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Distributed microscopic actuation analysis of paraboloidal membrane shells of different geometric parameters

机译：不同几何参数抛物面膜壳的分布式微观驱动分析

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摘要

Paraboloidal membrane shells of revolution are commonly used as key components for advanced aerospace structures and aviation mechanical systems. Due to their high flexibility and low damping property, active vibration control is of significant importance for these in-orbit membrane structures. To explore the dynamic control behavior of space flexible paraboloidal membrane shells, precision distributed actuation and control effectiveness of free-floating paraboloidal membrane shells with piezoelectric actuators are investigated. Governing equations of the shell structronic system are presented first. Then, distributed control forces and control actions are formulated. A transverse mode shape function of the paraboloidal shell based on the membrane approximation theory and specified boundary condition is assumed in the modal control force analysis. The actuator induced modal control forces on the paraboloidal shell are derived. The expressions of microscopic local modal control forces are obtained by shrinking the actuator area into infinitesimal and the four control components are investigated respectively to predict the spatial microscopic actuation behavior. Geometric parameter (height-radius ratio and shell thickness) effects on the modal actuation behavior are explored when evaluating the micro-control efficiency. Four different cases are discussed and the results reveal the fact that shallow (e.g., antennas/reflectors) and deep (e.g., rocket/missile fairing) paraboloidal shells exhibit totally different modal actuation behaviors due to their curvature differences. Analytical results in this paper can serve as guidelines for optimal actuator placement for vibration control of different paraboloidal structures.
机译：旋转抛物面膜壳通常用作高级航空航天结构和航空机械系统的关键组件。由于它们的高柔韧性和低阻尼特性，主动振动控制对于这些在轨膜结构非常重要。为了探索空间柔性抛物面膜壳的动态控制行为，研究了带有压电致动器的自由浮动抛物面膜壳的精确分布致动和控制效果。首先介绍了壳结构系统的控制方程。然后，制定分散的控制力和控制动作。在模态控制力分析中，假定了基于膜近似理论和指定边界条件的抛物面壳的横向模式形状函数。推导了抛物面壳上执行器引起的模态控制力。通过将致动器面积缩小到无穷小，获得微观局部模态控制力的表达式，并分别研究四个控制分量以预测空间微观致动行为。在评估微控制效率时，探讨了几何参数（高半径比和壳体厚度）对模态驱动行为的影响。讨论了四种不同的情况，结果揭示了一个事实，即浅（如天线/反射器）和较深（如火箭/导弹整流罩）的抛物面壳由于其曲率差异而呈现出完全不同的模态驱动行为。本文的分析结果可作为最佳致动器位置的准则，以用于不同抛物面结构的振动控制。

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