计算力学学报2017，Vol.34Issue(1)：17-26,10.DOI:10.7511/jslx201701002
磁场中旋转运动圆板的分叉与混沌研究
Bifurcation and chaos of a rotating circular plate in magnetic field
摘要
Abstract
Numerical simulation was used to research the bifurcation and the chaos of rotating circular plate in magnetic field.Firstly,based on the thin plate theory and Maxwell Equations,the expressions of kinetic energy,potential energy,virtual work by external force and electromagnetic force were derived.Using Hamilton's principle,the nonlinear non-axisymmetric magnetoelastic vibration differential equations for vibration of the rotating circular plate in the magnetic field were investigated.Secondly,the Galerkin method and Bessel mode shape function were used to derive the ordinary differential equations for axisymmetric transverse vibration.Finally,the primary resonance of the circular plat fixed boundary was studied.Considering the first order mode shape function,the results such as bifurcation diagrams and Poincare map were obtained under the control parameters of magnetic induction,transverse force magnitude and frequency respectively.The influence of bifurcation parameters on the bifurcation and chaos of system was discussed.The results show that the bifurcation parameters affect the stability of the system,and with the system experiences a complicated process from chaos to multi periodic motion to chaos as these parameters vary.关键词
磁弹性/圆板/贝塞尔函数/分叉/混沌Key words
magneto-elastic/circular plate/Bessel/bifurcation/chaos分类
数理科学引用本文复制引用
胡宇达,朴江民..磁场中旋转运动圆板的分叉与混沌研究[J].计算力学学报,2017,34(1):17-26,10.基金项目
国家自然科学基金(11472239) （11472239）
河北省自然科学基金(A2015203023) （A2015203023）
河北省高等学校自然科学研究重点项目(ZD20131055)资助项目. （ZD20131055）
