Planar Whitehead graphs with cyclic symmetry arising from the study of Dunwoody manifolds

Abstract Stress analysis and determination of eigen pairs of a typical turbocharger compressor impeller have been carried out using the concept of cyclic symmetry. A simplified model treating the blade and the hub as isolated elements has also been attempted. The limitations of the simplified model have been brought out. The results of the finite element model using the cyclic symmetric approach have been discussed.

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Experimental Study of Blade Vibration in Centrifugal Compressors

Volume 6: Structures and Dynamics, Parts A and B ◽

10.1115/gt2011-45928 ◽

2011 ◽

Author(s):

Andrew H. Lerche ◽

J. Jeffrey Moore ◽

Timothy C. Allison

Keyword(s):

High Cycle Fatigue ◽

Axial Flow ◽

Modal Testing ◽

Mode Shapes ◽

Cyclic Symmetry ◽

Centrifugal Compressors ◽

Compressor Blades ◽

Blade Vibration ◽

Phase Cancellation ◽

Blade Failure

Blade vibration in turbomachinery is a common problem that can lead to blade failure by high cycle fatigue. Although much research has been performed on axial flow turbomachinery, little has been published for radial flow machines such as centrifugal compressors and radial inflow turbines. This work develops a test rig that measures the resonant vibration of centrifugal compressor blades. The blade vibrations are caused by the wakes coming from the inlet guide vanes. These vibrations are measured using blade mounted strain gauges during a rotating test. The total damping of the blade response from the rotating test is compared to the damping from the modal testing performed on the impeller. The mode shapes of the response and possible effects of mistuning are also discussed. The results show that mistuning can affect the phase cancellation which one would expect to see on a system with perfect cyclic symmetry.

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Vibration Analysis of a Nonlinear System With Cyclic Symmetry

Journal of Engineering for Gas Turbines and Power ◽

10.1115/1.4001989 ◽

2010 ◽

Vol 133 (2) ◽

Cited By ~ 15

Author(s):

Aurélien Grolet ◽

Fabrice Thouverez

Keyword(s):

Nonlinear Differential Equations ◽

Geometrical Nonlinearity ◽

Harmonic Balance Method ◽

Dynamic Responses ◽

Cyclic Symmetry ◽

Force Amplitude ◽

Closed Curves ◽

Nonlinear Modes ◽

Nonlinear Localization ◽

Engine Order

This work is devoted to the study of nonlinear dynamics of structures with cyclic symmetry under geometrical nonlinearity using the harmonic balance method (HBM). In order to study the influence of the nonlinearity due to large deflection of blades, a simplified model has been developed. It leads to nonlinear differential equations of the second order, linearly coupled, in which the nonlinearity appears by cubic terms. Periodic solutions in both free and forced cases are sought by the HBM coupled with an arc length continuation and stability analysis. In this study, specific attention has been paid to the evaluation of nonlinear modes and to the influence of excitation on dynamic responses. Indeed, several cases of excitation have been analyzed: punctual one and tuned or detuned low engine order. This paper shows that for a localized, or sufficiently detuned, excitation, several solutions can coexist, some of them being represented by closed curves in the frequency-amplitude domain. Those different kinds of solution meet up when increasing the force amplitude, leading to forced nonlinear localization. As the closed curves are not tied with the basic nonlinear solution, they are easily missed. They were calculated using a sequential continuation with the force amplitude as a parameter.

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Some Co-Circular Crack Problems with Cyclic Symmetry

Partial Differential and Integral Equations - International Society for Analysis, Applications and Computation ◽

10.1007/978-1-4613-3276-3_20 ◽

1999 ◽

pp. 267-276

Author(s):

Jianke Lu

Keyword(s):

Circular Crack ◽

Cyclic Symmetry ◽

Crack Problems

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A WAVE FINITE ELEMENT STRATEGY TO COMPUTE THE DYNAMIC FLEXIBILITY MODES OF STRUCTURES WITH CYCLIC SYMMETRY AND ITS APPLICATION TO DOMAIN DECOMPOSITION

Proceedings of the 6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COMPDYN 2015) ◽

10.7712/120117.5434.17179 ◽

2017 ◽

Author(s):

Jean-Mathieu Mencik

Keyword(s):

Finite Element ◽

Domain Decomposition ◽

Cyclic Symmetry

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Identities for curvature tensors in generalized Finsler space

Filomat ◽

10.2298/fil0902034z ◽

2009 ◽

Vol 23 (2) ◽

pp. 34-42 ◽

Cited By ~ 1

Author(s):

Milan Zlatanovic ◽

Svetislav Mincic

Keyword(s):

Finsler Space ◽

Cyclic Symmetry ◽

Symmetric Connection ◽

Two Indices ◽

Curvature Tensors

In the some previous works we have obtained several curvature tensors in the generalized Finsler space GFN (the space with non-symmetric basic tensor and non-symmetric connection in Rund's sence). In this work we study identities for the mentioned tensors (the antisymmetriy with respect of two indices, the cyclic symmetry, the symmetry with respect of pairs of indices).

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An EFG-SBM based partitioning algorithm for two-dimensional elastic analysis of cyclically symmetrical structures

Engineering Computations ◽

10.1108/ec-09-2013-0229 ◽

2015 ◽

Vol 32 (2) ◽

pp. 452-472 ◽

Cited By ~ 2

Author(s):

Xiaofeng Guo ◽

Yiqian He ◽

Haitian Yang

Keyword(s):

Computational Cost ◽

Elastic Analysis ◽

Two Dimensional ◽

Cyclic Symmetry ◽

Content Type ◽

System Equations ◽

Partitioning Algorithm ◽

Displacement Constraints ◽

Element Free ◽

Symmetric Structures

Purpose – The purpose of this paper is to exploit the cyclic symmetry to reduce the computational expense of scaled boundary method (SBM) which may cumber its further application. Design/methodology/approach – A partitioning EFG-SB (Element-free Galerkin-SB) algorithm is proposed for the two-dimensional elastic analysis of cyclically symmetric structures. Findings – By utilizing the cyclic symmetry and partitioning algorithm, the whole computational cost can be significantly reduced. Three numerical examples are given to illustrate the advantages of the proposed algorithm. Originality/value – It is proved that the matrices of eigenvalue and system equations of EFG-SBM for cyclically symmetric structures are block-circulant so long as a kind of symmetry-adapted reference coordinate system is adopted. No matter whether displacement constraints are cyclically symmetric or not, the partition is available for the eigenvalue equations. Therefore the major computational cost can be saved via the proposed partitioning algorithm. This paper provides an efficient algorithm for the two-dimensional elastic analysis of cyclically symmetric structures using EFG-SBM. A higher computing efficiency can be expected since the proposed partitioning algorithm facilitates parallel processing.

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Comparative Performance of Isotropic and Composite Bladed Disks

15th Design Automation Conference: Volume 3 — Mechanical Systems Analysis, Design and Simulation ◽

10.1115/detc1989-0122 ◽

1989 ◽

Author(s):

P. Seshu ◽

V. Ramamurti

Keyword(s):

Steady State ◽

Shell Element ◽

Cyclic Symmetry ◽

Bladed Disks ◽

Comparative Performance ◽

Composite Blade ◽

Bladed Disk ◽

Plate And Shell ◽

Representative Model ◽

Symmetry Method

Abstract Using a 3-noded, multilayered anisotropic triangular plate and shell element combined with cyclic symmetry method, a comparison has been drawn on the steady state as well as free vibration behaviour of isotropic and composite bladed disks, taking into account all the geometric and material complexities. Results are presented for a representative model for three cases – isotropic bladed disk, isotropic disk-composite blade, and composite bladed disk.

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