A Finite Element Model for Distributed Parameter Turborotor Systems

1972 ◽  
Vol 94 (1) ◽  
pp. 126-132 ◽  
Author(s):  
R. L. Ruhl ◽  
J. F. Booker
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Forced Response ◽  
Speed Ratio ◽  
Distributed Parameter ◽  
Parameter Study ◽  
Element Formulation ◽  
Dimensional Parameter ◽  
Discrete Parameter

A specific numerical calculation procedure is outlined for a general turborotor-bearing system in which distributed inertia and elasticity are consistently represented. Bearings are represented by up to sixteen linear cross coupled coefficients each for stiffness and for damping. Discrete (as well as distributed) masses are allowed. As an example, for stability analysis (free response) a non-dimensional parameter study is made for the special case of a simple rotor supported on two short (Ocvirk) fluid film bearings. A comparison of discrete and distributed parameter rotor representations shows that the discrete parameter model predicts onset of instability at a lower speed ratio and is, therefore, more conservative. For unbalanced response (forced response), comparison is made to Prohl’s method, which represents mass discretely. A considerable reduction in the number of degrees of freedom necessary for accurate system representation is observed with the finite element formulation.

scholarly journals Building Spectral Element Dynamic Matrices Using Finite Element Models of Waveguide Slices and Elastodynamic Equations

2013 ◽  
Vol 20 (3) ◽  
pp. 439-458 ◽  
Author(s):  
P.B. Silva ◽  
A.L. Goldstein ◽  
J.R.F. Arruda
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Transfer Matrix ◽  
Cross Section ◽  
Element Model ◽  
Spectral Element ◽  
Forced Response ◽  
Spectral Elements ◽  
Element Formulation ◽  
Element Mesh

Structural spectral elements are formulated using the analytical solution of the applicable elastodynamic equations and, therefore, mesh refinement is not needed to analyze high frequency behavior provided the elastodynamic equations used remain valid. However, for modeling complex structures, standard spectral elements require long and cumbersome analytical formulation. In this work, a method to build spectral finite elements from a finite element model of a slice of a structural waveguide (a structure with one dimension much larger than the other two) is proposed. First, the transfer matrix of the structural waveguide is obtained from the finite element model of a thin slice. Then, the wavenumbers and wave propagation modes are obtained from the transfer matrix and used to build the spectral element matrix. These spectral elements can be used to model homogeneous waveguides with constant cross section over long spans without the need of refining the finite element mesh along the waveguide. As an illustrating example, spectral elements are derived for straight uniform rods and beams and used to calculate the forced response in the longitudinal and transverse directions. Results obtained with the spectral element formulation are shown to agree well with results obtained with a finite element model of the whole beam. The proposed approach can be used to generate spectral elements of waveguides of arbitrary cross section and, potentially, of arbitrary order.

Analysis of the Influence of Blade Pattern Characteristics on the Forced Response of Mistuned Blisks With a Cyclic CMS-Based Substructure Model

2010 ◽  
Author(s):  
Andreas Hohl ◽  
Lars Panning ◽  
Jo¨rg Wallaschek
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Degrees Of Freedom ◽  
Vibrational Energy ◽  
Normal Modes ◽  
Element Model ◽  
Forced Response ◽  
Symmetry Approach ◽  
Full Structure ◽  
Value Decomposition

In turbomachinery applications bladed disks and blisks are subjected to high dynamic loads due to fluctuating gas forces. The dynamic excitation results in high vibration amplitudes which can lead to high cycle fatigue failures (HCF). Herein, the blades are almost identical but differ due to wear or small manufacturing tolerances. These small deviations of the blade properties can lead to a localization of the vibrational energy in single blades and even higher risk of HCF. Intentional mistuning, for example an alternating alignment of two different blades AB around the blisk, has been studied in literature to decrease the sensitivity against statistical mistuning. Using a Component Mode Synthesis (CMS) based mistuning model the influence of intentional mistuning on blisks is analyzed in this paper. Therein, the CMS of the disk is calculated with a fast and accurate cyclic symmetry approach. Therefore, the CMS of the disk can be calculated with one disk segment of the underlying Finite Element Model. The so called Wave Based Substructuring (WBS) is used to reduce the (numerous) coupling degrees of freedom between the disk and the blades with a truncated set of waves. The orthogonal waves are derived with a Singular Value Decomposition or a QR decomposition from the normal modes at the coupling degrees of freedom (DOF) calculated by a cyclic modal analysis of the full structure. In a case study the Reduced Order Model (ROM) of a spatial Finite Element Model is used to determine the influence of intentional mistuning with additional statistical mistuning on the forced response of blisks.

Finite-Element Analysis for a Timoshenko Beam Subjected to a Moving Mass

2006 ◽  
Vol 220 (5) ◽  
pp. 669-678 ◽  
Author(s):  
P Lou ◽  
G-L Dai ◽  
Q-Y Zeng
Keyword(s):  
Finite Element ◽  
Timoshenko Beam ◽  
Present Method ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Element Formulation ◽  
Moving Mass ◽  
Element Analysis ◽  
Assumed Mode Method ◽  
Various Boundary Conditions

This article presents a finite-element formulation of a Timoshenko beam subjected to a moving mass. The beam is discretized into a number of simple elements with four degrees of freedom each. The inertial effects of the moving mass are incorporated into a finite-element model. The equation of motion in matrix form with time-dependent coefficients for a Timoshenko beam subjected to a moving mass is derived from the variational approach. The equation is solved by the direct step-by-step integration method to obtain the dynamic response of a Timoshenko beam and the contact force between the moving mass and the beam. The correctness of this present method is validated by means of comparison with the solution obtained by the assumed-mode method. The present method can be effectively used in computation for a Timoshenko beam with various boundary conditions. Numerical simulations are performed to demonstrate the efficiency of the present method.

Forced Response Assessment Using Modal Force Based Indicator Functions

2008 ◽  
Author(s):  
M. Vahdati ◽  
C. Breard ◽  
G. Simpson ◽  
M. Imregun
Keyword(s):  
Finite Element ◽  
Structural Model ◽  
Stokes Equations ◽  
Linear Time ◽  
Response Assessment ◽  
Element Model ◽  
Forced Response ◽  
Navier Stokes ◽  
Modal Force ◽  
Indicator Functions

This paper will focus on core-compressor forced response with the aim to develop two design criteria, the so-called chordwise cumulative modal force and heightwise cumulative force, to assess the potential severity of the vibration levels from the correlation between the unsteady pressure distribution on the blade’s surface and the structural modeshape. It is also possible to rank various blade designs since the proposed criterion is sensitive to changes in both unsteady aerodynamic loads and the vibration modeshapes. The proposed methodology was applied to a typical core-compressor forced response case for which measured data were available. The Reynolds-averaged Navier-Stokes equations were used to represent the flow in a non-linear time-accurate fashion on unstructured meshes of mixed elements. The structural model was based on a standard finite element representation from which the vibration modes were extracted. The blade flexibility was included in the model by coupling the finite element model to the unsteady flow model in a time-accurate fashion. A series of numerical experiments were conducted by altering the stator wake and using the proposed indicator functions to minimize the rotor response levels. It was shown that a fourfold response reduction was possible for a certain mode with only a minor modification of the blade.

Finite Element Formulation and Vibration Frequency Analysis of a Fluid Filled Pipe

2005 ◽  
Author(s):  
Yi Jia ◽  
Reinaldo E. Madeira ◽  
Frederick Just-Agosto
Keyword(s):  
Finite Element ◽  
Coriolis Force ◽  
Frequency Analysis ◽  
Cross Sections ◽  
Vibration Frequency ◽  
Dynamic Performance ◽  
Element Model ◽  
Piping System ◽  
Element Formulation ◽  
Variable Cross

This paper presents the formulation of a finite element model and vibration frequency analysis of a fluid filled pipe having variable cross sections. The finite element method with consideration of Coriolis force developed in [1] was adopted for frequency analysis of a pipe in this study. The stiffness matrix, the c-matrix (Coriolis force) and mass (for dynamic analysis) matrix that contain all parameters of the fluids properties and flow conditions have been developed. The numerical model was employed to simulate the dynamic performance of the piping system with the specific configurations for an application. A critical relationship between the natural frequencies and pipe geometry has been established. The results of frequencies analysis of the piping system gave us an insight whether a resonance frequency might occur.

A Parallel Solution Strategy for Finite Element Models

1996 ◽  
Author(s):  
Jordan J. Cox ◽  
Jeffrey A. Talbert ◽  
Eric Mulkay
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Decomposition Methods ◽  
Finite Element Models ◽  
Unique Contribution ◽  
Matrix Equations ◽  
Parallel Solution ◽  
The Finite Element Model ◽  
Parallel Fashion

Abstract This paper presents a method for naturally decomposing finite element models into sub-models which can be solved in a parallel fashion. The unique contribution of this paper is that the decomposition strategy comes from the geometric features used to construct the solid model that the finite element model represents. Domain composition and domain decomposition methods are used to insure global compatibility. These techniques reduce the N2 behavior of traditional matrix solving techniques, where N is the number of degrees of freedom in the global set of matrix equations, to a sum of m matrices with n2 behavior, where n represents the number of degrees of freedom in the smaller sub-model matrix equations.

Finite Element Model of the Human Knee Joint to Study Tibio-Femoral Contact Mechanics

2000 ◽  
Author(s):  
Tammy Haut Donahue ◽  
Maury L. Hull ◽  
Mark M. Rashid ◽  
Christopher R. Jacobs
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Degrees Of Freedom ◽  
Soft Tissues ◽  
Element Model ◽  
Human Knee ◽  
Human Knee Joint ◽  
Solid Models ◽  
Flexion Extension ◽  
A New Technique

Abstract A finite element model of the tibio-femoral joint in the human knee was created using a new technique for developing accurate solid models of soft tissues (i.e. cartilage and menisci). The model was used to demonstrate that constraining rotational degrees of freedom other than flexion/extension when the joint is loaded in compression markedly affects the load distribution between the medial and lateral sides of the joint. The model also was used to validate the assumption that the bones can be treated as rigid.

Parameter study on a finite element model of the middle ear / Parameterstudie an einem Finite-Elemente-Modell des Mittelohrs

2010 ◽  
Vol 55 (1) ◽  
pp. 19-26 ◽  
Author(s):  
Marc Hoffstetter ◽  
Florian Schardt ◽  
Thomas Lenarz ◽  
Sabine Wacker ◽  
Erich Wintermantel
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Middle Ear ◽  
Element Model ◽  
Parameter Study ◽  
Finite Elemente

Finite Element Model Based Full Spectrum Response Analysis of a Cracked Rotor With Internal and External Damping

2019 ◽  
Author(s):  
Dipendra Kumar Roy ◽  
Rajiv Tiwari
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Rotor System ◽  
Response Analysis ◽  
Stable Operation ◽  
Internal Damping ◽  
Full Spectrum ◽  
Fault Parameters ◽  
Spectrum Response

Abstract The ratio of internal and external damping is one of the important fault parameters and it leads to instability of a rotor shaft at higher spin speeds. The crack in a rotor is one of the sources of its instability due to the crack internal damping. A rotor with crack internal damping that originates from the rubbing action between the two crack faces. For a sustained stable operation of the rotor, it is imperative to analyze rotor parameters such as the internal and external damping and other parameters, like the additive crack stiffness and disc eccentricity. Therefore, the present work considers a full spectrum response analysis of a transverse cracked shaft based on the finite element method. The rotary and translations of inertia are considered including of gyroscopic effect in the rotor system. The transverse crack is modeled based on the switching crack assumption. The crack in the rotor gives forcing with multiple harmonics with the forward and backward. The equation of motion has been developed for the rotor system having four degrees of freedom at each node and using MATLAB™ Simulink the responses are generated for a numerical example.

Performance Characteristics of a Smart Flexible Beam With Distributed ACLD Elements

2002 ◽  
Author(s):  
L. C. Hau ◽  
Eric H. K. Fung
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Viscoelastic Model ◽  
Element Model ◽  
Flexible Beam ◽  
Constrained Layer Damping ◽  
Optimal Output ◽  
Modes Of Vibration ◽  
Original Size

The finite element method, in conjunction with the Golla-Hughes-McTavish (GHM) viscoelastic model, is employed to model a clamped-free beam partially treated with active constrained layer damping (ACLD) elements. The governing equations of motion are converted to a state-space form for control system design. Prior to this, since the resultant finite element model has too many degrees of freedom due to the addition of dissipative coordinates, a model reduction is performed to revert the system back to its original size. Finally, optimal output feedback gains are designed based on the reduced models. Numerical simulations are performed to study the effect of different element configurations, with various spacing and locations, on the vibration control performance of a “smart” flexible ACLD treated beam. Results are presented for the damping ratios of the first two modes of vibration. It is found that improvement on the second mode damping can be achieved by splitting a single ACLD element into two and placing them at appropriate positions of the beam.

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