Measurement of Fan Vibration Using Double Pulse Holography

1978 ◽  
Vol 100 (4) ◽  
pp. 655-663 ◽  
Author(s):  
B. S. Hockley ◽  
R. A. J. Ford ◽  
C. A. Foord
Keyword(s):  
Vibration Mode ◽  
Mechanical Vibration ◽  
Propagation Speed ◽  
Double Pulse ◽  
Mode Shapes ◽  
Vibration Modes ◽  
Television System ◽  
Temporal Phase ◽  
Frequency Split ◽  
Laser Holography

Supersonic unstalled flutter in gas turbine fans is a self-excited instability in which mechanical vibrations give rise to unsteady aerodynamic forces which drive the mechanical vibration. The phenomenon is very sensitive to the deflected shapes of the blades and to the spatial and temporal phases of the blades’ responses. This paper is concerned with the measurement of vibrational behavior on static fans and relating it to flutter. Accurate detailed data on the blade and disk vibration mode shapes of fans up to 2.2 m diameter has been measured using double pulse laser holography. Both axial and tangential components of the blade mode shape are obtained by taking holograms from two directions. The analysis of the holograms is performed with the aid of a computer linked television system which generates the required blade mode shapes directly from the photographs of the hologram reconstructions. The disk mode measurements on real fans have shown the existence of pairs of spatially orthogonal vibration modes which have similar shapes (e.g. both 4D) but slightly different natural frequencies. This frequency split between modes means that the flutter wave will experience a cyclic variation in amplitude and propagation speed as it travels round the fan. In addition, the temporal phase angle between twist and flap in a single blade, which is generally assumed to be 90 deg, will vary from blade to blade.

The Use of Modan 3D in Experimental Modal Analysis

2013 ◽  
Vol 486 ◽  
pp. 36-41 ◽  
Author(s):  
Róbert Huňady ◽  
František Trebuňa ◽  
Martin Hagara ◽  
Martin Schrötter
Keyword(s):  
Modal Analysis ◽  
Vibration Analysis ◽  
High Speed ◽  
Mechanical Vibration ◽  
Steel Sample ◽  
Experimental Modal Analysis ◽  
Image Correlation ◽  
Optical Methods ◽  
Mode Shapes ◽  
Vibration Modes

Experimental modal analysis is a relatively young part of dynamics, which deals with the vibration modes identification of machines or their parts. Its development has started since the beginning of the eighties, when the computers hardware equipment has improved and the fast Fourier transform (FFT) could be used for the results determination. Nowadays it provides an uncountable set of vibration analysis possibilities starting with conventional contact transducers of acceleration and ending with modern noncontact optical methods. In this contribution we mention the use of high-speed digital image correlation by experimental determination of mode shapes and modal frequencies. The aim of our work is to create a program application called Modan 3D enabling the performing of experimental modal analysis and operational modal analysis. In this paper the experimental modal analysis of a thin steel sample performed with Q-450 Dantec Dynamics is described. In Modan 3D the experiment data were processed and the vibration modes were determined. The reached results were verified by PULSE modulus specialized for mechanical vibration analysis.

Identifying VIV Vibration Modes by Use of the Empirical Orthogonal Functions Technique

2002 ◽  
Author(s):  
Gudmund Kleiven
Keyword(s):  
Model Test ◽  
Vibration Mode ◽  
Multivariate Data ◽  
Empirical Orthogonal Functions ◽  
Mode Shapes ◽  
Data Sets ◽  
Vibration Modes ◽  
Ocean Engineering ◽  
Orthogonal Functions ◽  
Related Technique

The Empirical Orthogonal Functions (EOF) technique has widely being used by oceanographers and meteorologists, while the Singular Value Decomposition (SVD being a related technique is frequently used in the statistics community. Another related technique called Principal Component Analysis (PCA) is observed being used for instance in pattern recognition. The predominant applications of these techniques are data compression of multivariate data sets which also facilitates subsequent statistical analysis of such data sets. Within Ocean Engineering the EOF technique is not yet widely in use, although there are several areas where multivariate data sets occur and where the EOF technique could represent a supplementary analysis technique. Examples are oceanographic data, in particular current data. Furthermore data sets of model- or full-scale data of loads and responses of slender bodies, such as pipelines and risers are relevant examples. One attractive property of the EOF technique is that it does not require any a priori information on the physical system by which the data is generated. In the present paper a description of the EOF technique is given. Thereafter an example on use of the EOF technique is presented. The example is analysis of response data from a model test of a pipeline in a long free span exposed to current. The model test program was carried out in order to identify the occurrence of multi-mode vibrations and vibration mode amplitudes. In the present example the EOF technique demonstrates the capability of identifying predominant vibration modes of inline as well as cross-flow vibrations. Vibration mode shapes together with mode amplitudes and frequencies are also estimated. Although the present example is not sufficient for concluding on the applicability of the EOF technique on a general basis, the results of the present example demonstrate some of the potential of the technique.

Modal Analysis for Swing-Arm of LED Die Bonder

2011 ◽  
Vol 422 ◽  
pp. 379-382
Author(s):  
Wei Chuang Quan ◽  
Mei Fa Huang ◽  
Zhi Yue Wang ◽  
Da Wei Zhang
Keyword(s):  
Modal Analysis ◽  
Vibration Mode ◽  
Three Dimensional ◽  
Element Model ◽  
Mode Shapes ◽  
Vibration Modes ◽  
Lead Frame ◽  
Swing Arm ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

Led die bonder used for bond lead frame and chip is one of the key equipment of led production line. The swing-arm is an important component of led die bonder and its dynamic characteristics will directly affect the piece accuracy. At present, the accuracy and efficiency of led die bonder are limited because of the vibration of the swing-arm. In solving this problem, a three-dimensional finite-element model for swing-arm is built to provide analytical frequencies and vibration modes. Then the modal distribution and vibration mode shapes for swing-arm are obtained after analyzing the modal by ansys10.0. Finally the dynamics effects of this structure by modal frequency and vibration mode are analyzed. The modal analysis of structural would provide the reference to dynamics analysis and structural optimization for swing-arm in practical use.

Mode Evolution of Cyclic Symmetric Rotors Assembled to Flexible Bearings and Housing

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
Hyunchul Kim ◽  
Nick Theodore Khalid Colonnese ◽  
I. Y. Shen
Keyword(s):  
Vibration Mode ◽  
Fluid Dynamic ◽  
Travelling Wave ◽  
Modal Testing ◽  
Mode Shapes ◽  
Vibration Modes ◽  
Phase Index ◽  
Symmetric Rotor ◽  
Cyclic Symmetric ◽  
Inertia Forces

This paper is to study how the vibration modes of a cyclic symmetric rotor evolve when it is assembled to a flexible housing via multiple bearing supports. Prior to assembly, the vibration modes of the rotor are classified as “balanced modes” and “unbalanced modes.” Balanced modes are those modes whose natural frequencies and mode shapes remain unchanged after the rotor is assembled to the housing via bearings. Otherwise, the vibration modes are classified as unbalanced modes. By applying fundamental theorems of continuum mechanics, we conclude that balanced modes will present vanishing inertia forces and moments as they vibrate. Since each vibration mode of a cyclic symmetric rotor can be characterized in terms of a phase index (Chang and Wickert, “Response of Modulated Doublet Modes to Travelling Wave Excitation,” J. Sound Vib., 242, pp. 69–83; Chang and Wickert, 2002, “Measurement and Analysis of Modulated Doublet Mode Response in Mock Bladed Disks,” J. Sound Vib., 250, pp. 379–400; Kim and Shen, 2009, “Ground-Based Vibration Response of a Spinning Cyclic Symmetric Rotor With Gyroscopic and Centrifugal Softening Effects,” ASME J. Vibr. Acoust. (in press)), the criterion of vanishing inertia forces and moments implies that the phase index by itself can uniquely determine whether or not a vibration mode is a balanced mode as follows. Let N be the order of cyclic symmetry of the rotor and n be the phase index of a vibration mode. Vanishing inertia forces and moments indicate that a vibration mode will be a balanced mode if n≠1,N−1,N. When n=N, the vibration mode will be balanced if its leading Fourier coefficient vanishes. To validate the mathematical predictions, modal testing was conducted on a disk with four pairs of brackets mounted on an air-bearing spindle and a fluid-dynamic bearing spindle at various spin speeds. Measured Campbell diagrams agree well with the theoretical predictions.

Mode Evolution of Asymmetric Rotors Assembled to Flexible Bearings and Housing

2009 ◽  
Author(s):  
Hyunchul Kim ◽  
I. Y. Shen
Keyword(s):  
Boundary Conditions ◽  
Vibration Mode ◽  
Fluid Dynamic ◽  
Modal Testing ◽  
Mode Shapes ◽  
Vibration Modes ◽  
Fixed Boundary ◽  
Practical Applications ◽  
Asymmetric Rotor ◽  
Surface Integrals

This paper is to study how vibration modes of a stationary asymmetric rotor evolve when it is assembled to a flexible housing via multiple bearing supports. Prior to the assembly, vibration modes of the rotor are classified as “balanced modes” and “unbalanced modes.” Balanced modes are those modes whose natural frequencies and mode shapes remain unchanged after the rotor is assembled to the housing via bearings. Otherwise, the vibration modes are classified as “unbalanced modes.” In this paper, we first develop two mathematical criteria to identify balanced modes. For the first criteria, the rotor is subjected to fixed boundary conditions at the bearings prior to assembly. In this case, a vibration mode will be a balanced mode if the reactions at the fixed boundary vanish. For the second criterion, the rotor is subjected to free boundary conditions (including the bearing points) prior to assembly. In this case, a vibration mode will be a balanced mode if the bearing locations are nodal points of the vibration mode. These mathematical criteria are then applied to a rotor consisting of a rigid hub supporting a flexible structure, which appears in many practical applications. For balanced modes, the criteria lead to a conclusion that surface integrals of modal forces and moments at the flexible-rigid rotor interface will vanish. Moreover, these surface integrals can be conveniently calculated using finite element methods. To validate the mathematical criteria, modal testing was conducted on a disk with 4 pairs of brackets mounted on a rigid spindle, a ball-bearing spindle and a fluid-dynamic bearing spindle.

scholarly journals Identification of Vibration Modes of Quartz Crystal Plates with Proportion of Strain and Kinetic Energies

2020 ◽  
Vol 25 (3) ◽  
pp. 392-407
Author(s):  
Qi Huang ◽  
Rongxing Wu ◽  
Lihong Wang ◽  
Longtao Xie ◽  
Jianke Du ◽  
...  
Keyword(s):  
Quartz Crystal ◽  
Vibration Mode ◽  
Plate Theory ◽  
Traditional Approach ◽  
Mode Shapes ◽  
Energy Concentration ◽  
Mindlin Plate ◽  
Vibration Modes ◽  
Coupled Modes ◽  
Mode Identification

For the design of quartz crystal resonators, finding and determining the vibration modes have always been very important and cumbersome. Vibration modes are usually identified through plotting displacement patterns of each coupled modes and making comparisons. Over the years, there is not much improvement in the identification procedure while tremendous efforts have been made in refining the equations of the Mindlin plate theory to obtain more accurate results, such as the adoption of the Finite Element Method (FEM) by implementing the high-order Mindlin plate equations for efficient analysis. However, due to the old fashioned mode identification method, the FEM application is still inadequate and cannot be fully automated for this purpose. To have this situation improved, a method using the proportions of strain and kinetic energies to characterize the energy level of each vibration mode is proposed. With solutions of displacements, the energy distribution of each vibration mode is calculated and the mode with the highest energy concentration at a specific frequency is designated as the dominant mode. The results have been validated with the traditional approach by plotting mode shapes at each frequency. Clearly, this energy approach will be advantageous with the FEM analysis for vibration mode identification automatically.

On the Vibration of Bolted Plate and Flange Assemblies

1994 ◽  
Vol 116 (4) ◽  
pp. 468-473 ◽  
Author(s):  
J.-G. Tseng ◽  
J. A. Wickert
Keyword(s):  
Data Storage ◽  
Natural Frequencies ◽  
Vibration Mode ◽  
Annular Plate ◽  
Approximate Model ◽  
Outer Edge ◽  
Mode Shapes ◽  
Vibration Modes ◽  
Laboratory Measurements ◽  
Structural Imperfections

The vibration of an annular plate that is free along its outer edge, and that is connected to a flange along its inner edge by bolts that are equally spaced in the circumferential direction, is studied. A disk with this geometry, or a stacked array of such disks, is common in applications involving data storage, rotating machinery, or brake systems. The periodic structural imperfections that are associated with the bolt pattern can have interesting implications for the plate’s dynamic response. Changes that occur in the natural frequencies and mode shapes as a result of such deviations from an ideally clamped inner edge are studied through laboratory measurements, and through an approximate model that captures the rotationally periodic character of the bolted plate and flange system. In the axisymmetric case, the natural frequencies of the plate’s “sine” and “cosine” vibration modes are repeated for a specified number of nodal diameters. Under the influence of a regular bolt pattern, and the resulting local variations of the stiffness and compression at the plate/flange interface, some natural frequencies are repeated and others split. This process depends on the number of bolts used to mount the plate, and on the number of nodal diameters present in a specific vibration mode. A straightforward criterion to predict the split and repeated modes is discussed.

scholarly journals Impact of Geometrical Imperfections on Estimation of Buckling and Limit Loads in a Silo Segment Using the Vibration Correlation Technique

Materials ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 567
Author(s):  
Łukasz Żmuda-Trzebiatowski ◽  
Piotr Iwicki
Keyword(s):  
Natural Frequencies ◽  
Vibration Mode ◽  
Mode Shapes ◽  
Correlation Technique ◽  
Limit Loads ◽  
Linear Buckling ◽  
Geometrical Imperfections ◽  
Linear Problems ◽  
Formed Channel ◽  
Corrugated Wall

The paper examines effectiveness of the vibration correlation technique which allows determining the buckling or limit loads by means of measured natural frequencies of structures. A steel silo segment with a corrugated wall, stiffened with cold-formed channel section columns was analysed. The investigations included numerical analyses of: linear buckling, dynamic eigenvalue and geometrically static non-linear problems. Both perfect and imperfect geometries were considered. Initial geometrical imperfections included first and second buckling and vibration mode shapes with three amplitudes. The vibration correlation technique proved to be useful in estimating limit or buckling loads. It was very efficient in the case of small and medium imperfection magnitudes. The significant deviations between the predicted and calculated buckling and limit loads occurred when large imperfections were considered.

scholarly journals Frequency spectrum of the human head–neck to mechanical vibrations

2017 ◽  
Vol 37 (3) ◽  
pp. 611-618 ◽  
Author(s):  
Bin Yang ◽  
Zheng Shi ◽  
Qun Wang ◽  
Feng Xiao ◽  
Tong-Tong Gu ◽  
...  
Keyword(s):  
Finite Element ◽  
Frequency Spectrum ◽  
Mechanical Vibration ◽  
Three Dimensional ◽  
Human Head ◽  
Element Model ◽  
Mode Shapes ◽  
Joint Disorder ◽  
Biomechanical Responses ◽  
Head Neck

This study is based on a real finite element human head–neck model and concentrates on its numerical vibration characteristic. Frequency spectrum and mode shapes of the finite element model of human head–neck under mechanical vibration have been calculated. These vibration characteristics are in good agreement with the previous studies. The simulated fundamental frequency of 35.25 Hz is fairly similar to the published documents, and rarely reported modal responses such as “mastication” and flipping of nasal lateral cartilages modes, however, are introduced by our three-dimensional modal analysis. These additional modes may be of interest to surgeons or clinicians who are specialized in temporomandibular or rhinoplasty joint disorder. Modal validation in terms of modal shapes proposes a necessity for elaborate modeling to identify each individual part’s extra frequencies. Furthermore, it also studies the influence of damping on resonant frequencies and biomechanical responses. It is discovered that damping has an inverse proportionality between damping effect on natural frequency and that on biomechanical responses.

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