Eur. Phys. J. Plus (2018) 133: 252
https://doi.org/10.1140/epjp/i2018-12077-y

Regular Article

Wave propagation in viscous-fluid-conveying piezoelectric nanotubes considering surface stress effects and Knudsen number based on nonlocal strain gradient theory

¹ Noise and Vibration Control Research Laboratory, School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran
² State Key Laboratory of Digital Manufacturing Equipment and Technology, School of Mechanical Science and Technology, Huazhong University of Science and Technology, 430074, Wuhan, China

^* e-mail: rtalebi@iust.ac.ir

Received: 12 February 2018
Accepted: 28 May 2018
Published online: 10 July 2018

Abstract

In this paper, size-dependent wave dispersion behavior of smart piezoelectric nanotubes conveying viscous fluid is analyzed considering surface stress effects and slip boundary conditions. The size effects of the nanotube are taken into account by making use of the nonlocal strain gradient theory (NSGT). To take the slip boundary conditions into consideration, the average velocity correction factor is utilized. The Newtonian method, in conjunction with the Rayleigh beam theory, is incorporated within the constitutive stress-strain relations of the surface and bulk of a piezoelectric material to derive the governing equations. The obtained equations involve size-dependent parameters, surface effects, slip boundary conditions, fluid viscosity and piezoelectric voltage. As a consequence, an analytical solution is applied to extract the wave dispersion relation of the nanotube. In addition, the influences of different factors, including nonlocal parameter, length scale parameter, surface effects, piezoelectric voltage, surface elastic modulus and surface residual stress on the wave dispersion characteristics of the piezoelectric nanotube, are examined. The effects of the piezoelectric voltage on the damping ratio of the nanotube are also studied. The obtained results in this paper are expected to be useful for more accurate prediction of the mechanical behaviors as well as of the wave propagation characteristics of viscous-fluid-conveying piezoelectric smart nanotubes. Meanwhile, the results will be helpful for efficient applications of piezoelectric nanotubes designing smart mechanical systems on a nanotechnology basis.