Free vibration analysis of SiCNTs based on strain gradient beam theory

Strain gradient beam theory has been extensively applied to micro- and nanoscale structures, but it has not been applied to the vibrational analysis of single-walled silicon carbide nanotubes (SiCNTs). This study presents a strain gradient Euler–Bernoulli beam formulation for the investigation of free vibration in SiCNTs under various boundary conditions. The resulting sixth-order differential equations are solved via the initial value method combined with an approximate transfer matrix approach to ensure numerical stability and efficiency. Convergence studies are conducted, and the results are validated against established benchmarks. A detailed parametric analysis reveals the significant influence of the strain gradient parameter on natural frequencies, underscoring the importance of higher-order elasticity in capturing nanoscale dynamic behavior. The proposed model offers a robust computational framework for vibration analysis at the nanoscale and provides practical insights for the design and optimization of nanoelectromechanical systems.