PARAMETRIC VIBRATION OF AXIALLY ACCELERATING RECTANGULAR PLATE IN TRANSVERSE MAGNETIC FIELD

The magneto-elastic parametric vibration problem of an axially moving current-conducting rectangular thin plate with pulsating speed in magnetic field was investigated. Based on the expressions of kinetic energy,strain energy and electromagnetic forces,the magneto-elastic parametric vibration equations of an axially moving rectangular thin plate were deduced by using Hamilton principle. Considering the problem of parametric vibration of an axially moving rectangular thin plate on simple supports with pulsating speed in transverse magnetic field,based on the displacement mode hypothesis,Mathieu equation contains two variable coefficients was obtained by using Galerkin method. Based on Floquet theory,by using averaging method,the stability of periodic solution of parametric vibration system was analyzed and the critical condition of stability was determined. By the numerical examples,the stability diagram and the vibration response diagram of parametric vibration system were obtained. The influence of axially moving velocity parameter on the vibration response and the stability of solution were analyzed. The results show that response curves correspond to the region of stable solution present periodic motion or quasi-periodic motion,while the region of unstable solution presents divergence form.