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

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 differential governing equations of porous material structures are derived based on the multiscale asymptotic homogenization method (AHM), and the macroscale and microscale explicit time-domain expressions of structural responses are further established. On this basis, the statistical moments of dynamic responses of porous material structures under non-stationary random excitations can be achieved with the explicit time-domain method (ETDM). The purposed method combines the advantages of AHM for high-efficient explicit formulation of macroscale and microscale dynamic responses of porous material structures and the advantages of ETDM for fast analysis of non-stationary random vibration problems. A numerical example is presented to validate the computational accuracy and efficiency of the present approach for non-stationary random vibration analysis of porous material structures.