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摘要:
充气展开自支撑臂是由层合铝膜和离散自支撑壳组成，可在无充气压力下实现对有效载荷的支撑。为提高充气展开自支撑臂振动特性预测精度，首先，基于Timoshenko梁理论和哈密顿原理，推导了自支撑臂振动微分方程，提出了考虑充气压力的预应力和构型变化的梁单元模型。该单元模型考虑了结构自支撑壳的离散分布特性，使建立的质量矩阵更接近自支撑臂结构的真实值。然后，通过实验对该模型进行验证，结果表明本文方法比传统梁单元模型具有更好的精度。最后，分析了充气压力和自支撑壳宽度等参数对自支撑臂结构振动模态的影响规律，结果可为充气展开自支撑臂的设计提供理论参考。
Abstract:The inflatable self-supporting boom, which is made of laminated aluminum film and local discrete self-supporting thin shell, has the ability to support the effective load at zero inner pressure. In order to improve the accuracy predicting the vibration characteristics of the inflatable self-supporting boom, the vibration differential equation of the self-supporting boom was first deduced based on the Timoshenko beam theory and Hamiltonian principle, and a new beam element model considering the prestress and configuration change for inflation pressure was proposed. Moreover, this beam element model also considers the discrete characteristics of the self-supporting shell in self-supporting boom, and the mass matrix established by this model is closer to true value. Then, this beam element model is verified by the vibration test results, and the verified results show that this model has better accuracy than the traditional beam element model. Finally, the influence of the inflatable pressure and the width of self-supporting shell on the vibration characteristics of the self-supporting booms is analyzed. This study would provide a theoretical reference for the design of the inflatable self-supporting boom.
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Key words:
- deployable structure /
- self-supporting /
- inflatable structures /
- prestress /
- vibration mode
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图 3 整体刚度矩阵或质量矩阵的组装方法
Figure 3. Assembly method of global stiffness matrix or mass matrix
图 4 本文方法和ANSYS Beam188的基频求解偏差随长细比的变化曲线
Figure 4. Variation curve of the first natural frequency solving deviation of proposed method and ANSYS Beam188 with slenderness ratios
图 5 自支撑臂固有频率随充气压力的变化曲线
Figure 5. Variation curves of self-supporting boom's natural frequency with internal pressure
图 7 自支撑壳宽度对自支撑臂固有频率的影响曲线
Figure 7. Effect curves of width of self-supporting shell on natural frequency of self-supporting boom
图 8 自支撑壳个数对自支撑臂固有频率的影响曲线
Figure 8. Effect curves of number of self-supporting shell on natural frequency of self-supporting boom
图 9 6个自支撑壳的自支撑臂截面示意图
Figure 9. Schematic of cross-section of self-supporting boom with six self-supporting shells
图 10 自支撑臂固有频率随φ1的变化曲线(φ2=90°)
Figure 10. Variation curves of self-supporting boom's natural frequency with φ1(φ2=90°)
图 11 自支撑臂固有频率随φ2的变化曲线(φ1=0°)
Figure 11. Variation curves of self-supporting boom's natural frequency with φ2(φ1=0°)
表 1 自支撑臂振动模态对比
Table 1. Comparison of self-supporting boom's vibration mode
充气压力/kPa 结构基频/Hz 偏差/% 实验[26] Beam188 本文方法 Beam188与实验偏差 本文方法与实验偏差 0 17.55 20.23 18.38 15.27 4.73 10 17.70 20.64 18.77 16.61 6.05 20 17.70 21.04 19.16 18.87 8.25 30 17.71 21.44 19.53 21.06 10.28 40 17.98 21.82 19.90 21.36 10.68 
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表 2 层合铝膜的材料属性
Table 2. Material properties of laminated aluminum membrane
参数 厚度/mm 弹性模量/GPa 泊松比 密度/(kg·m-3) 数值 0.1 12.36 0.3 1 960
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表 3 自支撑壳的材料属性
Table 3. Material properties of self-supporting shell
参数 宽度/mm 厚度/mm 弹性模量/GPa 泊松比 密度/(kg·m-3) 数值 15 0.2 150 0.3 4 535
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