Lateral Vibration of a Micro Overhung Rotor-Disk Subjected to an Axial Load Based on the Modified Strain Gradient Theory

This paper focuses on the size dependency of lateral vibration of a micro overhung rotor-disk system subjected to an axial load based on the modified strain gradient theory. The governing equations of motions as well as the boundary conditions are derived from Hamilton’s principle. The assumed modes approach is employed to transform the governing partial differential equations into a set of infinite ordinary differential equations. The first two natural frequencies and associated instability rotational speeds of the system are analytically determined. The effects of variation in the parameters, such as the rotational speed, material length scale parameters, axial load and rotor length, on the natural frequencies and instability speeds are discussed and presented. The results obtained reveal that each of the material length scale parameters has a significant impact on the vibration response characteristics of the system.