Sound wave propagation in single-walled carbon nanotubes using nonlocal elasticity

Based on the Bernoulli–Euler and Timoshenko beam theories, a single-elastic beam model using nonlocal elasticity is developed for the wave propagation in carbon nanotubes (CNTs). The small-scale effect is taken into consideration in the present theory. Frequency equations and modal shape functions of Timoshenko beams structures with some typical boundary conditions are also derived from nonlocal elasticity. In addition, the applicability of the two beam models is explored by numerical simulations. The research work reveals the significance of the small-scale effect on wave propagation in single-walled CNTs.