In-Plane Vibration of a Deployable Segmented Ring

2020 ◽  
Vol 20 (07) ◽  
pp. 2071007
Author(s):  
C. Y. Wang
Keyword(s):  
Vibration Mode ◽  
Mode Shapes ◽  
Space Structures ◽  
Graphene Sheets ◽  
Vibration Frequencies ◽  
Elastic Ring ◽  
Nonlinear Dynamical ◽  
Classical Vibration ◽  
First Time ◽  
Number Of Segments

The in-plane vibrations of regular polygonal rings composed of rigid segments joined by torsional springs are studied for the first time. The nonlinear dynamical difference equations are formulated and solved by perturbation about the equilibrium state. As the number of segments increase, the frequencies, if aptly normalized, converge to the classical vibration frequencies of a continuous elastic ring. The vibration mode shapes are illustrated. The tiling of many identical polygons is discussed. Possible applications include the vibrations of space structures and graphene sheets.

Exact Vibration Solution for Exponentially Tapered Cantilever With Tip Mass

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
C.Y. Wang ◽  
C. M. Wang
Keyword(s):  
Numerical Methods ◽  
Free Vibration ◽  
Cantilever Beam ◽  
Technical Note ◽  
Mode Shapes ◽  
Constant Thickness ◽  
Vibration Frequencies ◽  
Tapered Cantilever Beam ◽  
Tip Mass ◽  
First Time

This technical note is concerned with the free vibration problem of a cantilever beam with constant thickness and exponentially decaying width. Existing analytical results for such a vibration beam problem are found to be incomplete because lower frequencies could not be obtained. Presented herein is the exact characteristic equation for generating the complete vibration frequencies for the considered vibrating beam problem. Also the note treated for the first time such a tapered cantilever beam with a tip mass. The exact solutions (frequencies and mode shapes) are important to engineers designing such tapered beams and the results serve as benchmarks for assessing the validity, convergence and accuracy of numerical methods and solutions.

Experimental and numerical investigations on novel models for mechanical behaviors of the elastic ring in aero-engine

2021 ◽  
pp. 095440622110130
Author(s):  
Zhong Luo ◽  
Lei Li ◽  
Yang Yang ◽  
Xiaojie Hou ◽  
Jiaxi Liu ◽  
...  
Keyword(s):  
3D Model ◽  
Maximum Stress ◽  
Simple Structure ◽  
Experimental Testing ◽  
Axial Direction ◽  
Elastic Ring ◽  
Load Range ◽  
Aero Engine ◽  
Stiffness Characteristics ◽  
First Time

The elastic ring is widely used in elastic support structures of aero-engine because of its simple structure and convenient manufacturing. In this paper, two elastic ring models, 3D and 2D models, are proposed, where the fillets between the bulges and ring are considered. The 2D model is more efficient for the calculation of stiffness characteristics. The 3D model can be used to obtain the maximum stress position in the axial direction. Then the experimental testing is carried out to verify the accuracy and effectiveness of the proposed models. Based on the proposed models, the stiffness nonlinearity and critical load of the elastic ring are found for the first time, which can be used to determine the normal working load range. Moreover, the elastic ring models with and without fillets are developed, and the effect of the fillets on stress is discussed. The results show that the stress is reduced by considering the fillets, which are not considered in the existing literature.

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.

Free Vibrations of Thick, Complete Conical Shells of Revolution From a Three-Dimensional Theory

2005 ◽  
Vol 72 (5) ◽  
pp. 797-800 ◽  
Author(s):  
Jae-Hoon Kang ◽  
Arthur W. Leissa
Keyword(s):  
Ritz Method ◽  
Three Dimensional ◽  
Axial Direction ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Vibration Frequencies ◽  
Shells Of Revolution ◽  
Dimensional Theory ◽  
Conical Shells ◽  
Cylindrical Coordinate

A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, complete (not truncated) conical shells of revolution in which the bottom edges are normal to the midsurface of the shells based upon the circular cylindrical coordinate system using the Ritz method. Comparisons are made between the frequencies and the corresponding mode shapes of the conical shells from the authors' former analysis with bottom edges parallel to the axial direction and the present analysis with the edges normal to shell midsurfaces.

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.

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

Materials ◽  
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.

Natural Frequencies and Normal Modes of a Spinning Timoshenko Beam With General Boundary Conditions

1992 ◽  
Vol 59 (2S) ◽  
pp. S197-S204 ◽  
Author(s):  
Jean Wu-Zheng Zu ◽  
Ray P. S. Han
Keyword(s):  
Boundary Conditions ◽  
Mode Shape ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Normal Modes ◽  
Single Mode ◽  
Mode Shapes ◽  
Simulation Studies ◽  
Classical Boundary ◽  
First Time

A free flexural vibrations of a spinning, finite Timoshenko beam for the six classical boundary conditions are analytically solved and presented for the first time. Expressions for computing natural frequencies and mode shapes are given. Numerical simulation studies show that the simply-supported beam possesses very peculiar free vibration characteristics: There exist two sets of natural frequencies corresponding to each mode shape, and the forward and backward precession mode shapes of each set coincide identically. These phenomena are not observed in beams with the other five types of boundary conditions. In these cases, the forward and backward precessions are different, implying that each natural frequency corresponds to a single mode shape.

DAMAGE DETECTION OF RC SLABS USING NONLINEAR VIBRATION FEATURES

2009 ◽  
Vol 09 (04) ◽  
pp. 687-709 ◽  
Author(s):  
XINQUN ZHU ◽  
HONG HAO
Keyword(s):  
Reinforced Concrete ◽  
Nonlinear Vibration ◽  
Structural Damage ◽  
Concrete Structures ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Reinforced Concrete Structures ◽  
Vibration Frequencies ◽  
Skeleton Curve ◽  
Time Frequency

Studied herein are the signatures of nonlinear vibration characteristics of damaged reinforced concrete structures using the wavelet transform (WT). A two-span RC slab built in 2003 was tested to failure in the laboratory. Vibration measurements were carried out at various stages of structural damage. The vibration frequencies, mode shapes, and damping ratios at each loading stage were extracted and analyzed. It is found that the vibration frequencies are not sensitive to small damages, but are good indicators when damage is severe. The dynamic responses are also analyzed in the time–frequency domain by WT and the skeleton curve is constructed to describe the nonlinear characteristics in the reinforced concrete structures. The results show that the skeleton curves are good indicators of damage in the reinforced concrete structures because they are more sensitive to small damages than vibration frequencies.

Analysis of Pulsations and Vibrations in Fluid-Filled Pipe Systems

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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