非线性弹性地基上受简谐激励矩形薄板主共振下的全局分岔  

GLOBAL BIFURCATION OF A THIN RECTANGULAR PLATE WITH A HARMONIC EXCITATION ON A NONLINEAR ELASTIC FOUNDATION

作　　者：俞卫琴[1] 陈芳启[2] 

机构地区：[1]上海工程技术大学基础数学学院,上海201620 [2]南京航空航天大学力学系,南京210016

出　　处：《机械强度》2011年第4期475-482,共8页Journal of Mechanical Strength

基　　金：国家自然科学基金(10972099);天津市自然科学基金重点项目(09JCZDJC26800)资助~~

摘　　要：研究位于非线性弹性地基上受均匀横向简谐激励作用的小挠度矩形薄板动力学模型的全局分岔问题。考虑主共振和1∶1内共振情形。由多尺度法得到平均方程,通过变换转化为近可积哈密顿系统。运用Kovacic-Wiggins全局摄动法,得到哈密顿共振情形下Silnikov型同宿轨和Smale马蹄混沌可能存在的充分条件。数值计算说明混沌存在。Global bifurcation of the small deformation thin rectangular plate on a nonlinear elastic foundation subjected to a harmonic excitation is investigated.The study focuses on primary resonance and 1∶1 internal resonance.Based on the amplitude and phase modulation equations derived by the method of multiple scales,a near integrable two-degree-of-freedom Hamilton system is obtained by a transformation.Employing Kovacic-Wiggins＇ global perturbation technique,a sufficient condition under which Silnikov type homoclinic orbit can exist and the existence of Smale horseshoe chaos are derived under Hamiltonian resonance.Numerical simulations are also given,which imply that chaos exists.

关 键 词：全局分岔 多尺度法 MELNIKOV方法 同宿轨道 混沌 

分 类 号：O322[理学—一般力学与力学基础]