收藏本站
《应用数学和力学》 2013年11期
收藏 | 投稿 | 手机打开
二维码
手机客户端打开本文

Principal parametric resonance of axially accelerating rectangular thin plate in magnetic field

胡宇达  张金志  
【摘要】:Nonlinear parametric vibration and stability is investigated for an axially accelerating rectangular thin plate subjected to parametric excitations resulting from the axial time-varying tension and axial time-varying speed in the magnetic field.Considering geometric nonlinearity,based on the expressions of total kinetic energy,potential energy,and electromagnetic force,the nonlinear magneto-elastic vibration equations of axially moving rectangular thin plate are derived by using the Hamilton principle.Based on displacement mode hypothesis,by using the Galerkin method,the nonlinear parametric oscillation equation of the axially moving rectangular thin plate with four simply supported edges in the transverse magnetic field is obtained.The nonlinear principal parametric resonance amplitude-frequency equation is further derived by means of the multiple-scale method.The stability of the steady-state solution is also discussed,and the critical condition of stability is determined.As numerical examples for an axially moving rectangular thin plate,the influences of the detuning parameter,axial speed,axial tension,and magnetic induction intensity on the principal parametric resonance behavior are investigated.
【作者单位】Key
【基金】:supported by the Natural Science Foundation of Hebei Province of China(No.E2010001254)
【分类号】:O441.4

中国知网广告投放
 快捷付款方式  订购知网充值卡  订购热线  帮助中心
  • 400-819-9993
  • 010-62791813
  • 010-62985026