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.