Nonlocal wave propagation analysis of a rotating nanobeam on a Pasternak foundation

Abstract

In this paper, the wave propagation analysis of a cantilever rotating nanobeam modeled as a thin beam based on the Euler–Bernoulli theory on a Pasternak foundation has been investigated using the nonlocal theory of elasticity. The governing partial differential equation of motion for a uniform rotating nanobeam is derived using the Hamilton principle considering the nonlocal parameter of small scale effect. The Spectrum and dispersion relations of non-dimensional wave number are obtained analytically. The effect of changes of different parameters including nonlocal scale parameter, non-dimensional rotational speed, non-dimensional rotational wave frequency ratio, and shear stiffness of the Pasternak foundation on the wave dispersion behavior of the non-dimensional wave number and phase and group speeds dispersions for the rotating nanotube have been studied. It is observed that the wave dispersion characteristics of the rotating nanobeam are extremely influenced by rotational speed, wave number, nonlocal length scale parameter, and shear stiffness of the Pasternak foundation. Moreover, the propagated flexural wave has been shown to exhibit non-dispersive behavior at very high rotational speeds.