Effect of thermal axial load on vibration of cracked single-walled carbon nanotubes modelled as Timoshenko nanobeams using nonlocal theory

Abstract

ABSTRACT This paper investigates free vibration of cracked single-walled carbon nanotubes modelled as Timoshenko nanobeams under axial thermal load. The main objective of this work is a deep, true, and precise formulation to analyse truly the thermal effects on the Timoshenko nanobeam model. Nonlocal elasticity theory is applied to Timoshenko beam model. It is assumed that a crack divides the beam into two segments. The crack is modelled by a torsional spring connecting the beam segments to each other. The thermal load acts as an axial force on the nanobeam. Galerkin’s method is used to solve the partial differential equation of motion. The effect of the crack location, crack severity, thermal load, and nonlocal parameter on the frequencies are examined. As the crack severity increases, the frequencies decrease except the modes in which the crack locates at one of their nodes. All mode frequencies decrease at the high temperatures and increase at the low temperatures. Increasing the nonlocal parameter causes a reduction in the frequencies at any temperature. The nonlocal parameter effect on the frequencies increases at high or elevated temperatures.