Nonlinear Vibration of Rotating Thin Disks

2000 ◽  
Vol 122 (4) ◽  
pp. 376-383 ◽  
Author(s):  
Albert C. J. Luo ◽  
C. D. Mote,
Keyword(s):  
Nonlinear Vibration ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Nonlinear Effects ◽  
Linear Vibration ◽  
Rotating Disks ◽  
Nodal Diameter ◽  
Von Karman ◽  
Thin Disks ◽  
Von Kármán

The response and natural frequencies for the linear and nonlinear vibrations of rotating disks are given analytically through the new plate theory proposed by Luo in 1999. The results for the nonlinear vibration can reduce to the ones for the linear vibration when the nonlinear effects vanish and for the von Karman model when the nonlinear effects are modified. They are applicable to disks experiencing large-amplitude displacement or initial flatness and waviness. The natural frequencies for symmetric and asymmetric responses of a 3.5-inch diameter computer memory disk as an example are predicted through the linear theory, the von Karman theory and the new plate theory. The hardening of rotating disks occurs when nodal-diameter numbers are small and the softening of rotating disks occurs when nodal-diameter numbers become larger. The critical speeds of the softening disks decrease with increasing deflection amplitudes. [S0739-3717(00)02004-3]

An Analytical Solution for the Nonlinear Vibration of Rotating, Thin Disks

1999 ◽  
Author(s):  
Albert C. J. Luo ◽  
C. D. Mote
Keyword(s):  
Nonlinear Vibration ◽  
Nonlinear Vibrations ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Nonlinear Effects ◽  
Computer Memory ◽  
Linear Vibration ◽  
Rotating Disks ◽  
Nodal Diameter ◽  
Thin Disks

Abstract The response, natural frequencies for the linear and nonlinear vibrations of rotating disks are given analytically through the Luo and Mote’s plate theory of 1998. The results for the nonlinear vibration can reduce to the ones for the linear vibration when the nonlinear effects vanish, and they are applicable to disks experiencing large-amplitude displacement or initial flatness and waviness. The natural frequencies for symmetric and asymmetric responses of a 3.5-inch diameter computer memory disk as an example are predicted through the linear theory, the von Karman theory and the new plate theory. The hardening of rotating disks occurs when nodal-diameter numbers are small and the softening of rotating disks occurs when nodal-diameter numbers becomes larger. The critical speeds of softening disks decrease with increasing deflection amplitudes.

Thermal Effects on the Natural Frequency of Nonlinear, Co-Rotating Disks

2005 ◽  
Author(s):  
Albert C. J. Luo ◽  
Nader Saniei ◽  
William Ray Harp
Keyword(s):  
Natural Frequency ◽  
Thermal Effects ◽  
Natural Frequencies ◽  
Computer Memory ◽  
Uniform Temperature ◽  
Rotating Disks ◽  
Nonlinear Free Vibration ◽  
Nodal Diameter ◽  
Disk Rotation ◽  
Asymmetric Responses

Thermal effects on the natural frequency for the nonlinear free vibration of co-rotating disks are investigated for non-uniform temperature distributions relative to airflow induced by disk rotation. The natural frequencies for symmetric and asymmetric responses of a 3.5 inch diameter computer memory disk are calculated. When the disk is heated, its stiffness becomes larger for the two lowest nodal diameter numbers and smaller for the other nodal diameter numbers. It implies that the vibration of heated, rotating disks for the higher nodal diameter numbers may be induced more easily than the cooled one.

NONLINEAR BENDING ANALYSIS OF FUNCTIONALLY GRADED PLATES UNDER PRESSURE LOADS USING A FOUR VARIABLE REFINED PLATE THEORY

2014 ◽  
Vol 11 (04) ◽  
pp. 1350062 ◽  
Author(s):  
MOHAMED ATIF BENATTA ◽  
ABDELHAKIM KACI ◽  
ABDELOUAHED TOUNSI ◽  
MOHAMMED SID AHMED HOUARI ◽  
KARIMA BAKHTI ◽  
...  
Keyword(s):  
Shear Stress ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Plate Theory ◽  
Functionally Graded ◽  
Shear Stresses ◽  
Functionally Graded Plates ◽  
Refined Plate Theory ◽  
Von Karman ◽  
Von Kármán

The novelty of this paper is the use of four variable refined plate theory for nonlinear analysis of plates made of functionally graded materials. The plates are subjected to pressure loading and their geometric nonlinearity is introduced in the strain–displacement equations based on Von–Karman assumptions. Unlike any other theory, the theory presented gives rise to only four governing equations. Number of unknown functions involved is only four, as against five in case of simple shear deformation theories of Mindlin and Reissner (first shear deformation theory). The plate properties are assumed to be varied through the thickness following a simple power law distribution in terms of volume fraction of material constituents. The theory presented is variationally consistent, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. The fundamental equations for functionally graded plates are obtained using the Von–Karman theory for large deflection and the solution is obtained by minimization of the total potential energy. Numerical results for functionally graded plates are given in dimensionless graphical forms; and the effects of material properties on deflections and stresses are determined. The results obtained for plate with various thickness ratios using the theory are not only substantially more accurate than those obtained using the CPT, but are almost comparable to those obtained using higher order theories having more number of unknown functions.

scholarly journals Nonlinear Donati compatibility conditions for the nonlinear Kirchhoff–von Kármán–Love plate theory

2013 ◽  
Vol 351 (9-10) ◽  
pp. 405-409 ◽  
Author(s):  
Philippe G. Ciarlet ◽  
Giuseppe Geymonat ◽  
Françoise Krasucki
Keyword(s):  
Plate Theory ◽  
Compatibility Conditions ◽  
Von Karman ◽  
Von Kármán

Maximizing the Natural Frequencies and Transverse Stiffness of Centrally damped, Circular Disks by Thickening the Clamped Part of the Disk

1999 ◽  
Vol 66 (4) ◽  
pp. 1017-1021 ◽  
Author(s):  
A. A. Renshaw
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Vibration Modes ◽  
Rotating Disks ◽  
Design Study ◽  
Nodal Diameter ◽  
Transverse Stiffness ◽  
Vibration Data ◽  
Two Alternatives ◽  
Circular Disks

The natural frequencies and transverse stiffness of centrally damped, circular disks are computed taking into account the flexibility of the central clamp and the thickness of the damped part of the disk. When compared to experimental vibration data, these predictions are more accurate than the traditional, perfect clamping predictions, particularly, for zero and one-nodal-diameter vibration modes. The reduction in natural frequency or transverse stiffness caused by clamping flexibility can be mitigated either by increasing the clamping stiffness or by increasing the hub thickness, defined here as the thickness of the disk sandwiched by the central clamp. A design study of these two alternatives for both stationary and rotating disks shows that increasing the hub thickness is often a more attractive design alternative.

On Large Deflection of Symmetric Composite Plates under Static Loading

1986 ◽  
Vol 200 (1) ◽  
pp. 13-19 ◽  
Author(s):  
M Gorji
Keyword(s):  
Shear Deformation ◽  
Plate Theory ◽  
Lateral Displacement ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Classical Plate Theory ◽  
Maximum Displacement ◽  
Von Karman ◽  
Non Linear ◽  
Von Kármán

The effect of transverse shear deformation on bending of elastic symmetric laminated composite plates undergoing large deformation (in the Von Karman sense) is considered in the present paper. The non-linear terms of the lateral displacement are considered as an additional set of lateral loads acting on the plate. The solution of a Von Karman type plate is therefore reduced to that of an equivalent plate with small displacements. This method offers an alternative technique for obtaining non-linear solutions to plate problems. The solutions of a number of example problems indicate that the non-linear shear deformation theory results, as expected, in higher values of the lateral displacement than the non-linear solutions from the classical plate theory. The difference in the values of the maximum displacement from both solutions, however, remains essentially constant beyond a certain value of the load. It is also noted that the linear and non-linear solutions deviate at a low value of w/h (w = maximum lateral displacement, h = thickness). Consequently, the extent of w/h within which the small deflection theory is applicable to composite plates is much lower than the value of 0.4 typically used for isotropic plates and depends, in general, upon lamination geometry and the degree of anisotropy.

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