Comparative size-dependent free vibration analysis of boron nitride and silicon carbide nanotubes based on strain gradient Euler–Bernoulli beam theory

Boron nitride nanotubes (BNNTs) and silicon carbide nanotubes (SiCNTs) have distinct mechanical stiffness and thermal stability profiles, making it necessary to consider their unique vibration behavior in the design of frequency-sensitive nanoelectromechanical systems. This study presents a systematic comparative analysis of their free vibration responses using strain gradient Euler–Bernoulli beam theory. An initial value method combined with an approximate transfer matrix approach is employed to compute the natural frequencies over a range of normalized length scale parameters ((Formula presented.)), considering higher-order boundary conditions across four classical support configurations: simply supported, clamped–simply supported, clamped–clamped, and clamped–free. The computational model is validated against benchmark data, demonstrating excellent agreement. Results indicate that BNNTs consistently exhibit approximately 1.5 times higher natural frequencies than SiCNTs under all examined conditions, with frequencies of both materials increasing as (Formula presented.) increases. First-type boundary conditions tend to yield slightly higher frequencies than Second-type ones, especially in higher vibration modes. These findings provide valuable guidance for the design and optimization of nanodevices and underscore the critical influence of higher-order boundary condition types and scale effects on nanoscale vibrational performance.