中文摘要：

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。

英文摘要：

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.