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

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.

KEYWORDS:

• Free vibration
• cracked
• thermal load
• timoshenko
• nonlocal elasticity

Acknowledgments

The authors are grateful to the University of Salahaddin-Erbil and Iran University of Science and Technology for supporting this work.

Disclosure statement

The authors declare that they have no competing interests.

Data availability statement

There is not any data for this paper.

Additional information

Funding

The authors declare that this paper does not have any funder.

Notes on contributors

Sardar S. Abdullah

Mr. Sardar Saleh Abdullah is a common Ph.D student in/of both Iran University of Science and Technology and University of Salahaddin-Erbil. His filed of investigation is vibration of metal, composite, and nano materials and friction welding.

Shahrokh H. Hashemi

Professor Shahrokh Hosseini Hashemi is professor in Iran university of science and technology and his specialization is vibration, continuum mechanics, and Nano

Nazhad A. Hussein

Nazhad Ahmed Hussein is professor of mechanical Engineering and is head of college of engineering of University of Salahaddin-Erbil whose specialization is vibration of composite and Nano-scale materials.

Reza Nazemnezhad

Dr. Nazemenezhad is lecturer in Damghan University and his specialization is vibration of Nano/micro-scale materials.