EFFECT OF AIR-MEMBRANE INTERACTION ON DYNAMIC PROPERTIES OF AN INFLATED MEMBRANE TUBE
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摘要: 充气薄膜管属于柔性结构，荷载作用下产生的变形，会引起其内压改变，进而导致外围薄膜刚度的变化，对其变形产生重要影响，表现出内充气体压力与外围薄膜变形相互耦合的特点。该文采用有限元方法分析气-膜耦合作用对充气薄膜管动力特性的影响及其随影响因素的变化规律。通过将内充气体看作小扰动线性势流以考虑气-膜耦合作用以及内充气体附加质量的影响；通过建立内充气体的三种等效模型，分别将内充气体作用等效为外围薄膜静力边界条件、考虑内充气体附加质量影响的静力边界条件以及小扰动线性势流体，并将其相应的有限元分析结果进行对比，研究气-膜耦合作用和内充气体附加质量对充气薄膜管自振特性的影响及其随初始内压、长细比、膜厚以及端部约束类型的变化规律。研究结果表明：气-膜耦合作用以及内充气体的附加质量对低阶自振模态没有明显影响；气-膜耦合作用对自振频率有较显著的影响作用，而内充气体附加质量的影响则较小；随初始内压和长细比的增加，气-膜耦合作用对频率的影响体现出因阶次不同而不同的变化规律；气-膜耦合作用对频率的影响随膜厚的增加而降低，随约束程度的减弱而增强。该文的研究成果揭示了气-膜耦合作用对充气薄膜管自振特性的影响规律，有助于深入认识充气薄膜管的动力行为，确保其设计计算的合理性和可靠性。Abstract: An inflated membrane tube is a kind of flexible structure. Its deformation will result in a change in the inner pressure and then affect the stiffness and deformation of the enveloping membrane. This phenomenon reflects the interaction between the pressure of inner air and the deformation of enveloping membrane. The authors, using the finite element method, analyze the effect of air-membrane interaction on the dynamic properties of an inflated membrane tube and its variation with influencing factors. The inner air is treated as a kind of linear potential fluid to consider the effects of air-membrane interaction and added mass of the inner air. Three finite element models of the inflated membrane tube are developed with different methods to treat the inner air, i.e., the inner air is treated respectively as the static boundary conditions of the enveloping membrane, the static boundary conditions plus the added mass, and a kind of linear potential fluid. The numerical results obtained from these three models are compared to study the influences of air-membrane interaction and added mass on dynamic properties of the tube and their variations with the initial inner pressure, slenderness ratio, membrane thickness and constraint type. The comparisons indicate that air-membrane interaction and added mass of the inner air have little influence on the low-order modal shapes; air-membrane interaction plays a significant role in the natural frequencies while the added mass of inner air has a very small effect; with an increase in the initial inner pressure and slenderness ratio, the influence of air-membrane interaction on natural frequencies varies differently for different orders; The influence of air-membrane interaction on natural frequencies decreases with the increasing membrane thickness and is gradually strengthened when the end constraints are weakened. The present research reveals the dynamic effect of air-membrane interaction and is helpful to the understanding of the dynamic behavior of inflated membrane tubes for their rational and reliable design.
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图 8 不同长细比情况下对应弯曲模态的频率比值
Figure 8. Ratios of frequencies corresponding to the bending mode shape for different slenderness ratios
材料 厚度
h/mm密度
ρ/(kg·m−3)弹性模量
E/MPa泊松比 体积模量
κ/MPaKapton膜 0.075 1500 3500 0.35 − 铝材 4 2700 72000 0.30 − 空气 − 1.29 − − 0.101 
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参数 数值 参数 数值 膜厚h/m 5.1×10−5 泊松比ν 0.34 弹性模量E/MPa 2.551×103 长度L/m 1.2065 内压P0/kPa 12.065 密度ρ/(kg/m3) 1420 半径r/m 0.0381 − −
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表 5 内充气体的等效模型
Table 5. Equivalent models of the inner air
模型 描述 M1 将内充气体等效为外围薄膜的静力边界条件(即将内充气压以外荷载的形式沿其法线法向施加在外围薄膜上)，不能考虑气-膜耦合作用以及内充气体附加质量的影响。外围薄膜的有限元模型见第2节。 M2 将内充气体等效为外围薄膜的静力边界条件，并通过修正薄膜密度的方法同时考虑内充气体附加质量的影响。外围薄膜的有限元模型见第2节。 M3 即本文建立的有限元模型(详见第2节)，将内充气体看作小扰动线性势流，同时考虑了气-膜耦合作用和内充气体附加质量的影响。外围薄膜和内充气体的有限元模型见第2节。
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表 6 影响因素及其他参数取值
Table 6. Values of the influencing factors and other parameters
影响因素 影响因素取值 其他参数取值 初始内压
P0/kPa2、4、6、8、10、12 r=50 mm、λ=7、
F-F、h=0.075 mm长细比λ 6、8、10、12、14 r=50 mm、P0=4 kPa、
F-F、h=0.075 mm膜厚h/mm 0.025、0.050、0.075、0.100 r=50 mm、P0=4 kPa、
λ=7、F-F端部约束 两端固定(F-F)、两端简支(S-S)、
一端固定一端简支(F-S)r=50 mm、P0=6 kPa、
λ=7、h=0.075 mm注：r为充气薄膜管半径。
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表 7 不同初始内压情况下的前5阶自振模态
Table 7. The first five mode shapes for different initial internal pressures
阶数 初始内压P0/kPa 2 4 6 8 10 12 1 
2 
3 
4 
5 
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表 8 不同长细比情况下前5阶自振模态
Table 8. The first five mode shapes for different slenderness ratios
阶数 长细比λ 6 8 10 12 14 1 
2 
3 
4 
5 
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表 9 不同膜厚情况下前5阶自振模态
Table 9. The first five modal shapes for different membrane thickness
阶数 膜厚h/mm 0.025 0.050 0.075 0.100 1 
2 
3 
4 
5 
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表 10 不同端部约束情况下前5阶自振模态
Table 10. The first five modal shapes for different end constraints
阶次 约束 两端固定 一固一简 两端简支 1 
2 
3 
4 
5 
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