The Bifurcation Analysis Of The Plate's Stability In Electromagnetic Field

Bifurcation problem originated studies on the elasticity, fluid dynamics, celestial mechanics and nonlinear vibration phenomena of instability in the 18th century, it has profound background. Until the 1970s, due to the promotion of power system, nonlinear analysis and nonlinear differential equations and other mathematical, the study on the bifurcation theory rapid development. Because magnetic elasticity theory research by the very significant problem with the coupling effect, it is bound to energy, transportation, national defense, and so have a wide range of applications. Therefore the theory of its related research has very important significance. At present, domestic and foreign scholars have made a lot of research on the role of mechanical load plates, shells chaotic motion. However, the study for mechanical load on the electromagnetic field coupled with the bifurcation also unusual. Papers in this regard some preliminary research work。The main aspects on the following:First, the infinite plate and strip simply supported the rectangular plate with the mechanical load in the electromagnetic field under a common Analysis by Galerkin electromagnetic field theory have been under movement stability equation. L-S about by the method of single-mode state of the system under the bifurcation problem that the stability and equilibrium bifurcation type, this mode is given under a number of issues related to bifurcation results.Secondly, the application of numerical methods bifurcation (average method) study of the system in the case of dual-mode state bifurcation, identify system balance and the balance on the stability of the situation. Get the corresponding conclusions.Finally, I compare the system in single-, dual-mode simulation of nonlinear behavior pattern, pointing out that a dual-mode single-mode state displacement mode displacement pattern that reflects the bifurcation of the system of internal changes.