环形天线结构的复杂动力学研究

部分改进高维系统的广义Melnikov方法研究含参非线性动力系统的混沌问题，并应用于研究环形天线结构的混沌运动等复杂非线性动力学行为.通过定义恰当的横截面,发展适用于研究五维含参非线性动力系统的Melnikov方法,获得系统发生Smale马蹄意义下混沌运动区域及判定定理.将所得理论结果应用于研究面内激励与横向激励共同作用下环形天线结构的混沌运动，得到系统发生混沌运动的不稳定区域及相应的参数控制条件.探讨阻尼系数、参数激励对系统动力学行为的影响，并利用数值模拟方法给出其相图构型，验证理论结果的正确性.

RESEARCH ON COMPLEX DYNAMICS OF A CIRCULAR ANTENNA STRUCTURE

Partial improved high-dimensional generalized Melnikov method is developed to study chaotic motions of a nonlinear dynamical system, and applied to investigate complex nonlinear dynamical behaviors ,i. e. , chaotic motions of a circular antenna structure. By defining appropriate cross-sections, the Melnikov function is developed for studying five dimensional parametric autonomous nonlinear dynamical systems, with the region of multipulse chaotic motion in the sense of Smale horseshoe and the judgement theorem being obtained. The theoretical results are applied to study chaotic motion of the circular antenna structure under combined in-plane excitation and transverse excitation. The unstable region of the system with multipulse chaotic vibration and the corresponding parameter conditions are derived. The influence of damping and parameter excitation coefficients on the dynamic behavior of the system are discussed. Phase diagrams are given by numerical simulation to verify the theoretical results.