Free transverse vibrations of cracked nanobeams using a nonlocal elasticity model

Abstract

In this paper, flexural vibrations of cracked micro- and nanobeams are studied. The model is based on the theory of nonlocal elasticity applied to Euler–Bernouilli beams. The cracked-beam model is established using a proper modification of the classical cracked-beam theory consisting of dividing the cracked element into two segments connected by a rotational spring located at the cracked section. This model promotes a discontinuity in bending slope, which is proportional to the second derivative of the displacements. Frequency equations of cracked nanobeams with some typical boundary conditions are derived and the natural frequencies for different crack positions, crack lengths, and nonlocal length parameters are calculated. The results are compared with those corresponding to the classical local model, emphasizing the differences occurring when the nonlocal effects are significant.