Torsional Vibration of a Nanobeam Under Magnetic Load and Surrounded With Torsional Spring, Based on the Modified Couple Stress Theory Using Power Series Method

This paper is concerned with the torsional vibration of the nanobeam under a longitudinal magnetic field and surrounded by a torsional spring. The small size effect is taken into account by considering the modified couple stress theory of elasticity for continuum mechanics, and the power series method (PSM) is utilized in order to compute the eigenfrequencies of the obtained differential equation. In order to prove the validity of the PSM, the obtained results are satisfactorily compared with those already existing. The influence of several variables of the system, such as magnetic field, couple stress parameter, and torsional spring on the frequency or on the rotation is well examined. Tables with numerical values, computed using the present method demonstrate that the PSM could be a suitable numerical method for analyzing a torsional vibration of a nanobeam, making the present work a benchmark for future works.