Nonlinear natural vibration of axially moving ferromagnetic thin plate under static magnetic force

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Journal of Vibration and Shock ›› 2023, Vol. 42 ›› Issue (11) : 207-214.

MU Yuan1,2, HU Yuda1,2

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Abstract

The natural vibration of a nonlinear system with different boundary constraints under the action of static magnetic force is studied for a ferromagnetic rectangular plate moving axially in plane. The magnetization force of ferromagnetic rectangular plate under external magnetic field is given according to electromagnetic theory. Based on the expressions of kinetic energy and strain energy, the nonlinear magneto-elastic vibration equation of axially moving ferromagnetic thin plate is deduced by using Hamiltonian variational principle. Considering three different boundary constraint types of simply supported by four sides, simply supported by opposite sides and free by opposite sides, and simply supported by opposite sides and clipped by side, the nonlinear ordinary differential vibration equation of thin plate under transverse constant magnetic field was obtained by Galerkin method, and the static deflection of thin plate under static magnetic force was determined. Using KBM method, the displacement analytical solution and natural frequency expression of nonlinear free vibration system are obtained. Matlab software was used for numerical calculation, and the variation of natural vibration with axial velocity, magnetic field intensity, initial value and so on was drawn, and the comparative analysis was carried out. The results show that the natural vibration frequency decreases with the increase of axial velocity and magnetic field intensity. The vibration frequency is related to the initial value and increases with the increase of the initial value. Different materials and boundary conditions directly affect the static magnetic force and deflection of the plate.

Key words

Ferromagnetic thin plate / Nonlinear natural vibration / Axial motion / Static magnetic force / KBM method

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MU Yuan1,2, HU Yuda1,2. Nonlinear natural vibration of axially moving ferromagnetic thin plate under static magnetic force[J]. Journal of Vibration and Shock, 2023, 42(11): 207-214

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