Dynamic behavior of thin and thick cracked nanobeams incorporating surface effects

Free transverse vibration of cracked nanobeams is investigated in the presence of the surface effects. Two nanobeam types, thin and thick, are studied using two beam theories, Euler–Bernoulli and Timoshenko. The influences of crack severity and position, surface density, rotary inertia and shear deformation, nanobeam dimension, mode number, satisfying balance condition between the surface layers and the bulk, boundary conditions and satisfying compatibility and boundary conditions with appropriate resultant moment and shear force are studied in details. It is found out that satisfying compatibility and boundary conditions with the resultant moment and shear force in presence of the surface effects and considering surface density neglected in previous work have significant effects on the natural frequencies of cracked nanobeams. In addition, rotary inertia and shear deformation cause a reduction in the crack and surface effects on the natural frequencies.