Aeroelastic Flutter Mechanisms of a Flexible Disk Rotating in an Enclosed Compressible Fluid

The aeroelastic stability of a thin, flexible disk rotating in an enclosed compressible fluid is investigated analytically through a discretization of the field equations of a rotating Kirchhoff plate coupled to the acoustic oscillations of the surrounding fluid. The discretization procedure exploits Green's theorem and exposes two different gyroscopic effects underpinning the coupled system dynamics: One describes the gyroscopic coupling between the disk and acoustic oscillations, and another arises from the disk rotation. The discretized dynamical system is cast in the compact form of a classical gyroscopic system and acoustic and disk mode coupling rules are derived. For the undamped system, coupled structure-acoustic traveling waves can destabilize through mode coalescence leading to flutter instability. A detailed investigation of the effects of dissipation arising from acoustic and disk damping predicts previously unknown instability mechanisms for this system. The results are expected to be relevant for the design of high speed, lore vibration, low-noise hard disk drives, and optical data storage systems.

[1]  H. Hosaka,et al.  Self-excited vibrations of a flexible disk rotating on an air film above a flat surface , 1992 .

[2]  S. M. Vogel,et al.  Natural Frequencies of Transversely Vibrating Uniform Annular Plates , 1965 .

[3]  Earl H. Dowell,et al.  Flutter of infinitely long plates and shells. I - Plate. , 1966 .

[4]  A. A. Renshaw.  Critical Speed for Floppy Disks , 1998 .

[5]  C. D. Mote,et al.  PREDICTION OF AEROELASTIC FLUTTER IN A HARD DISK DRIVE , 2000 .

[6]  C. D. Mote,et al.  Absence of one nodal diameter critical speed modes in an axisymmetric rotating disk , 1992 .

[7]  A. Love.  A treatise on the mathematical theory of elasticity , 1892 .

[8]  C. D. Mote,et al.  Natural Frequencies Of A Thin Disk, Clamped By Thick Collars With Friction At The Contacting Surfaces, Spinning At High Rotation Speed , 1993 .

[9]  C. D. Mote,et al.  On the Instability Mechanisms of a Disk Rotating Close to a Rigid Surface , 1995 .

[10]  C. D. Mote,et al.  Aerodynamically Excited Vibration And Flutter Of A Thin Disk Rotating At Supercritical Speed , 1993 .

[11]  F. Fahy.  Sound and structural vibration , 1985 .

[12]  Leonard Meirovitch,et al.  A New Method of Solution of the Eigenvalue Problem for Gyroscopic Systems , 1974 .

[13]  Anil K. Bajaj,et al.  Numerical Simulations of Flutter Instability of a Flexible Disk Rotating Close to a Rigid Wall , 2003 .

[14]  Robert G. Parker,et al.  Spatial Discretization of Axially Moving Media Vibration Problems , 2000 .

[15]  C. D. Mote,et al.  Mathematical analysis of stability of a spinning disk under rotating, arbitrarily large damping forces , 1996 .

[16]  Jack Dongarra,et al.  Templates for the Solution of Algebraic Eigenvalue Problems , 2000, Software, environments, tools.

[17]  Morten Hartvig Hansen,et al.  ESTIMATION OF NONCONSERVATIVE AERODYNAMIC PRESSURE LEADING TO FLUTTER OF SPINNING DISKS , 2001 .

[18]  Takao Torii,et al.  Self-Excited Oscillations of a Circular Disk Rotating in Air , 1992 .

[19]  Flutter of an Infinitely Long Panel in a Duct , 1995 .

[20]  A. A. Renshaw,et al.  Aerodynamically Excited Vibration Of A Rotating Disk , 1994 .

[21]  U. S. Shirahatti,et al.  A Technique for the Modal Analysis of Sound-Structure Interaction Problems , 1994 .

[22]  E. Dowell,et al.  Acoustoelasticity - General theory, acoustic natural modes and forced response to sinusoidal excitation, including comparisons with experiment , 1977 .