The Study Of Dynamic Stability Parameter Vibration Problem In Thin Rectangular Plate Under Magnetic Field

Structure dynamic stability of parametric vibration problem widely exists in many engineering applications, such as ship and ocean engineering, civil engineering and many other fields. However, our knowledge and understanding of the structure dynamic stability phenomenon are far from complete currently. Oriented at the scientific research needs in civil and marine ship and ocean engineering fields, by using electric mechanics theory and theories of structural vibrations and dynamics stability, this dissertation presented and applied finite element(FEM) numerical method to deeply investigated the fundamental aspects of dynamic stability of parameter vibration problem of a thin rectangle plate under the magnetic field, the main research work of this dissertation are as follows:Firstly, this paper derived control equation of the rectangular thin plate in transverse magnetic field environment. Then, the stability equation was sorted into the standard form of Mathieu equation. Through a numerical example of simply supported thin rectangular plate, this paper got several electromagnetic and structural factors which affected the dynamic instability region. Some suggestions for engineering design also presented in this paper. Finally, based on the Mindlin-plate theory, this paper deduced four node plate-membrane unit and shaped finite element formulation, established the magneto-elastic Finite Element Model. By writing Fortran programs, the magneto-elastic vibration and dynamic stability problems were solved numerically. It is concluded that the stability of the thin plate can be improved obviously by increasing the value of magnetic induction B when the other conditions are fixed, while improving the thickness of the plate is proved not to be so effective.This dissertation is devoted to studying the structural parameters of the vibration problem in the magnetic field. The present research findings which can provide theoretical guidance and new ideas for the improvement of structural resonance and dynamic stability in the field of ship and ocean engineering.