In this research, we study the effects of small-scale parameter on the static buckling of carbon nanotubes, based on a proposed model using nonlocal theory, energy principles, variational methods and strain gradient approach. Based on this model, we derive all classical and nonlocal boundary conditions as well as governing equations. Therefore, closed-form and exact critical buckling loads of nanobeams with various end conditions are investigated. Moreover, we study the effects of small scales, Pasternak elastic medium, thermal loading and rotary inertia on dynamic buckling of single- and double-walled carbon nanotubes based on nonlocal Euler-Bernoulli and Timoshenko beams and Donnell shell models. In addition, we study nonlinear dynamic pulse buckling of double-walled carbon nanotubes under impact loads. Further, wave propagation analysis of carbon nanotubes are investigated using nonlocal elastic beam and shell models in order to determine the effects of small scales, axial compressive loads, Pasternak elastic medium, thermal loading, rotary inertia and van der Waals forces on single- and double-walled carbon nanotubes. Finally, for validating these numerical results, they are compared with numerical and MD results in the literature and found to be in good agreement with them. These findings are useful in manufacturing the nano-sensors for detecting pathogens in a bio medium. Keywords: Carbon nanotubes, Dynamic buckling, Wave propagation, Nonlocal theory.
