The advanced three-dimensional braided composite structure has excellent integrity, which can effectively avoid the problems of interlayer stress jump and interface debonding that may occur in traditional composite laminated structures. However, most of the existing references on the three-dimensional braided composite structure are fragmented, and there is little research on their vibrations. Taking the cylindrical shell of a rocket as the object and considering the complex flight environment, a general framework for the vibration problems of the three-dimensional braided composite shell is proposed for the first time. The equivalent mechanical parameters of the three-dimensional braided composite material are calculated based on the volume averaging method. Then, the nonlinear dynamic model of the three-dimensional braided composite cylindrical shell is established, and the natural vibration characteristics are analyzed. Under the case of 1:1 internal resonance, the pseudo-arc length continuation method is used to solve the nonlinear resonant responses of this nonlinear system. Finally, we apply the fourth-order Runge-Kutta algorithm to study the chaotic dynamics of the three-dimensional braided composite cylindrical shell model. This framework presented in this paper can be extended to the study of nonlinear vibrations and chaotic dynamics of other three-dimensional braided composite structures.

中文翻译：

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三维编织复合圆柱壳的非线性谐振响应和混沌动力学

先进的三维编织复合材料结构具有优异的整体性，可有效避免传统复合材料层合结构中可能出现的层间应力跳跃和界面脱粘问题。然而，现有关于三维编织复合材料结构的文献大多较为零散，对其振动的研究甚少。以火箭圆柱壳为对象，考虑复杂的飞行环境，首次提出了三维编织复合材料壳振动问题的通用框架。基于体积平均法计算了三维编织复合材料的等效力学参数。然后，建立了三维编织复合材料圆柱壳的非线性动力学模型，并分析了其自振特性。在1:1内谐振情况下，采用伪弧长延拓法求解该非线性系统的非线性谐振响应。最后，应用四阶龙格-库塔算法研究三维编织复合圆柱壳模型的混沌动力学。本文提出的框架可以扩展到其他三维编织复合材料结构的非线性振动和混沌动力学的研究。