基于积水随机分布模型的蜂窝夹芯板湿热振动特性

Hygrothermal vibration characteristics of honeycomb sandwich panels based on a random water-ingress distribution model

  • 摘要: 针对民用飞机蜂窝夹芯结构积水空间分布不确定以及湿热、高低温循环作用下动力响应难以表征的问题,建立含积水蜂窝夹芯板湿—热—力耦合分析模型。基于Python对ABAQUS进行二次开发,采用蒙特卡洛随机抽样构建10%~40%积水体积占比下的随机积水模型,并在自由边界条件下开展模态分析;结合完整板和20%积水板的温度及高低温循环模态试验,对有限元模型进行验证。进一步依据20%积水循环试验的一阶固有频率反演等效刚度保持系数,通过弹性模量和剪切模量折减将循环次数引入有限元模型,并对不同积水状态下的循环动力响应进行数值预测。结果表明:每种积水工况建立的100个随机模型,其前三阶累计平均频率在样本量达到20后趋于稳定;随机模型与均质模型的前三阶平均固有频率相对差异为0.28%~0.84%,在300 K、20%积水工况下二者的平均相对误差分别为6.59%和7.10%,随机模型可进一步表征积水空间非均匀性引起的频率离散性;当积水体积占比由10%增加至40%时,随机模型的一、二、三阶固有频率分别下降9.99%、6.53%和5.65%;温度由300 K升至350 K时,20%积水试件一阶固有频率下降6.46%;高低温循环次数超过100次后,结构固有频率下降幅度明显增大,经历200次循环后,20%积水试件前三阶固有频率分别下降16.68%、18.82%和21.18%。在不同积水状态等效性能折减规律的假设下,数值预测表明初始积水量增加会加剧循环后的频率衰减。研究结果可为航空蜂窝夹芯结构的动力性能评估与损伤决策提供理论依据。

     

    Abstract: To characterize the dynamic response of aircraft honeycomb sandwich structures subjected to spatially nonuniform water ingress, hygrothermal conditions, and high–low-temperature cycling, a hygro-thermo-mechanical model of water-ingressed honeycomb sandwich panels was developed. A Python-based secondary development of ABAQUS was implemented, and Monte Carlo sampling without replacement was employed to generate random water-ingress models with water-volume fractions ranging from 10% to 40%. Modal analyses were performed under free–free boundary conditions, and the finite-element model was evaluated using modal tests on intact and specimens with a water-volume fraction of 20% under different temperatures and cycle numbers. An equivalent stiffness retention coefficient was further identified from the first natural frequency measured in the 20% water-ingress cycling test. The cycle number was introduced into the finite-element model by reducing the elastic and shear moduli, and the cyclic responses at different initial water-volume fractions were subsequently predicted. The results showed that, for the 100 random realizations generated at each water-volume fraction, the cumulative means of the first three natural frequencies became stable when the sample size reached 20. The relative differences between the random and homogenized models ranged from 0.28% to 0.84%. At 300 K and a water-volume fraction of 20%, the average relative errors of the first three natural frequencies were 6.59% and 7.10% for the random and homogenized models, respectively. The main advantage of the random model was its capability to characterize the frequency variability induced by spatially nonuniform water ingress. When the water-volume fraction increased from 10% to 40%, the first three natural frequencies of the random model decreased by 9.99%, 6.53%, and 5.65%, respectively. When the temperature increased from 300 K to 350 K, the first natural frequency of the specimen with 20% water ingress decreased by 6.46%. The frequency reduction became more pronounced after 100 high–low-temperature cycles, and after 200 cycles, the first three natural frequencies of the 20% water-ingress specimen decreased by 16.68%, 18.82%, and 21.18%, respectively. Under the assumption that different initial water-volume fractions share the same equivalent stiffness-reduction law, the numerical predictions indicated that a higher initial water-volume fraction intensified the cyclic frequency reduction. The findings provide a theoretical basis for dynamic performance evaluation and damage management decision-making of aeronautical honeycomb sandwich structures.

     

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