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Abstract: In this Letter, the effects of the viscous fluid on the propagation characteristics of elastic waves in carbon nanotubes are studied. Based on the nonlocal continuum theory, the small scales effects are also considered. The equations of wave motion are derived and the dispersion relation is presented. Numerical simulations are performed with the consideration of different scale coefficients to discuss the influence of the viscous fluid. From the results, it can be observed that the dispersion relation can be changed by the fluid viscosity obviously. Moreover, due to the fluid viscosity, the wave frequency will be reduced to a low region and the elastic wave behaviors can be significantly influenced by the viscous fluid velocity. [Copyright &y& Elsevier]

Abstract: In this paper, the propagation characteristics of the elastic wave in fluid-conveying double-walled carbon nanotubes are investigated. The nonlocal continuum theory is applied to discuss the dispersion relation with small scale effects. The interaction of the double tubes is considered with the van der Waals interaction pressure and the equation of the flexural wave for the double-walled Euler–Bernoulli beam model is derived. The properties of the frequency and the amplitude ratio are proposed with different wave numbers and fluid velocities. From this work, it can be observed that the small scale effects should be considered in the investigation of the elastic wave propagation in fluid-conveying double-walled nanotubes. [Copyright &y& Elsevier]

Abstract: Variational principles are derived for multi-walled carbon nanotubes undergoing buckling using the semi-inverse method. Derivations are based on the continuum modelling of nanotubes taking into account small scale effects via the nonlocal theory of elasticity. Natural and geometric boundary conditions for multi-walled nanotubes are derived which leads to a set of coupled boundary conditions. [Copyright &y& Elsevier]