Abstract
Nanobeams are extensively used in the arena of modern science and technology. The dynamic model of nanobeam with steps and cracks is formed by the combination of classical beam theory and nonlocal theory of elasticity. Homotopy perturbation method is employed to solve the governing equations for two steps nanobeam. The results of this approximation method are compared with the results of exact solution technique. Our vital concern is to analyse the effect of rotatory inertia on the dynamic behaviour of nanobeam. The effect of crack severity, crack and step position, step height ratio, axial load on the vibration of nanobeam are also studied. The results show that the effect of rotatory inertia is very significant in the nanobeam and its influence increases with the increase of mode of frequency.
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