Modelling of vibrations of rotating nanoscale beams surrounded by a magnetic field and subjected to a harmonic thermal field using a state-space approach

Abstract

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.