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.

Thermal Effects on the Natural Frequency of Rotating Disks Experiencing Large Deflection

2000 ◽  
Author(s):  
Albert C. J. Luo ◽  
Nader Saniei
Keyword(s):  
Natural Frequency ◽  
Thermal Effects ◽  
Large Deflection ◽  
Natural Frequencies ◽  
Computer Memory ◽  
Rotating Disks ◽  
Nonlinear Free Vibration ◽  
Nodal Diameter ◽  
Disk Rotation ◽  
Turbulent Airflow

Abstract Thermal effects on the natural frequency for the nonlinear free vibration of rotating disks are investigated for non-uniform temperature distributions relative to the laminar and turbulent 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.

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.

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.

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]

scholarly journals Theoretical Analysis on the Nonlinear Free Vibration of a Tri-Cross String

2017 ◽  
Vol 2017 ◽  
pp. 1-17
Author(s):  
Bo Pan ◽  
Jingda Tang ◽  
Ryuichi Tarumi ◽  
Fulin Shang ◽  
Yanbo Wang ◽  
...  
Keyword(s):  
Constitutive Equation ◽  
Theoretical Analysis ◽  
Free Vibration ◽  
Natural Frequency ◽  
Analytical Solutions ◽  
Vibration Amplitude ◽  
Natural Frequencies ◽  
Geometrical Nonlinearity ◽  
Governing Equations ◽  
Nonlinear Free Vibration

Here we present a theoretical analysis on the nonlinear free vibration of a tri-cross string system, which is an element of space net-antennas. We derived the governing equations from Hamilton’s principle and obtained a linearized solution by the standard perturbation method. The semi-analytical solutions of the governing equations have not been provided referring to the solution of plate vibrating problem. This analysis revealed that natural frequencies of the tri-cross string depend on the vibration amplitude due to the geometrical nonlinearity in the constitutive equation. The geometric parameters, such as the diameters and the lengths of the constituent strings, also affect the frequency through the nonlinearity of the tri-cross string. The nonlinear natural frequency shows coupled characteristic; that is, the natural frequency of the tri-cross string varies with that of the constituent strings, but the contribution of each constituent string to the natural frequency is in different proportions.

scholarly journals Effects of Elliptical Hole on the Correlation of Natural Frequency with Buckling Load of Basalt Laminates Composite Plates

2020 ◽  
Vol 27 (1) ◽  
pp. 216-225
Author(s):  
Buntheng Chhorn ◽  
WooYoung Jung
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Basalt Fiber ◽  
Orientation Angle ◽  
Elliptical Hole ◽  
Composite Plates ◽  
Buckling Load ◽  
Mode Shapes ◽  
Geometric Ratio

AbstractRecently, basalt fiber reinforced polymer (BFRP) is acknowledged as an outstanding material for the strengthening of existing concrete structure, especially it was being used in marine vehicles, aerospace, automotive and nuclear engineering. Most of the structures were subjected to severe dynamic loading during their service life that may induce vibration of the structures. However, free vibration studied on the basalt laminates composite plates with elliptical cut-out and correlation of natural frequency with buckling load has been very limited. Therefore, effects of the elliptical hole on the natural frequency of basalt/epoxy composite plates was performed in this study. Effects of stacking sequence (θ), elliptical hole inclination (ϕ), hole geometric ratio (a/b) and position of the elliptical hole were considered. The numerical modeling of free vibration analysis was based on the mechanical properties of BFRP obtained from the experiment. The natural frequencies as well as mode shapes of basalt laminates composite plates were numerically determined using the commercial program software (ABAQUS). Then, the determination of correlation of natural frequencies with buckling load was carried out. Results showed that elliptical hole inclination and fiber orientation angle induced the inverse proportion between natural frequency and buckling load.

scholarly journals A Vibration-Based Structural Health Monitoring System for Transmission Line Towers

Electronics ◽  
2019 ◽  
Vol 8 (5) ◽  
pp. 515 ◽  
Author(s):  
Long Zhao ◽  
Xinbo Huang ◽  
Ye Zhang ◽  
Yi Tian ◽  
Yu Zhao
Keyword(s):  
Structural Health Monitoring ◽  
Transmission Line ◽  
Natural Frequency ◽  
Health Monitoring ◽  
Structural Changes ◽  
Natural Frequencies ◽  
Transmission Tower ◽  
Health Monitoring System ◽  
Wind Speeds ◽  
Before And After

In this paper, we present a vibration-based transmission tower structural health monitoring system consisting of two parts that identifies structural changes in towers. An accelerometer group realizes vibration response acquisition at different positions and reduces the risk of data loss by data compression technology. A solar cell provides the power supply. An analyser receives the data from the acceleration sensor group and calculates the transmission tower natural frequencies, and the change in the structure is determined based on natural frequencies. Then, the data are sent to the monitoring center. Furthermore, analysis of the vibration signal and the calculation method of natural frequencies are proposed. The response and natural frequencies of vibration at different wind speeds are analysed by time-domain signal, power spectral density (PSD), root mean square (RMS) and short-time Fouier transform (STFT). The natural frequency identification of the overall structure by the stochastic subspace identification (SSI) method reveals that the number of natural frequencies that can be calculated at different wind speeds is different, but the 2nd, 3rd and 4th natural frequencies can be excited. Finally, the system was tested on a 110 kV experimental transmission line. After 18 h of experimentation, the natural frequency of the overall structure of the transmission tower was determined before and after the tower leg was lifted. The results show that before and after the tower leg is lifted, the natural frequencies of each order exhibit obvious changes, and the differences in the average values can be used as the basis for judging the structural changes of the tower.

Vibration Characteristics of Rotating Thin Disks—Part I: Experimental Results

2012 ◽  
Vol 79 (4) ◽  
Author(s):  
Ramin M. H. Khorasany ◽  
Stanley G. Hutton
Keyword(s):  
Frequency Response ◽  
Natural Frequency ◽  
Linear Theory ◽  
Lateral Force ◽  
Vibration Characteristics ◽  
Experimental Results ◽  
Rotating Disks ◽  
Critical Speeds ◽  
Applied Forces ◽  
Thin Disks

Analysis of the linear vibration characteristics of unconstrained rotating isotropic thin disks leads to the important concept of “critical speeds.” These critical rotational speeds are of interest because they correspond to the situation where a natural frequency of the rotating disk, as measured by a stationary observer, is zero. Such speeds correspond physically to the speeds at which a traveling circumferential wave, of shape corresponding to the mode shape of the natural frequency being considered, travel around the disk in the absence of applied forces. At such speeds, according to linear theory, the blade may respond as a space fixed stationary wave and an applied space fixed dc force may induce a resonant condition in the disk response. Thus, in general, linear theory predicts that for rotating disks, with low levels of damping, large responses may be encountered in the region of the critical speeds due to the application of constant space fixed forces. However, large response invalidates the predictions of linear theory which has neglected the nonlinear stiffness produced by the effect of in-plane forces induced by large displacements. In the present paper, experimental studies were conducted in order to measure the frequency response characteristics of rotating disks both in an idling mode as well as when subjected to a space fixed lateral force. The applied lateral force (produced by an air jet) was such as to produce displacements large enough that non linear geometric effects were important in determining the disk frequencies. Experiments were conducted on thin annular disks of different thickness with the inner radius clamped to the driving arbor and the outer radius free. The results of these experiments are presented with an emphasis on recording the effects of geometric nonlinearities on lateral frequency response. In a companion paper (Khorasany and Hutton, 2010, “Vibration Characteristics of Rotating Thin Disks—Part II: Analytical Predictions,” ASME J. Mech., 79(4), p. 041007), analytical predictions of such disk behavior are presented and compared with the experimental results obtained in this study. The experimental results show that in the case where significant disk displacements are induced by a lateral force, the frequency characteristics are significantly influenced by the magnitude of forced displacements.

Vibration of Beams with a Single Delamination under Axial Loading

2011 ◽  
Vol 675-677 ◽  
pp. 477-480
Author(s):  
Dong Wei Shu
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Analytical Solutions ◽  
Axial Load ◽  
Natural Frequencies ◽  
Axial Loading ◽  
Composite Beams ◽  
Mode Shapes ◽  
Equilibrium Conditions ◽  
Monotonic Relation

In this work analytical solutions are developed to study the free vibration of composite beams under axial loading. The beam with a single delamination is modeled as four interconnected Euler-Bernoulli beams using the delamination as their boundary. The continuity and the equilibrium conditions are satisfied between the adjoining beams. The studies show that the sizes and the locations of the delaminations significantly influence the natural frequencies and mode shapes of the beam. A monotonic relation between the natural frequency and the axial load is predicted.

Nonlinear Resonant Motion of Traveling Waves in Rotating Disks

2000 ◽  
Author(s):  
Albert C. J. Luo ◽  
Chin An Tan
Keyword(s):  
Traveling Waves ◽  
Rotation Speed ◽  
Rotating Disk ◽  
Disk Drive ◽  
Computer Memory ◽  
Rotating Disks ◽  
Resonant Wave ◽  
Linear And Nonlinear ◽  
Resonant Spectrum ◽  
Disk Drive Industry

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.

Sign in / Sign up

Export Citation Format

Share Document