Stochastic Bifurcation Of Current Carrying Thin Rectangular Plate In A Magnetic Field

Rectangular thin plates because of its large deformation and easy to flutter characteristics, make it has been widely used in various engineering fields. With the continuous development of modern high technology, people to study the nonlinear dynamic characteristics in thin plate in the electromagnetic environment is becoming more and more common, and stochastic bifurcation as a kind of complex nonlinear phenomena have caused people’s great attention, but it is rarely found in research reports that the plate’ random bifurcation in the electromagnetic field and mechanical field, so the theory of nonlinear stochastic dynamics are used to research the rectangular thin plate’s stochastic bifurcation is very necessary. This paper makes the following works:This paper first simple introduced the magnetic elasticity and stochastic bifurcation’s research background and research status, then presents the relevant theory about electrodynamics and stochastic which are needed to research rectangular thin plate’s stochastic bifurcation. On the basis of the nonlinear equations of motion, a nonlinear random vibration equation of a current carrying thin rectangular plate is established in a magnetic field, it is simplified as a nonlinear dynamics differential equation by using Galerkin variation method, then the equation is equivalent to be a one-dimensional It?stochastic differential equation by applying the stochastic average theory of a quasi non-integrable Hamilton system, the local stochastic stability of the system was judged by using the maximum Lyapunov index, its global stability of the system was also judged by using the singular boundary theory; the steady-state probability density function of the system is solved through the FPK equation method to research the stochastic Hopf bifurcation behavior of rectangular thin plate. take four-edge simple supported, two opposite edges are fixed and others are simply supported rectangular thin plat and four-edge fixed rectangular thin plate as an example. Through numerical simulation and the Matlab software drawing, get the steady state probability density function diagram,The size of the parameters is studied for researching stochastic Hopf bifurcation according to the change of the image’s shape.The research results show that rectangle thin plate contains very complicate dynamicbehavior when it under the coupling effect of electromagnetic field and mechanical field, it provides reference value for the reliability design of the electromagnetic element.