Nonlinear natural vibration of ferromagnetic rectangular thin plate under constant magnetic field

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Journal of Vibration and Shock ›› 2023, Vol. 42 ›› Issue (3) : 74-82.

TAO Shanze1,2, HU Yuda1,2

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Abstract

By establishing the mechanical model of the ferromagnetic rectangular plate in the magnetic field, the nonlinear natural vibration under the constant magnetic field is studied, and the static load effect is considered. According to the Hamiltonian variational principle, the magneto-elastic nonlinear vibration equation of the rectangular plate in magnetic field, the expressions of magnetizing electromagnetic and eddy current electromagnetic forces are given. Based on the perturbation expansion method, the static deflection and nonlinear perturbation equations under action of magnetostatic force are determined. The approximate analytical solution and natural frequency expression of the vibration system are obtained by means of Galerkin method and multi-scale method. Through numerical calculations, for the rectangular thin plates of three materials, characteristic curves of natural frequency with time, magnetic field strength, initial value, plate aspect ratios etc. are given. The results show that the natural frequency increases with time and eventually tends to a certain value. With the change of magnetic fields in top and bottom surface, it may show a symmetrical trend. As the aspect ratios increases, natural frequency may decrease gradually, which means the system presents a typical nonlinear characteristics. In addition, the analytical solution and the numerical solution obtained in paper are in good consistence.

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TAO Shanze1,2, HU Yuda1,2. Nonlinear natural vibration of ferromagnetic rectangular thin plate under constant magnetic field[J]. Journal of Vibration and Shock, 2023, 42(3): 74-82

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