In-Plane Vibration Mode Shapes for Rotating Disks: Exact Solution

The free in-plane vibration of a shallow circular arch with uniform cross-section is investigated by taking into account axial extension, shear deformation and rotatory inertia effects. The exact solution of the governing differential equations is obtained by the initial value method. By employing the same solution procedure, the solutions are also given for the other cases, in which each effect is considered alone, as well as no effect. The frequency coefficients are obtained for the lowest five vibration modes of arches with five combinations of classical boundary conditions, and various slenderness ratios and opening angles. The results show that the shear deformation and rotatory inertia effects are also very important as well as the axial extension effect, even if a slender shallow arch is considered. The discrepancies among the results of the five cases decrease, when opening angle increases for a constant radius and slenderness ratio. The effects of the boundary conditions and the slenderness ratio of the arch are investigated. The discrepancies among the results of the cases become much more important in higher modes. The mode shapes of a shallow arch are obtained for each case.

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

Materials ◽

10.3390/ma14030567 ◽

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.

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

21st International Conference on Offshore Mechanics and Arctic Engineering, Volume 1 ◽

10.1115/omae2002-28425 ◽

2002 ◽

Cited By ~ 3

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.

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Simultaneous Measurement of Plate Natural Frequencies and Vibration Mode Shapes Using ESPI

Conference Proceedings of the Society for Experimental Mechanics Series - Imaging Methods for Novel Materials and Challenging Applications, Volume 3 ◽

10.1007/978-1-4614-4235-6_10 ◽

2012 ◽

pp. 85-90

Author(s):

P. Georgas ◽

G. S. Schajer

Keyword(s):

Simultaneous Measurement ◽

Natural Frequencies ◽

Vibration Mode ◽

Mode Shapes

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Detection of Material Degradation of a Composite Cylinder Using Mode Shapes and Convolutional Neural Networks

Materials ◽

10.3390/ma14216686 ◽

2021 ◽

Vol 14 (21) ◽

pp. 6686

Author(s):

Bartosz Miller ◽

Leonard Ziemiański

Keyword(s):

Neural Networks ◽

Convolutional Neural Networks ◽

Composite Structures ◽

Vibration Mode ◽

Numerical Study ◽

Mode Shapes ◽

Zone Size ◽

Composite Cylinder ◽

Material Degradation ◽

Damaged Zone

This paper presents a numerical study of the feasibility of using vibration mode shapes to identify material degradation in composite structures. The considered structure is a multilayer composite cylinder, while the material degradation zone is, for simplicity, considered a square section of the lateral surface of the cylinder. The material degradation zone size and location along the cylinder axis are identified using a deep learning approach (convolutional neural networks, CNNs, are applied) on the basis of previously identified vibration mode shapes. The different numbers and combinations of identified mode shapes used to assess the damaged zone size and location were analyzed in detail. The final selection of mode shapes considered in the identification procedure yielded high accuracy in the identification of the degradation zone.

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Analysis of Pulsations and Vibrations in Fluid-Filled Pipe Systems

Volume 3B: 15th Biennial Conference on Mechanical Vibration and Noise — Acoustics, Vibrations, and Rotating Machines ◽

10.1115/detc1995-0478 ◽

1995 ◽

Author(s):

Christ A. F. de Jong

Keyword(s):

Energy Flow ◽

Vibration Mode ◽

Pipe Wall ◽

Acoustic Energy ◽

Mode Shapes ◽

Strongly Coupled ◽

Torsional Waves ◽

Pipe Systems ◽

Poisson Contraction ◽

Excessive Noise

Abstract Pressure pulsations and mechanical vibrations in pipe systems may cause excessive noise and may even lead to damage of piping or machinery. In fluid-filled pipe systems pulsations and vibrations will be strongly coupled. A calculation method has been developed for the simulation of coupled pulsations and vibrations in pipe systems. The analytical method is based upon the transfer matrix method. It describes plane pressure waves in the fluid and extensional, bending and torsional waves in the pipe wall. Fluid pulsations and pipe wall vibrations are coupled at discontinuities (e.g. elbows and T-junctions) and via Poisson contraction of the pipe wall. For a given source description, the model calculates levels of vibration, mode shapes, vibro-acoustic energy flow, etc. The method has been validated experimentally on a test rig consisting of two straight pipes and an elbow. The predicted pulsation and vibration levels agree reasonably well with the measurements.

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In-Plane Vibration Analysis of Rotating Tapered Timoshenko Beams

International Journal of Applied Mechanics ◽

10.1142/s1758825116500642 ◽

2016 ◽

Vol 08 (05) ◽

pp. 1650064 ◽

Cited By ~ 9

Author(s):

Jianshi Fang ◽

Ding Zhou

Keyword(s):

Chebyshev Polynomials ◽

Coupling Effect ◽

Mode Shapes ◽

Transverse Motion ◽

Timoshenko Beams ◽

Rotational Angle ◽

Plane Vibration ◽

Present Solution ◽

Boundary Functions ◽

Geometric Boundary

Modal analysis of rotating tapered cantilevered Timoshenko beams undergoing in-plane vibration is investigated. The coupling effect of axial motion and transverse motion is considered. The Kane dynamic method is applied to deriving the governing eigenvalue equations. The displacement and rotational angle components are approximately described by the products of Chebyshev polynomials and corresponding boundary functions. Chebyshev polynomials guarantee the numerical robustness while the boundary functions guarantee the satisfaction of the geometric boundary conditions. The excellent convergence of the present solution is exhibited. The results are compared with those available in literature, good agreement is observed. The parametric studies on modal characteristics are presented in detail. The tuned rotational speed is examined and the eigenvalue loci veering phenomenon along with the corresponding mode shapes is investigated.

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