载流圆板在磁场中的随机稳定性分析
发布时间：2018-08-28 15:22
【摘要】：本文根据大挠度板壳力学基础理论和电磁弹性力学理论,建立了载流圆板的非线性磁弹性随机振动力学模型,采用伽辽金变分法将其变换成非线性常微分动力学方程.通过拟不可积哈密顿系统的平均理论将该方程等价为一个一维伊藤随机微分方程.通过计算该方程的最大Lyapunov指数判断该系统的局部随机稳定性,并进一步采用基于随机扩散过程的奇异边界理论判断该系统的全局稳定性.最后通过讨论该系统的稳态概率密度函数图的形状变化讨论了该动力系统的随机Hopf分岔的变化规律,并采用数值模拟对理论分析进行了验证.
[Abstract]:Based on the basic theory of large deflection plate and shell mechanics and the theory of electromagnetic elasticity, a nonlinear magnetoelastic random vibration dynamic model of a circular plate carrying current is established. The Galerkin variational method is used to transform the model into a nonlinear ordinary differential dynamic equation. By means of the averaging theory of the quasi-integrable Hamiltonian system, the equation is equivalent to a one-dimensional Ito stochastic differential equation. The local stochastic stability of the system is determined by calculating the largest Lyapunov exponent of the equation, and the global stability of the system is further determined by the singular boundary theory based on the stochastic diffusion process. Finally, the variation of random Hopf bifurcation of the dynamic system is discussed by discussing the shape change of the steady-state probability density function graph of the system, and the theoretical analysis is verified by numerical simulation.
【作者单位】： 燕山大学建筑工程与力学学院;中国科学院力学研究所国家非线性力学重点实验室(LNM);燕山大学理学院;
【基金】：国家自然科学基金(51174175) 河北省自然科学基金(A2012203140)
【分类号】：O327;O241.8
本文编号：2209803
[Abstract]:Based on the basic theory of large deflection plate and shell mechanics and the theory of electromagnetic elasticity, a nonlinear magnetoelastic random vibration dynamic model of a circular plate carrying current is established. The Galerkin variational method is used to transform the model into a nonlinear ordinary differential dynamic equation. By means of the averaging theory of the quasi-integrable Hamiltonian system, the equation is equivalent to a one-dimensional Ito stochastic differential equation. The local stochastic stability of the system is determined by calculating the largest Lyapunov exponent of the equation, and the global stability of the system is further determined by the singular boundary theory based on the stochastic diffusion process. Finally, the variation of random Hopf bifurcation of the dynamic system is discussed by discussing the shape change of the steady-state probability density function graph of the system, and the theoretical analysis is verified by numerical simulation.
【作者单位】： 燕山大学建筑工程与力学学院;中国科学院力学研究所国家非线性力学重点实验室(LNM);燕山大学理学院;
【基金】：国家自然科学基金(51174175) 河北省自然科学基金(A2012203140)
【分类号】：O327;O241.8
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