Dynamic transverse vibration characteristics and vibro-buckling analyses of axially moving and rotating nanobeams based on nonlocal strain gradient theory

Dynamic transverse vibration characteristics and vibro-buckling analyses of axially moving nanobeam and rotating nanobeam based on nonlocal strain gradient theory are investigated. The axially moving model involves axial velocity in kinetic energy, and the effect of rotating is added as Coriolis acceleration to energy relation for rotating model. Governing equations of two dynamical models are derived by Hamilton’s principle. Meanwhile, corresponding classical and high order non-classical boundaries are also given. Numerical results are obtained by employing Galerkin approach for double simply supported boundary. Results for influence of axial velocity on transverse vibration characteristics illustrate that natural frequencies decrease with increasing axial velocity. However, frequencies of rotating nanobeam model are splitted into forward and backward frequencies with increasing rotating velocity. It is found that forward frequencies increase and backward frequencies decrease with elevated rotating velocity. It is revealed that the nonlocal effect weakens the rigidity and the strain gradient effect strengthens the rigidity. Finally, vibro-buckling analyses of two models, referring to fundamental frequencies vanishing for axially moving model and frequencies corresponding to rotating velocity for rotating model, are shown.