In view of vast potential applications of the flexible thin rotating disks, the knowledge of their vibration characteristics have been received extensive attention in the past few years. Rotating disks are the principal components in engineering systems such as flywheels, torsional disk dampers, turbine blades, circular saws, hard-disk drives for computers, optical memory disks (CD and DVD) and etc. With the advent of these components, demand to increase their efficiency and to reduce access times for reaching the operating speed has led to progressive increases in the rotational speed of these components. Therefore, vibration analysis for rotating disks has gain higher attention in recent research works. While the main emphasis has always been given to linear and non-linear transverse vibration of the rotating disk. Nevertheless, during recent years it has been realized that in-plane vibration can also play a significant role in the design of rotating disks. Much of the recent interest is due to the important significance for vibration and noise reductions caused by in-plane vibrations in varieties of the practical applications.

An analytical method is developed for the determination of modal vibration characteristics of high speed rotating annular disks. A systematic approach based on established solutions for the linear in-plane free vibrations of the disks which satisfy the displacement and stresses compatibilities is developed. The disk is considered to be a homogeneous, thin and elastic isotropic, and it is rotating at constant angular speed. The developed analytical solution was obtained by implementing the two-dimensional plane stress theory. In this research, fixed-free and free-free boundary conditions for the annular disks are considered, and natural frequencies, as well as mode shapes of the rotating disks, are computed. The mode shapes are represented by eight functions in polar coordinates. The dimensionless natural frequency parameters are depicted for free vibration of the system for a range of dimensionless rotation speed and radius ratios. In addition, the results provide a number of non-dimensional critical speeds. 

The presented results include variations of the geometrical shape of the disk by considering radial and tangential displacement of all points within the disk for different mode shapes. In this research, the main objectives are to provide the analytical solution for the determination of the natural frequencies and present their mode shapes for stresses and displacements of the rotating annular disk. It should be noted that the disk is rotating at a constant angular speed, and no external forces are acting on it. Furthermore, the analysis is conducted for a steady-state rotational disk for the wide range of rotating speed.


In-Plane Vibration Mode Shapes for Rotating Disks: Exact Solution

Division / Sponsors: 
Aerospace, Bioengineering, Applied Mechanics, Design Engineering Division, Advanced Energy Systems, Manufacturing Engineering Division, Noise Control and Acoustics, Nondestructive Evaluation, Diagnosis, and Prognosis (NDPD), Nuclear Engineering Division, Process Industries Division, Fluids Engineering, Heat Transfer, Materials, Microelectromechanical Systems, Safety Engineering and Risk Analysis, Computers & Information in Engineering


Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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