On Centrifugal Softening in Finite Element Method Rotordynamics

2013 ◽  
Vol 81 (1) ◽  
Author(s):  
Giancarlo Genta ◽  
Mario Silvagni
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Numerical Models ◽  
Three Dimensional ◽  
General Purpose ◽  
Rotating Beam ◽  
Fem Modeling ◽  
Rotating System ◽  
Softening Effect

The centrifugal softening effect is an alleged and elusive reduction of the natural frequencies of a rotating system with increasing speed which is sometimes found in finite element rotordynamics. This reduction may, in some instances, be large enough to cause some of the natural frequencies to vanish, leading to a sort of elastic instability. Some doubts can, however, be cast on the phenomenon itself and on the mathematical models causing it to appear. The aim of the present work is to shed some light on centrifugal softening and to discuss the assumptions that are at the basis of three-dimensional FEM modeling in rotordynamics. One and two degrees of freedom models, such as the ones introduced by Rankine and Jeffcott, are first studied and then the classical rotating beam, ring, disk, and membrane are addressed. Some numerical models, built using the FEM, are then solved using both dedicated and general purpose codes. In all cases no strong centrifugal softening is found.

Selection of Degrees of Freedom for Dynamic Analysis

1987 ◽  
Vol 109 (1) ◽  
pp. 65-69 ◽  
Author(s):  
K. W. Matta
Keyword(s):  
Finite Element ◽  
Dynamic Analysis ◽  
Degrees Of Freedom ◽  
General Purpose ◽  
Component Mode Synthesis ◽  
Complex Structures ◽  
Large Complex ◽  
Static Condensation ◽  
Basis Vectors ◽  
Selection Of

A technique for the selection of dynamic degrees of freedom (DDOF) of large, complex structures for dynamic analysis is described and the formulation of Ritz basis vectors for static condensation and component mode synthesis is presented. Generally, the selection of DDOF is left to the judgment of engineers. For large, complex structures, however, a danger of poor or improper selection of DDOF exists. An improper selection may result in singularity of the eigenvalue problem, or in missing some of the lower frequencies. This technique can be used to select the DDOF to reduce the size of large eigenproblems and to select the DDOF to eliminate the singularities of the assembled eigenproblem of component mode synthesis. The execution of this technique is discussed in this paper. Examples are given for using this technique in conjunction with a general purpose finite element computer program GENSAM[1].

Effective Shear Area in One Dimensional Ship Hull Finite Element Models to Predict Natural Frequencies of Vibration

2013 ◽  
Author(s):  
Osvaldo Pinheiro de Souza e Silva ◽  
Severino Fonseca da Silva Neto ◽  
Ilson Paranhos Pasqualino ◽  
Antonio Carlos Ramos Troyman
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Experimental Tests ◽  
Numerical Results ◽  
Computational Method ◽  
Scale Model ◽  
Dimensional Model ◽  
One Dimensional ◽  
Shear Area

This work discusses procedures used to determine effective shear area of ship sections. Five types of ships have been studied. Initially, the vertical natural frequencies of an acrylic scale model 3m in length in a laboratory at university are obtained from experimental tests and from a three dimensional numerical model, and are compared to those calculated from a one dimensional model which the effective shear area was calculated by a practical computational method based on thin-walled section Shear Flow Theory. The second studied ship was a ship employed in midshipmen training. Two models were made to complement some studies and vibration measurements made for those ships in the end of 1980 decade when some vibration problems in them were solved as a result of that effort. Comparisons were made between natural frequencies obtained experimentally, numerically from a three dimensional finite element model and from a one dimensional model in which effective shear area is considered. The third and fourth were, respectively, a tanker ship and an AHTS (Anchor Handling Tug Supply) boat, both with comparison between three and one dimensional models results out of water. Experimental tests had been performed in these two ships and their results were used in other comparison made after the inclusion of another important effect that acts simultaneously: the added mass. Finally, natural frequencies experimental and numerical results of a barge are presented. The natural frequencies numerical results of vertical hull vibration obtained from these approximations of effective shear areas for the five ships are finally discussed.

scholarly journals The method of direct finite perturbation of numerical models for studying of the dynamic, stiffness and strength properties for thin-walled elements of engineering constructions.

2014 ◽  
Vol 2014 (4) ◽  
pp. 114-124
Author(s):  
Юрий Костенко ◽  
Yuriy Kostenko ◽  
Анатолий Чепурной ◽  
Anatoliy Chepurnoy ◽  
Александр Литвиненко ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Natural Frequencies ◽  
Numerical Models ◽  
Dynamic Stiffness ◽  
Strength Properties ◽  
Test Problems ◽  
Finite Element Models ◽  
Direct Perturbation ◽  
Thin Walled

The methods of direct perturbation for finite element models of thin-walled engineering constructions for sensitivity analysis of their strength, stiffness and dynamic characteristics to the change in their thickness are proposed. The approach for prediction of distribution for natural frequencies migration as result of change in their thickness are presented. The applicability of the linearized models to determine displacements, stresses and natural frequencies slightly thinned design compared to the nominal (original) are shown. The examples of test problems are given.

Finite Element Analysis of Elliptical Chord

2013 ◽  
Vol 3 (4) ◽  
pp. 44-61
Author(s):  
K. S. Narayana ◽  
R. T. Naik ◽  
R. C. Mouli ◽  
L. V. V. Gopala Rao ◽  
R. T. Babu Naik
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Compressive Load ◽  
Dynamic Strength ◽  
Element Analysis ◽  
T Joints ◽  
Shell Elements ◽  
Tubular Joints ◽  
Plane Bending

The work presents the Finite element study of the effect of elliptical chords on the static and dynamic strength of tubular T-joints using ANSYS. Two different geometry configurations of the T-joints have been used, namely Type-1 and Type-2. An elastic analysis has been considered. The Static loading conditions used are: axial load, compressive load, In-plane bending (IPB) and Out-plane bending (OPB). The natural frequencies analysis (dynamic loading condition) has also been carried out. The geometry configurations of the T-joints have been used, vertical tubes are called brace and horizontal tubes are called chords. The joint consists of brace joined perpendicular to the circular chord. In this case the ends of the chord are held fixed. The material used is mild steel. Using ANSYS, finite element modeling and analysis of T-joint has been done under the aforementioned loading cases. It is one of the most powerful methods in use but in many cases it is an expensive analysis especially due to elastic–plastic and creep problems. Usually, three dimensional solid elements or shell elements or the combination of two types of elements are used for generating the tubular joints mesh. In tubular joints, usually the fluid induced vibrations cause the joint to fail under resonance. Therefore the natural frequencies analysis is also an important issue here. Generally the empirical results are required as guide or comparison tool for finite element investigation. It is an effective way to obtain confidence in the results derived. Shell elements have been used to model the assembled geometry. Finite element ANSYS results have been validated with the LUSAS FEA and experimental results, that is within the experimentation error limit of ten percentage.

Stiff-String Basis Functions for Vibration Analysis of High Speed Rotating Beams

2008 ◽  
Vol 75 (2) ◽  
Author(s):  
Jagadish Babu Gunda ◽  
Ranjan Ganguli
Keyword(s):  
Finite Element ◽  
High Speed ◽  
Natural Frequencies ◽  
Basis Functions ◽  
Beam Equation ◽  
Rotating Beam ◽  
Rotating Beams ◽  
Centrifugal Stiffening ◽  
Convergence Study ◽  
Stiffening Effect

A new rotating beam finite element is developed in which the basis functions are obtained by the exact solution of the governing static homogenous differential equation of a stiff string, which results from an approximation in the rotating beam equation. These shape functions depend on rotation speed and element position along the beam and account for the centrifugal stiffening effect. Using this new element and the Hermite cubic finite element, a convergence study of natural frequencies is performed, and it is found that the new element converges much more rapidly than the conventional Hermite cubic element for the first two modes at higher rotation speeds. The new element is also applied for uniform and tapered rotating beams to determine the natural frequencies, and the results compare very well with the published results given in the literature.

scholarly journals A Novel Highly Accurate Finite-Element Family

2017 ◽  
Vol 2017 ◽  
pp. 1-20
Author(s):  
Giovanni Bernardini ◽  
Fabio Cetta ◽  
Luigi Morino
Keyword(s):  
Finite Element ◽  
Structural Dynamics ◽  
Hermite Interpolation ◽  
Natural Frequencies ◽  
Finite Thickness ◽  
Three Dimensional ◽  
Numerical Results ◽  
Small Thickness ◽  
Modes Of Vibration ◽  
Patch Technique

A novel Nth order finite element for interior acoustics and structural dynamics is presented, with N arbitrarily large. The element is based upon a three-dimensional extension of the Coons patch technique, which combines high-order Lagrange and Hermite interpolation schemes. Numerical applications are presented, which include the evaluation of the natural frequencies and modes of vibration of (1) air inside a cavity (interior acoustics) and (2) finite-thickness beams and plates (structural dynamics). The numerical results presented are assessed through a comparison with analytical and numerical results. They show that the proposed methodology is highly accurate. The main advantages however are (1) its flexibility in obtaining different level of accuracy (p-convergence) simply by increasing the number of nodes, as one would do for h-convergence, (2) the applicability to arbitrarily complex configurations, and (3) the ability to treat beam- and shell-like structures as three-dimensional small-thickness elements.

Prediction of Blade Flutter in a Tuned Rotor

1985 ◽  
Author(s):  
Jianmin Xu ◽  
Zhaohong Song
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Rotating Blades ◽  
Multiple Degrees Of Freedom ◽  
Strip Theory ◽  
Blade Flutter ◽  
Good Agreement

This paper is about blade flutter in a tuned rotor. With the aid of the combination of three dimensional structural finite element method, two dimensional aerodynamical finite difference method and strip theory, the quasi-steady models in which two degrees of freedom for a single wing were considered have been extended to multiple degrees of freedom for the whole blade in a tuned rotor. The eigenvalues solved from the blade motion equation have been used to judge whether the system is stable or not. The calculating procedure has been formed and using it the first stage rotating blades of a compressor where flutter had occurred, have been predicted. The numerical flutter boundaries have good agreement with the experimental ones.

A Local Refinement Technique for B-Spline Finite Element Shell Modeling

2013 ◽  
Author(s):  
Antonio Carminelli ◽  
Giuseppe Catania
Keyword(s):  
Finite Element ◽  
Displacement Field ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Element Model ◽  
Complex Structures ◽  
Local Refinement ◽  
B Spline ◽  
Spline Finite Element ◽  
Shell Finite Element

This paper presents a refinement technique for a B2-spline degenerate isoparametric shell finite element model for the analysis of the vibrational behavior of thin and moderately thick-walled structures. Complex structures to be refined are modeled by means of FE B-spline patches assembled with C0 continuity as usual in FE technique. The model refinement was performed by adding, on the domain of the selected patch, a tensorial set of polynomial B-spline functions, defined on local clamped knot vectors, and normalizing all the functions so that the resulting displacement field remain polynomial and continuous overall the domain except on the boundaries of the refined subdomain. A degrees of freedom trasformation, based on the knot-insertion algorthim, is adopted in order to guarantee the C0 continuity of the displacement field on the boundaries of the refined subdomain. Two numerical examples are presented in order to test the proposed approach. The natural frequencies of two structures, computed by means of the proposed modelling technique, are compared with reference results available in the literature or computed by means of reference standard FE models. Strengths and limits of the approach are finally discussed.

Experimental and Numerical Investigations of Tractive Performance of Off-Road Tires on Gravel Terrain

2019 ◽  
Vol 17 (08) ◽  
pp. 1950055 ◽  
Author(s):  
Haiyang Zeng ◽  
Wei Xu ◽  
Mengyan Zang ◽  
Peng Yang
Keyword(s):  
Finite Element ◽  
Numerical Models ◽  
Three Dimensional ◽  
Great Influence ◽  
Coupling Method ◽  
Experimental Device ◽  
Tractive Force ◽  
3D Finite Element ◽  
Numerical Investigations ◽  
Soil Bin

In this work, an indoor soil-bin is designed to investigate the tire–terrain interaction mechanisms for the off-road tires rolling on the gravel terrain. The soil-bin test is carried out by the indoor soil-bin experimental device and the three-dimensional (3D) finite element (FE) and discrete element (DE) coupling method under the same particles conditions, respectively. First, with the indoor soil-bin measurement system, the repeatability of the soil-bin experiments is employed to validate the experimental device and the numerical models. Moreover, the tractive performance experiments of the off-road tires with two tread patterns, smooth and grooved interacting with gravel terrain, are performed at the slip of 10%, 20% and 30%, respectively, to obtain the tractive force and the rim sinkage. Second, the corresponding numerical models are also established, and simulated by the FE–DE coupling method, where the FEM and the DEM are used to describe the off-road tires and the gravel terrain, respectively. The tractive mechanisms of the off-road tires in interaction with the gravel terrain such as the tractive force and the rim sinkage are investigated numerically. Meanwhile, The dynamics and discontinuity of the gravel assembly are described by the presented approach. Besides, both the results of the simulations and experiments indicate that tread patterns and slip conditions have great influence on the tire tractive performance. Finally, the numerical simulations and the experimental results qualitatively show good agreements, which certifies the effectiveness of the FE–DE coupling method in the tractive performance analysis of tire–gravel terrain interactions.

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