Vibration Characteristics of Rotating Thin Disks—Part II: Analytical Predictions

2012 ◽  
Vol 79 (4) ◽  
Author(s):  
Ramin M. H. Khorasany ◽  
Stanley G. Hutton
Keyword(s):  
Frequency Response ◽  
Rotational Speed ◽  
Plate Theory ◽  
Lateral Displacement ◽  
Travelling Waves ◽  
Stationary Wave ◽  
Companion Paper ◽  
Vibration Characteristics ◽  
Experimental Results ◽  
Thin Disks

This paper is concerned with the geometric nonlinear analysis of the lateral displacement of thin rotating disks when subjected to a space fixed stationary force. Of particular interest is the development of the stationary wave and the effect of this wave on the frequency response of the disk as a function of its rotational speed. The predictions of this analysis are compared with experimental data obtained in a companion paper (Khorasany and Hutton, “Vibration Characteristics of Rotating Thin Disks—Part I: Experimental Results,” ASME J. Appl. Mech., 79(4), p. 041006). The governing equations are based on Von Kármán plate theory. A Galerkin solution of the governing non linear equations is developed. The eigenfunctions derived from the linear analysis of a stationary disk are used as approximations to the spatial response of the disk, and the eigenfunctions of the biharmonic equation as approximations for the stress function. Using the developed solution, the equilibrium configuration of the disk under the application of a space fixed force is found. In order to facilitate the prediction of the frequency response, as a function of disk rotational speed, the governing nonlinear equations are linearized around the equilibrium solution. The linearized equations are then used to find the eigenvalues of the spinning disk under the application of a space fixed force. The effect of different levels of nonlinearity on the disk frequencies is studied and compared with experimental results. The analysis is shown to produce an accurate representation of the measured response. Of particular interest is the disk response at speeds close to and above the linear critical speed. In this region, both the analysis and the experimental results display frequency “lock-in” behavior in which the frequency of backward travelling waves becomes constant for supercritical speeds. No speed exists for which backward travelling waves have zero frequency. Thus, critical speeds do not exist in the presence of geometric nonlinearities.

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 Characteristics of Guided Circular Saws: Experimental and Numerical Analyses

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Ramin M. H. Khorasany ◽  
Ahmad MohammadPanah ◽  
Stanley G. Hutton
Keyword(s):  
Rigid Body ◽  
External Force ◽  
Plate Theory ◽  
Lateral Displacement ◽  
Experimental Results ◽  
Experimental Investigations ◽  
Governing Equations ◽  
Air Jet ◽  
Vibrational Characteristics ◽  
Circular Saws

Studying the vibrational characteristics of guided circular saws is of particular interest in the current study. Guided circular saws are free in both the inner and outer rim. They are restrained from having axial motion by using two space-fixed guide pads in either side of the blade. Because of the small clearance between the guide pads and the saw blade, the blade is capable of having rigid body tilting and a translational degree of freedom. At first, we attempted to develop an understanding regarding the vibrational characteristics of such disks through experimental investigations. An electromagnet was used to generate random white noise for the purpose of exciting the bending waves. Using inductance displacement probes, the frequencies and amplitudes of the disk vibrations were measured and the mean deflections were plotted. In the next step, a space-fixed external force (air jet) was used to excite the disks in the lateral direction. The experimental results indicate that the blade frequencies show a significant change as a result of the initial lateral displacement imposed by the external force. It was also seen that due to the presence of the external force, a stationary wave develops and collapses at a higher speed. For the numerical simulations, the nonlinear governing equations based on Von Kármán plate theory were used. The effect of rigid body degrees of freedom was taken into account. As an approximation, the guide pads were modeled with four space-fixed springs. Using Galerkin’s method, the governing equations were discretized and their equilibrium solutions were found. After linearizing the governing equations around the equilibrium solution, the effect of nonlinearity on the amplitude and frequency response of the guided blade was investigated. It was seen that the numerical results were in close agreement with the experimental results.

On the Frequency Response of a Spinning Disk With Large Deformations

2010 ◽  
Author(s):  
Ramin M. H. Khorasany ◽  
Stanley G. Hutton
Keyword(s):  
Frequency Response ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Rotating Disk ◽  
Nonlinear Frequency ◽  
Response Characteristics ◽  
Geometrical Nonlinear ◽  
Oscillation Frequencies ◽  
Multi Mode ◽  
Different Levels

In this paper, the effect of geometrical nonlinear terms, caused by a space fixed point force, on the frequencies of oscillations of a rotating disk with clamped-free boundary conditions is investigated. The nonlinear geometrical equations of motion are based on Von Karman plate theory. Using the eigenfunctions of a stationary disk as approximating functions in Galerkin’s method, the equations of motion are transformed into a set of coupled nonlinear Ordinary Differential Equations (ODEs). These equations are then used to find the equilibrium positions of the disk at different discrete blade speeds. At any given speed, the governing equations are linearized about the equilibrium solution of the disk under the application of a space fixed external force. These linearized equations are then used to find the oscillation frequencies of the disk considering the effect of large deformation. Using multi mode approximation and different levels of nonlinearity, the frequency response of the disk considering the effect of geometrical nonlinear terms are studied. It is found that at the linear critical speed, the nonlinear frequency of the corresponding mode is not zero. Results are presented that illustrate the effect of the magnitude of disk displacement upon the frequency response characteristics. It is also found that for each mode, including the effect of the geometrical nonlinear terms due to the applied load causes a separation in the frequency responses of its backward and forward traveling waves when the disk is stationary. This effect is similar to the effect of a space fixed constraint in the linear problem. In order to verify the numerical results, experiments are conducted and the results are presented.

Calculation of Component Mode Synthesis Matrices From Measured Frequency Response Functions, Part 2: Application

1998 ◽  
Vol 120 (2) ◽  
pp. 509-516 ◽  
Author(s):  
J. A. Morgan ◽  
C. Pierre ◽  
G. M. Hulbert
Keyword(s):  
Frequency Response ◽  
Coupled System ◽  
Companion Paper ◽  
Component Mode Synthesis ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Measured Frequency ◽  
Measured Frequency Response ◽  
Coupled Beams ◽  
The Individual

This paper demonstrates how to calculate Craig-Bampton component mode synthesis matrices from measured frequency response functions. The procedure is based on a modified residual flexibility method, from which the Craig-Bampton CMS matrices are recovered, as presented in the companion paper, Part I (Morgan et al., 1998). A system of two coupled beams is analyzed using the experimentally-based method. The individual beams’ CMS matrices are calculated from measured frequency response functions. Then, the two beams are analytically coupled together using the test-derived matrices. Good agreement is obtained between the coupled system and the measured results.

scholarly journals Free Vibration Analysis of Fiber Metal Laminated Straight Beam

2018 ◽  
Vol 16 (1) ◽  
pp. 944-948 ◽  
Author(s):  
Sinan Maraş ◽  
Mustafa Yaman ◽  
Mehmet Fatih Şansveren ◽  
Sina Karimpour Reyhan
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
High Performance ◽  
Free Vibration Analysis ◽  
Vibration Characteristics ◽  
Numerical Results ◽  
Experimental Results ◽  
Hybrid Structures ◽  
Straight Beam ◽  
Fiber Metal

AbstractIn recent years, studies on the development of new and advanced composite materials have been increasing. Among these new technological products, Fiber Metal Laminates (FML), and hybrid structures made of aluminium, carbon, glass or aramid fiber, are preferred especially in the aircraft industry due to their high performance. Therefore, free vibration analysis is necessary for the design process of such structures. In this study, the vibration characteristics of FML for clamped-free boundary conditions were investigated experimentally and numerically. Firstly, numerical results were obtained using Finite Element Method (FEM) and then these results were compared with the experimental results. It was seen that the numerical results were in good agreement with the experimental results. As the theoretical model was justified, the effects of various parameters such as number of layers, fiber orientations, and aluminium layer thickness on the in-plane vibration characteristics of the FML straight beam were analysed using FEM. Thus, most important parameters affecting the vibration characteristics of the hybrid structures were determined.

Experimental Research on Rotating Skimmer

2003 ◽  
Author(s):  
Minoru Chino ◽  
Kenji Takizawa ◽  
Takashi Yabe
Keyword(s):  
Experimental Research ◽  
Rotational Speed ◽  
Rotation Speed ◽  
Experimental Results ◽  
Injection System ◽  
Benchmark Test ◽  
Injection Speed ◽  
Structure Interaction ◽  
Wide Range ◽  
Computer Codes

This paper provides the experimental results on skimmer and gives some detailed information useful for benchmark test of computer codes that are now able to simulate the fluid-structure interaction. For this purpose, we specially designed the injection system that imposes reproducible rotational speed and injection speed on the skipper. The effect of rotation is discussed by changing rotation speed in a wide range.

Fabrication and finite element analysis of vibrating parallel film actuator made with cellulose acetate for potential haptic application

2016 ◽  
Vol 230 (15) ◽  
pp. 2720-2727 ◽  
Author(s):  
Md Mohiuddin ◽  
Asma Akther ◽  
Eun Byul Jo ◽  
Hyun Chan Kim ◽  
Jaehwan Kim
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Cellulose Acetate ◽  
Vibration Characteristics ◽  
Experimental Results ◽  
Vibration Velocity ◽  
Frequency Range ◽  
Actuation Frequency ◽  
Element Analysis ◽  
Wide Range

The present study investigates a film actuator made with dielectric cellulose acetate films separated by narrow spacers as a means of electrostatic actuation for potential haptic application. Fabrication process for the actuator is explained along with experiments conducted over a wide frequency range of actuation frequency. A valid finite element simulation of the actuator is made on the quarter section of the actuator by using full 3D finite elements. Vibration characteristics such as fundamental natural frequency, mode shape and output velocity in the frequency range for haptic feeling generation are obtained from the finite element analysis and compared with the experimental results. Experimental results demonstrate that the finite element model is practical and effective enough in predicting the vibration characteristics of the actuator for haptic application. The film actuator shows many promising properties like high transparency, wide range of actuation frequency and high vibration velocity for instance.

Plastic Collapse of Thin Internally Pressurized Torispherical Shells

1979 ◽  
Vol 101 (4) ◽  
pp. 311-320 ◽  
Author(s):  
S. K. Radhamohan ◽  
G. D. Galletly
Keyword(s):  
Strain Hardening ◽  
Yield Stress ◽  
Material Properties ◽  
Parametric Study ◽  
Companion Paper ◽  
Experimental Results ◽  
Plastic Collapse ◽  
Approximate Design ◽  
Mode Of Failure ◽  
Hardening Coefficient

The plastic collapse pressures of internally pressurized thin torispherical shells are given in the present paper. The influence of both the geometric parameters (i.e., r/D, RS/D and D/t) and the material properties (yield stress σyp and the strain-hardening coefficient) on the plastic collapse pressures were investigated. Both steel and aluminium shells were analyzed and, based on the present parametric study, approximate design equations for calculating the plastic collapse pressures are suggested. The asymmetric buckling pressures, pcr, for torispherical shells (obtained from a companion paper) are also compared with the plastic collapse pressures, pc, to determine which are the lower and, thus, control the mode of failure. In addition, the approximate design equations for pcr and pc are compared with some experimental results on small machined models; the agreement between theory and test was quite good.

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