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- Title
Primary parametric resonance, stability analysis and bifurcation characteristics of an axially moving ferromagnetic rectangular thin plate under the action of air-gap field.
- Authors
Hu, Yuda; Tian, Yuxin
- Abstract
The primary parametric resonance of a ferromagnetic rectangular thin plate with axial time-varying velocity in the air-gap field is researched. Through building the analytical model of air-gap field between the elastic plate and armature, the dynamic changes of air-gap field during resonance are determined. On account of electromagnetic boundary conditions, intraplate magnetic field distribution under the magnetization effect is obtained. Within the framework of magneto-electro-elastic theory and Hamilton principle, the motion governing equation of the axially moving ferromagnetic plate subjected to air-gap magnetizing force is finally deduced. For the simply supported constraint, applying the Galerkin method, the ordinary differential vibration equation of plate under parametric excitations is obtained by separating time–space variable. The multiscale method is applied to investigate the parametric vibration behavior of plate. Based on Lyapunov stability theory, the stability criterion of steady-state amplitude solutions is acquired. Through numerical methods, the correctness of analytical results is verified. The effects of armature and time-varying parameters on the static deflection, steady-state response amplitude, and the regional distribution of stable solutions are studied. The dynamic stability and bifurcation characteristics of the system are explored. Eventually, the results reveal that the static deflection caused by the air-gap magnetizing force makes the thin plate more rigid. The increase of armature and time-varying parameters causes the stable solutions to reduce and then grow by affecting the stiffness and excitation. At high magnetic potential amplitude, high velocity, and small tension, the system motion exhibits prominent chaotic characteristics.
- Subjects
PARAMETRIC vibration; HAMILTON-Jacobi equations; FERROMAGNETIC resonance; EQUATIONS of motion; RESONANCE; ORDINARY differential equations
- Publication
Nonlinear Dynamics, 2024, Vol 112, Issue 11, p8889
- ISSN
0924-090X
- Publication type
Article
- DOI
10.1007/s11071-024-09457-3