矩形薄板在面内随机参数激励下的随机稳定性与分岔研究

王洪礼;葛根;许佳

振动与冲击 ›› 2009, Vol. 28 ›› Issue (9) : 91-94,1.

PDF(1600 KB)
PDF(1600 KB)
振动与冲击 ›› 2009, Vol. 28 ›› Issue (9) : 91-94,1.
论文

矩形薄板在面内随机参数激励下的随机稳定性与分岔研究

  • 王洪礼,葛根,许佳
作者信息 +

STOCHASTIC STABILITY AND BIFURCATION FOR A THIN RECTANGULAR PLATE SUBJECT TO IN-PLANE STOCHASTIC PARAMETRICAL EXCITATION5461

  • WangHongli,GeGen,Xujia
Author information +
文章历史 +

摘要

本文根据小挠度薄板的弹性理论建立了矩形薄板的受面内随机激励的振动模型,并用Galerkin变分法将其化简为常微分非线性动力学方程。又利用拟不可积Hamilton平均理论将方程等价为一个一维的Ito随机微分方程,并通过计算系统的最大Lyapunov指数来研究系统的局部随机稳定性,同时利用奇异边界理论研究了模型的全局稳定性,最后通过稳态概率密度函数的形状研究了系统参数对发生的随机Hopf分岔现象的影响,发现随机Hopf分岔在两个关键值附近发生,数值模拟结果验证了理论分析的正确性。

Abstract

One stochastic dynamical model of a thin rectangular plate subject to in-plate stochastic parametrical excitation is proposed based on elastic theory and Galerkin’s approach. At first the model is simplified applying the stochastic average theory of quasi-integral Hamilton system. Secondly, the methods of Lyapunov exponent and boundary classification associated with diffusion process respectively is utilized to analyze the local and global stochastic stability of the trivial solution of system. Finally, it is explored that the stochastic Hopf bifurcation of the model according to the qualitative changes in stationary probability density of system response. It is concluded that the stochastic Hopf bifurcation occurs at two critical parametric values. And the results of numerical simulation support the theoretical analysis.

关键词

矩形薄板 / Galerkin变分法 / 随机稳定性 / 随机Hopf分岔

Key words

thin rectangular plate / Galerkin’s approach / stochastic stability / stochastic Hopf bifurcation

引用本文

导出引用
王洪礼;葛根;许佳. 矩形薄板在面内随机参数激励下的随机稳定性与分岔研究[J]. 振动与冲击, 2009, 28(9): 91-94,1
WangHongli;GeGen;Xujia. STOCHASTIC STABILITY AND BIFURCATION FOR A THIN RECTANGULAR PLATE SUBJECT TO IN-PLANE STOCHASTIC PARAMETRICAL EXCITATION5461[J]. Journal of Vibration and Shock, 2009, 28(9): 91-94,1
中图分类号: O322   

PDF(1600 KB)

2541

Accesses

0

Citation

Detail

段落导航
相关文章

/