vibration equation in thermal environment is derived by means of Kirchhoff’s thin plate theory and the Hamiltonian principle. The transverse nonlinear vibration differential equation of the inner and outside-clamped ring plate under static load is obtained by using the Galerkin method; moreover, perturbation solution of static deflection is carried out. An improved L-P method is employed to solve the strongly nonlinear vibration equation. The vibration response and nonlinear natural frequency expression are developed. Through numerical examples, natural frequency characteristic curves of the rotating FGM ring plate are plotted. The Runge Kutta method is applied to obtain vibration response, phase and power spectrum diagrams. The influence of different parameters on natural vibration characteristics is analyzed. The results show that analytical solutions are consistent with numerical solutions, and the natural frequency decreases with an increase in the metal content and surface temperature, but grows with an increase in the rotational speed.

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

Li Zhe, Hu Yu Da, Li Wen Qiang

Journal of Theoretical and Applied Mechanics

2019

Vol. 57 nr 4

883--895

Magneto-elastic nonlinear non-axisymmetric resonance is investigated for a rotating annular plate in a double-direction magnetic field. According to transverse and longitudinal magneto- -elastic non-axisymmetric vibration equations of the thin annular plate, and considering the influence of the static load term, non-axisymmetric vibration differential equations by combined parametric and forced excitations are obtained through application of the Galerkin method. Then, the method of multiple scales is applied to solve differential vibration equations. By numerical computations, the influence of magnetic induction intensity, inner and outer diameters, excitation and radial forces on transverse and longitudinal resonance characteristics are analyzed.