磁场中旋转运动圆板的分叉与混沌研究

发布时间：2018-04-18 00:22

本文选题：磁弹性 + 圆板　；参考：《计算力学学报》2017年01期

【摘要】：应用数值模拟方法研究磁场中旋转运动圆板的分叉与混沌问题。首先,基于薄板理论和麦克斯韦电磁场方程组,给出了动能、应变势能、外力虚功以及电磁力的表达式,再利用哈密顿原理,得到磁场中旋转运动圆板横向振动的非轴对称非线性磁弹性振动微分方程组。其次,采用贝塞尔函数作为圆板的振型函数进行伽辽金积分,得到了轴对称情况下横向振动的常微分方程组表达式。最后,针对主共振,取周边夹支边界条件的圆板作为算例,得到了当振型函数取一阶时,将磁感应强度、外激励振幅和激励频率作为控制参数的分叉图及庞加莱映射图等计算结果,并讨论了分叉参数对系统的分叉与混沌的影响。数值计算结果表明,这些控制参数的变化影响系统稳定性,在分叉参数逐渐变化的过程中,系统经历从混沌到多倍周期运动再到混沌的往复过程。
[Abstract]:The bifurcation and chaos problems of rotating circular plates in magnetic field are studied by numerical simulation.Firstly, based on the theory of thin plate and Maxwell's equations of electromagnetic field, the expressions of kinetic energy, strain potential energy, imaginary work of external force and electromagnetic force are given, and then the Hamiltonian principle is used.The differential equations of nonaxisymmetric nonlinear magnetoelastic vibration of circular plates with rotating motion in a magnetic field are obtained.Secondly, Bessel function is used as the mode function of circular plate to carry out Galerkin integral, and the ordinary differential equation system expression of transverse vibration under axisymmetric condition is obtained.Finally, for the main resonance, taking the circular plate with the boundary condition of the peripheral clamped branches as an example, the magnetic induction intensity is obtained when the mode function is of the first order.The bifurcation diagram and Poincare map of external excitation amplitude and frequency as control parameters are calculated. The effects of bifurcation parameters on bifurcation and chaos of the system are discussed.The numerical results show that the variation of these control parameters affects the stability of the system. In the process of the bifurcation parameters changing gradually, the system goes through a reciprocating process from chaos to the motion of multiple periods and then to chaos.
【作者单位】：燕山大学河北省重型装备与大型结构力学可靠性重点实验室;
【基金】：国家自然科学基金(11472239) 河北省自然科学基金(A2015203023) 河北省高等学校自然科学研究重点项目(ZD20131055)资助项目
【分类号】：O32

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