Free vibration analysis of multi-cracked nanobeam using nonlocal elasticity theory

The aim of this paper is to study the free lateral vibration of multi-cracked nanobeams, and consequently finding the natural frequencies of the cracked nanobeams using two methods. The model of the beam is Euler-Bernoulli in which shear effect has been neglected. Crack is assumed to divide the beam into two segments and these segments are connected to each other by a linear spring and a rotational spring. The crack induces more flexibility to the beam and reduces the stiffness of the beam and consequently influences the dynamic response and the natural frequencies of the beam. Cases of double-cracked and triple-cracked nanobeams are studied. It is observed that when the number of the cracks are increased, the natural frequencies will be decreased. Nonlocal elasticity theory is exposed to the equation of motion. Nonlocal parameter and number of the cracks affect the natural frequencies of the nanobeams. For the case of cantilever, the results are slightly different in contrast to simply supported and clamped-clamped cases. It has been shown that some frequency modes remain constant when the crack severity increases, because of the location of the crack which is a node for a certain mode of vibration.