Nonlinear Resonant Motion of Traveling Waves in Rotating Disks

2000 ◽  
Author(s):  
Albert C. J. Luo ◽  
Chin An Tan

Abstract The resonant conditions for traveling waves in rotating disks are derived. The nonlinear resonant spectrum of a rotating disk is computed from the resonant conditions. Such a resonant spectrum is useful for the disk drive industry to determine the range of operational rotation speed. The resonant wave motions for linear and nonlinear, rotating disks are simulated numerically for a 3.5-inch diameter computer memory disk.

Author(s):  
Itsuro Kajiwara ◽  
Naoki Hosoya

This paper proposes a contactless vibration testing system for rotating disks based on an impulse response excited by a laser ablation. High power YAG pulse laser is used in this system for producing an ideal impulse force on structural surface without contact. The contactless vibration testing system is composed of a YAG laser, laser Doppler vibrometer and spectrum analyzer. This system makes it possible to measure vibration characteristics of structures under operation, such as vibration measurement of a rotating disk. The effectiveness of this system is confirmed by experimental and theoretical analyses. In this paper, a platter of hard disk drive is employed as an experimental object. Vibration characteristics of a rotating and non-rotating platter are measured and compared with the results of theoretical analysis.


Geophysics ◽  
1984 ◽  
Vol 49 (7) ◽  
pp. 1105-1114 ◽  
Author(s):  
James D. Klein ◽  
Tom Biegler ◽  
M.D. Horne

A phenomenological laboratory investigation has been conducted of the IP response of pyrite, chalcopyrite, and chalcocite. The technique that was used is standard in electrochemistry and employs rotating disk electrodes. The effect of rotation is to stir the electrolyte and thus to restrict the maximum distance available for diffusion of electroactive aqueous species. For high rotation speed and low excitation frequencies, the mean diffusion length exceeds the thickness of the diffusion layer. The net effect is to reduce the electrode impedance at low frequency. The thickness of the diffusion layer and thus the impedance at low frequency can be controlled by the rotation speed. Measurements using rotating disk electrodes have been conducted in both the time domain and the frequency domain. For both pyrite and chalcopyrite, the results were the same: no dependence on rotation was observed. For frequency domain measurements with chalcocite, a strong dependence on rotation was observed. The interpreted diffusion layer thickness was found to depend on rotation speed to the [Formula: see text] power, in agreement with results predicted by hydrodynamic theory. The results of this study imply that there are two physical processes responsible for electrode polarization in the IP method. For chalcocite and perhaps other related copper sulfide minerals, the probable mechanism is diffusion of copper ions in the groundwater. In case, the phenomenon is correctly described by the Warburg impedance. Chalcocite’s distinctive response is thought to be related to its forming a reversible oxidation‐reduction couple with cupric ions in solution. No other common sulfide mineral forms a reversible couple with its cations in solution. For the other minerals of this study, the lack of dependence on rotation implies that diffusion of active species in the electrolyte is not the controlling process. Possible alternate mechanisms include surface controlled processes such as surface diffusion or adsorption phenomena. Ancillary data obtained during this study indicate the interface impedance of chalcopyrite is proportional to the electrode potential which in turn can be controlled by rotation speed, electrolyte composition, or application of an external dc current or voltage. This implies that the surface concentration of active species is dependent on electrode potential.


2000 ◽  
Author(s):  
Moreshwar Deshpande ◽  
C. D. Mote

Abstract A model for the in-plane oscillations of a thin rotating disk has been derived using a nonlinear strain measure to calculate the disk energy. This accounts for the stiffening of the disk due the radial expansion resulting from its rotation. The corresponding non-dimensionalized natural frequencies are seen to depend only on rotation speed and have been calculated. The radially expanded disk configuration is linearly stable over the range of rotation speeds studied here. The sine and cosine modes for all nodal diameters couple to each other at all nonzero rotation speeds and the strength of this coupling increases with rotation speed. This coupling causes the reported frequencies of the stationary disk to split. The zero, one and two nodal diameter in-plane modes do not have a critical speed corresponding to the vanishing of the backward travelling wave frequency. The use of a linear strain measure in earlier work incorrectly predicts instability of the rotating equilibrium and the existence of critical speeds in these modes.


2020 ◽  
Vol 55 (5-6) ◽  
pp. 159-171
Author(s):  
Hassan Mohamed Abdelalim Abdalla ◽  
Daniele Casagrande ◽  
Luciano Moro

The behavior of thermo-mechanical stresses in functionally graded axisymmetric rotating hollow disks with variable thickness is analyzed. The material is assumed to be functionally graded in the radial direction. First, a two-dimensional axisymmetric model of the functionally graded rotating disk is developed using the finite element method. Exact solutions for stresses are then obtained assuming that the plane theory of elasticity holds. These solutions are in accordance with finite element ones, thus showing the validity of the assumption. Finally, in order to reduce the maximum equivalent stress along the radius, the optimization of the material distribution is addressed. To avoid subsequent finite element simulations in the optimization process, which can be computationally demanding, a nonlinear constrained optimization problem is proposed, for which the solution is obtained numerically by the sequential quadratic programming method, showing prominent results in terms of equivalent stress uniformity.


1994 ◽  
Vol 61 (1) ◽  
pp. 186-191 ◽  
Author(s):  
Kai-Yuan Yeh ◽  
R. P. S. Han

A rotating disk with varying thickness and inhomogeneity, and subjected to a steady, inhomogeneous temperature field is analyzed. To handle the arbitrary profile, the disk is discretized into a series of uniform annular disks possessing constant material properties and then solved by the step-reduction method. Analytic expressions for thermoelastic stresses are given, and based on these results, the formulation is extended to include the calculation of shrink fit, the solving of the inverse problem for equistrength rotating disks, and the computations of plastic stresses and creep at elevated temperatures.


1946 ◽  
Vol 13 (1) ◽  
pp. A45-A52
Author(s):  
A. Stanley Thompson

Abstract A general method was found by which the problem of the rotating disk with any arbitrary profile could be solved, including the effect of plastic flow and of variable temperature, and including the change with temperature of modulus of elasticity, coefficient of thermal expansion, and allowable stress. The solution requires for its application to a specific disk only the elementary arithmetic involved in completion of a tabular form sheet. Two applications of the method are made. For an arbitrary disk profile, an integral equation was found which converges rapidly to the radial stress distribution in a series of successive substitutions. For an arbitrary choice of radial stress, the necessary disk profile can be found in one calculation. Appendix 1 gives an example of the use of the method for the design of a partially plastic disk with a central hole.


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