Truncated conical shells are essential components of rocket booster nozzles and thrust vector control (TVC) systems for the propulsion of multi-stage launch vehicles. The TVCs assist the ascent of launch vehicles by directing the resultant thrust from the boosters, acting as a follower force that might trigger instability. Previous studies on the instability of aerospace structures have mostly focused on beams, plates, and cylindrical shells. This study analyses a truncated conical shell under a follower force of constant magnitude, considering thickness-wise gradation of material properties employed for thermal management. The governing equations are derived following Hamilton's principle, considering first-order shear deformation theory, and solved using the finite element method. Clamped and free boundaries are assumed at the small and large ends. The influence of mass and stiffness proportional damping is considered. Although strong flutter appears as the dominant instability mode, instances of erratic weak instabilities are also observed for undamped and lightly damped cases. Damping enhances stability, but its effect becomes saturated. The flutter loads are presented for varying non-dimensional parameters, characterizing the shell geometry and material properties.

中文翻译：

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从动力作用下功能梯度锥壳的颤振


截锥形壳是用于推进多级运载火箭的火箭助推器喷嘴和推力矢量控制（TVC）系统的重要组成部分。 TVC 通过引导助推器产生的推力来协助运载火箭上升，充当可能引发不稳定的跟随力。以往对航空航天结构不稳定性的研究主要集中在梁、板和圆柱壳上。本研究分析了在恒定大小的从动力下的截锥形壳，考虑了用于热管理的材料特性的厚度方向梯度。根据哈密顿原理，考虑一阶剪切变形理论，推导出控制方程，并使用有限元方法求解。假定小端和大端处有夹紧边界和自由边界。考虑了质量和刚度比例阻尼的影响。尽管强颤振似乎是主要的不稳定模式，但在无阻尼和轻微阻尼的情况下也观察到不稳定的弱不稳定性的情况。阻尼增强了稳定性，但其效果已饱和。颤振载荷针对不同的无量纲参数而呈现，表征了壳体几何形状和材料特性。