Nonlinear Vibration Of Axially Moving Thin Plates In Magnetic Field

A variety of engineering systems with axially moving such as power transmissionbelts, tapes, band saw, paper and the composite material laminate of aerospace engineer-ing etc.can be simplified as axially moving plates in engineering practice application.Therefore, the investigation on vibration of the axially moving plates is significant notonly in thoeretical but also in engineering practice.In this paper, research works ofnonlinear magnetoelastic vibration of the axially moving strip thin plates subjected to antransverse magnetic field have done.First, based on the electromagnetic theory,electrodynamics equation electromagne-tic forces are deduced. A sets of nonlinear magnetoelastic vibration equation of theaxially moving strip thin plates which in the mechanic filed and magnetic filed are givenby using Hamiltonian variational principle. Substitute the displacement solution into thevibration equation which meet the boundary condition of two opposite ends simplysupported and two opposite ends free, using the method of Galerkin to integrate it andmake it dimensionles, then the Duffing type vibration differential equation is deduced.Second, solve the problems of nonlinear free vibration, main resonances and com-bination resonances by using the method of Multiple Scales, and the first approximateanalytic solutions is deduced, and amplitude-frequency fuctions of main resonances andcombination resonances are also obtained. based on the lyapunov stability theory, thediscriminant of stable solutions is obtained, and the stability of stable solution isanalyzed.At last, by means of calculated example, the time history response plots and phasecharts of three vibration conditions: nonlinear free vibration, main resonances and com-bination resonances are obtained. In cases of mian resonances and combination resonan-ces, spectrum charts is obtained, and obtained the amplitude frequency curve by theamplitude frequency response equation. The influences of system's vibration characteris-tics under the condition of magnetic induction intensity, speed, frequency tuning parame-ters, incentive amplitude, thickness of the electromagnetic parameters and mechanical parameters are analyzed, and the complex dynamic behaviors of axially moving systems:such as as single-frequency periodic motion, quasi-period motion and dou-bling-periodmotion are discussed.