Merwan, Behar2026-01-192026-01-192025-01-20https://dspace.univ-tlemcen.dz/handle/112/25588This thesis introduces a novel mathematical formulation to investigate the vibration behavior of rotating smart nanoshafts. The model integrates Euler-Bernoulli beam theory with the nonlocal strain gradient theory and Maxwell's electrostatic equations. The smart nanoshaft structure is composed of a single-walled boron nitride nanotube (SWBNNT), chosen for its exceptional piezoelectric and magnetic properties, which make it highly suitable for rotating components in nanoelectromechanical systems (NEMS). The electro-mechanical equations of motion are derived using Hamilton's principle and solved semi-analytically through Galerkin-based closed-form solutions. Forthermore, the effects of rotating speed, mode number, external voltage, temperature change, geometrical parameters, material length scale, and nonlocal parameters on natural frequencies and critical speed are investigated. This work represents the first comprehensive analysis of these factors under various boundary conditions for rotating smart nanoshafts, offering valuable insights into their vibrational dynamics. The results are contextualized within the existing literature, demonstrating the accuracy and efficiency of the proposed model. This establishes the formulation as a robust numerical tool for analyzing the behavior of rotating nanoscale structures.enGalerkin closed-form solutionSmart nanotubepiezoelectric materialrotating nanotubeCritical speedEuler-Bernoulli beam theory.Thesis