Lateral vibrations of a microrotating shaft-disk system subjected to an axial load based on the modified strain gradient theory

In this article, the lateral vibrational behavior of a microrotating shaft-disk system subjected to an axial load is studied based on the modified strain gradient stress theory to capture size dependency. Hamilton's principle is used to derive governing equations of motion of the micro rotating shaft-disk system by calculating the kinetic and potential energies of the system. Then, the governing partial differential equations have been transformed into a set of infinite ordinary differential equations by using the assumed modes approach. By analytical method, the first two natural frequencies and also the instability rotational speed of the system are determined. Finally, the numerical results of the natural frequencies and also the threshold of instability speed of the system are presented with respect to different values of the system parameters such as the material length scale parameters, the axial load, the rotor length, the rotational speed, and also the location of the thin rigid disk on the microrotating shaft. The results show that the material length scale parameters and also the location of the thin rigid disk are extremely effective on the vibrational behavior characteristics of the system.