Nonlocal Finite Element Modeling of Stochastic Vibrations in Thermo-Piezoelectric Fluid-Conveying Carbon Nanotubes

This study examines the random vibrations of a fluid containing thermopiezoelectric single-walled carbon nanotubes (SWCNTs), taking into account the Knudsen number and surface effects. A variable small-scale parameter is used in the Galerkin finite element method, which is based on nonlocal elasticity theory. The probabilistic response, namely the standard deviation of dynamic displacements, is generated by combining Monte Carlo simulations with the Newmark integration scheme. Good agreement is shown by validation against previous numerical results and Eringen’s nonlocal elasticity model. Under various boundary conditions, the impact of changing load and nonlocal factors on nanotube dynamics is investigated. The response is amplified by random load variations: the displacement dispersion is greater than the variation directly caused by the load. While small-scale effects predominate at higher wave number ranges, the Knudsen number modulates complex wave frequencies at both low and high wave numbers. Fluid flow behavior is also heavily influenced by system parameters.