In-Plane Free Vibration and Stability of High Speed Rotating Annular Disks and Rings
Analytical method is presented for the determination of free vibration characteristics of high speed viscoelastic rotating disks. In the development of this analytical solution, two-dimensional elastodynamic theory is employed and the viscoelastic materia
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In-Plane Free Vibration and Stability of High Speed Rotating Annular Disks and Rings Hamid R. Hamidzadeh and Ehsan Sarfaraz
Abstract Analytical method is presented for the determination of free vibration characteristics of high speed viscoelastic rotating disks. In the development of this analytical solution, two-dimensional elastodynamic theory is employed and the viscoelastic material for the medium is allowed by assuming complex elastic moduli. The general governing equations of motion are derived and a solution for a single rotating disk with different boundary conditions is developed for a wide range of rotating speeds and any radius ratios, such as those for solid disks or thin rings. The proposed solution is used to investigate the influences of hysteretic material damping on dimensionless natural frequencies and modal loss factors for the rotating disks. Furthermore, the solution is expanded to consider the effect of adding disk segment with different material on the inner or outer sides of a disk on the natural frequencies and critical speeds of the equivalent single disk. The dimensionless results for these cases are presented for a wide range of rotational speeds. Keywords In-plane free vibration • Plane stress • Annular disk • Rotating disks • Rotating rings • Natural frequency • Modal loss factor • Compound disks • Discontinuous medium • Critical speed
22.1 Introduction Due to immense potential applications of the flexible thin rotating disks, the significance of their vibration characteristics has been emphasized in recent years. Rotating disks are the principal components in various rotating machinery. Their H.R. Hamidzadeh () • E. Sarfaraz Department of Mechanical and Manufacturing Engineering, Tennessee State University, Nashville, TN 37209, USA e-mail: [email protected]; [email protected] J.A.T. Machado et al. (eds.), Discontinuity and Complexity in Nonlinear Physical Systems, Nonlinear Systems and Complexity 6, DOI 10.1007/978-3-319-01411-1__22, © Springer International Publishing Switzerland 2014
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applications can vary from space structures to torsional disk dampers and from turbine rotors to computer storage devices and brake systems. It is known that dynamic response and stability of rotating disk depends on its rotational speed. It should be noted that to design a rotating disk, the knowledge of modal vibrations and critical speeds are essential. Vibration of rotating disk can occur as two types, in-plane and out-of-plane bending vibration. In-plane vibration occurs in the radial direction and can be coupled with the causing torsional vibration. Torsional vibration can occur in the disk surface angular displacement only which can vary with the radius. Out-ofplane bending vibration, the so-called transverse vibration, occurs on the direction occurring perpendicular to the plane of rotation. Depending on the amplitude of vibrations, the established publications have used linear or nonlinear approaches. In the linear methods, the effect
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