Multiscale Modeling of Elastic Waves in Carbon-Nanotube-Based Composite Membranes

A multiscale model is developed for vertically aligned carbon nanotube (CNT)-based membranes that are made for water purification or gas separation. As a consequence of driving fluids through the membranes, they carry stress waves along the fiber direction. Hence, a continuum mixture theory is established for a representative volume element to characterize guided waves propagating in a periodically CNT-reinforced matrix material. The obtained coupled governing equations for the CNT-based composite are found to retain the integrity of the wave propagation phenomenon in each constituent, while allowing them to coexist under analytically derived multiscale interaction parameters. The influence of the mesoscale characteristics on the continuum behavior of the composite is demonstrated by dispersion curves of harmonic wave propagation. Analytically established continuum mixture theory for the CNT-based composite is strengthened by numerical simulations conducted in COMSOL for visualizing mode shapes and wave propagation patterns.