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<p>This paper investigates the stochastic vibration of thermo-piezoelectric fluid-conveying single-walled carbon nanotubes (SWCNTs), incorporating the effects of the Knudsen number and surface characteristics. The Galerkin finite element method, based on nonlocal elasticity theory, is employed to account for variations in the small-scale parameter. Probabilistic characteristics are evaluated using Monte Carlo simulations coupled with the Newmark integration scheme, based on the standard deviation of dynamic displacements. The proposed methodology is validated through comparison with the Eringen-type nonlocal elasticity solution, demonstrating excellent agreement. Furthermore, the effects of load variability and nonlocal parameters on the dynamic behavior of SWCNTs under various boundary conditions are systematically analyzed. Results show that random load disturbances significantly impact the dynamic response, with displacement scattering exceeding predictions based solely on load deviations. The Knudsen number affects complex wave frequencies across both low and high wave numbers, whereas small-scale effects become dominant at higher ranges. Numerical results further illustrate the influence of system parameters on the fluid–structure interaction behavior of the nanotubes.</p>

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Stochastic nonlocal vibrations in fractional thermo-piezoelectric fluid-conveying carbon nanotubes

  • 期刊论文

  • 发表日期：

    2026年3月24日

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  • Rajendran Selvamani,
  • Thangamuni Prabhakaran,
  • Mawaheb Al-Dossari,
  • N. S. Abd EL-Gawaad,
  • M. Ijaz Khan

摘要

This paper investigates the stochastic vibration of thermo-piezoelectric fluid-conveying single-walled carbon nanotubes (SWCNTs), incorporating the effects of the Knudsen number and surface characteristics. The Galerkin finite element method, based on nonlocal elasticity theory, is employed to account for variations in the small-scale parameter. Probabilistic characteristics are evaluated using Monte Carlo simulations coupled with the Newmark integration scheme, based on the standard deviation of dynamic displacements. The proposed methodology is validated through comparison with the Eringen-type nonlocal elasticity solution, demonstrating excellent agreement. Furthermore, the effects of load variability and nonlocal parameters on the dynamic behavior of SWCNTs under various boundary conditions are systematically analyzed. Results show that random load disturbances significantly impact the dynamic response, with displacement scattering exceeding predictions based solely on load deviations. The Knudsen number affects complex wave frequencies across both low and high wave numbers, whereas small-scale effects become dominant at higher ranges. Numerical results further illustrate the influence of system parameters on the fluid–structure interaction behavior of the nanotubes.