In this paper, the torsional vibration of cracked nanobeam was studied based on a nonlocal elasticity theory. The location of the crack is simulated by a torsional spring which links segments of nanobeam together. Also, different boundary conditions, including clamped-free, clamped-clamped and clamped-torsional spring, were considered. Furthermore, a detailed parametric study was conducted to investigate the influence of crack location, nonlocal parameter, length of nanobeam, spring constant and end supports on the torsional vibration.

In this article surface effects are considered to study the electromechanical coupling behavior of piezoelectric nanobeams with the non-local Euler-Bernoulli beam theory. The equation of motion for piezoelectric nanobeams with considering both surface effect and nonlocal effect is achieved and exact term for natural frequencies is derived for simply supported conditions. In the following the axial load effect on the natural frequencies piezoelectric nanobeams has been studied.