多孔结构多尺度随机振动分析的渐近均匀化-时域显式法

An Asymptotic-Homogenization Explicit Time-Domain Method for Random Multiscale Vibration Analysis of Porous Material Structures

由于具有高比强、高比刚度等优点,多孔结构在土木工程、机械工程和航天航空工程等领域得到了广泛应用.在随机动力荷载作用下多孔结构的随机响应分析是值得关注的研究方向之一.采用多尺度渐近均匀化法,推导了周期性多孔结构动力问题的多尺度控制微分方程,并建立了多孔结构宏观和细观动力响应的时域显式表达式.在此基础上,结合结构随机振动时域显式法,实现了非平稳随机激励下多孔结构动力响应统计矩的计算.所提出的渐近均匀化-时域显式法,一方面可以发挥多尺度动力分析渐近均匀化法的计算优势,高效建立多孔结构宏观和细观动力响应的时域显式表达式;另一方面也可以利用随机振动时域显式法的计算特点,快速精确地求解非平稳随机激励下多孔结构的随机振动问题.通过数值算例,验证了所提方法在多孔结构非平稳随机振动问题求解中的计算精度和计算效率.

Porous material structures have been widely used in civil engineering,mechanical engineering,aerospace engineering and other fields due to their high specific strength and specific stiffness.The stochastic response analysis of porous material structures under random excitations deserves more attention.The multiscale governing differential equations for porous material structures were derived based on the multiscale asymptotic-homogenization method(AHM),and the macroscale and microscale explicit time-domain expressions of structural responses were further established.On this basis,the statistical moments of dynamic responses of porous material structures under non-stationary random excitations were achieved with the explicit time-domain method(ETDM).The proposed method combines the advantages of the AHM for high-efficiency explicit formulation of macroscale and microscale dynamic responses of porous material structures and the benefits of the ETDM for fast analysis of non-stationary random vibration problems.A numerical example shows the computation accuracy and efficiency of the presented approach for non-stationary random vibration analysis of porous material structures.