عنوان مقاله [English]
In this paper, the size-dependent vibration of nanoscale beams with simultaneously longitudinal and rotational motions is analyzed based on Eringen nonlocal theory. Also, for the first time, a parametric study is performed to explain the surface effects, viscoelastic-Pasternak substrates characteristics, thermal loads, geometric properties, symmetric and asymmetric cross-sections, axial and follower loads on the dynamics and stability of the system. First, the dynamic equations of the system are obtained using the Hamilton principle. Then, with the help of the Galerkin discretization method, the natural frequencies of the system are determined. To ensure the accuracy of the proposed model and method, the present study results are compared and validated with those of published articles. Stability maps and Campbell diagrams are drawn for different working conditions. The results showed that increasing the surface elastic modulus and residual stress improves the vibration frequencies and the dynamic instability threshold of the system. It is also found that with increasing system thickness/length, the axial velocity of static instability decreases/increases. In addition, it is observed that in contrast to the nonlocality effects, the system performance improves with increasing the elastic and shear coefficients of the substrate. The results of the present study significantly help designers and engineers control the vibration of bi-gyroscopic nanostructures.