Magnetic Elasticity Chaotic Motion Of A Thin Rectangular Plate With Large Deflection

Thin plate is one of the common components of engineering structures, they areusually working in the coupled of multi-field,such as mechanical field, electromagneticfields and so on. The dynamic characteristics of the system have an important impact ofthe structural safety. Therefore, the research of multi-field coupling dynamics problem ofthe magnetic-elastic thin plate has important theoretical significance and practicalapplication value.On the basis theory of plate and shell magnetic-elastic mechanics, according to thelarge deflection rectangular sheet, the paper discussed the chaotic property of systemunder coupled action of mechanical load field and electromagnetic field. The mainresearch content is as follows:Firstly, introduced the related topics research status at home and abroad, and relevantknowledge of mechanics theory and electromagnetic force expression, deduced thenonlinear magnetic-elastic vibration equation of thin plate.Secondly, briefly expounds the basic knowledge of bifurcation and chaos theory.Introduces the general system bifurcation type, bifurcation form, three basic types of onedimensional bifurcation and several commonly used research of chaos method andMelnikov method.Finally, based on the theory of plate and shell magnetic-elastic mechanics,usingGalerkin principle deduced the vibration equation of the large deflection rectangular sheetunder the common action of mechanical load and electromagnetic field, study the chaoticmotion characteristics under the coupled action field of mechanical load andelectromagnetic field. Through the concrete example, numerical calculation and numericalsimulation of the system and obtained the bifurcation diagram, displacement oscillogramdiagram, phase plane track diagram and poincare section diagram. Then discussed thechaos movement of the system about the mechanical load and electromagnetic fieldparameters.The results of the study show that structural components under the action of coupledfield like electromagnetic field,mechanical field and other physical field contains quite rich and complex dynamic behavior.