https://doi.org/10.1140/epjp/s13360-021-01257-7
Regular Article
Modelling of vibrations of rotating nanoscale beams surrounded by a magnetic field and subjected to a harmonic thermal field using a state-space approach
1
Department of Mathematics, College of Science and Arts, Jouf University, Al-Qurayyat, Saudi Arabia
2
Department of Mathematics, Faculty of Science, Mansoura University, 35516, Mansoura, Egypt
3
Department of Basic Sciences, University of Engineering and Technology, Peshawar, Pakistan
4
Department of Mathematics, Faculty of Science, Taif University, P.O. Box 11099, 21944, Taif, Saudi Arabia
5
Department of Teacher Training in Electrical Engineering, Renewable Energy Research Centre, Faculty of Technical Education, King Mongkut’s University of Technology North Bangkok, 1518 Pracharat 1 Road, Bangsue, 10800, Bangkok, Thailand
Received:
12
August
2020
Accepted:
20
February
2021
Published online:
1
March
2021
In this study, a mathematical model for rotating thermal nanobeams is presented. A system of equations is derived that describes the thermoelastic behaviour of rotating nanoscale beams. The proposed model is based on Eringen’s nonlocal elasticity theory, Euler–Bernoulli's assumptions, and generalized thermoelasticity with two different phase lags. The nanoscale beam material is completely surrounded by an axial magnetic field and exposed to a time-dependent variable temperature field. The Laplace transform in the state-space approach is employed to solve the problem studied. Because of the difficulty in finding the inversion of the Laplace transforms, it was obtained numerically using one of the techniques based on the technique of the Fourier series expansion. The significance of different parameters such as the rotational angular velocity, nonlocal parameter, temperature change, and magnetic field on the nanobeam response has been investigated. Moreover, the results obtained are verified with the corresponding results from the literature.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021
