The Effect of Close or Repeated Eigenvalues on the Updating of Model Parameters from FRF Data

1992 ◽  
Vol 114 (4) ◽  
pp. 514-520 ◽  
Author(s):  
M. I. Friswell ◽  
J. E. T. Penny
Keyword(s):  
Natural Frequencies ◽  
Analytical Models ◽  
Mode Shapes ◽  
Model Parameters ◽  
Finite Element Models ◽  
Reduced Order ◽  
Vibration Data ◽  
Modal Model ◽  
Equation Error ◽  
Error Method

Methods to update the parameters of finite element models using measured vibration data usually use the experimentally derived modal model, that is, the system natural frequencies, damping coefficients, and mode shapes. Alternatively the frequency response functions have been used directly to update condensed analytical models and so avoid the sometimes difficult step of deriving the modal model. Previously the authors suggested an algorithm using FRF data that is basically a weighted equation error method based on a reduced order model. This paper investigates the performance of the algorithm for systems with closely coupled or repeated natural frequencies or eigenvalues.

scholarly journals Comparison Between Calculated and Measured Free-Free Modes for a Flexible Rotor

1998 ◽  
Author(s):  
José A. Vázquez ◽  
Lloyd E. Barrett
Keyword(s):  
Natural Frequencies ◽  
Forced Response ◽  
Modal Testing ◽  
Analytical Models ◽  
Mode Shapes ◽  
Reduced Order Models ◽  
Response Functions ◽  
Flexible Rotor ◽  
Reduced Order ◽  
Response Characteristics

Many industrial machines nowadays are sold based on analysis performed on mathematical models of the rotors, bearings, substructures, and other components. The validity of the analysts therefore depends on the accuracy of the models themselves. When the rotor is available, modal testing may be used to validate the model of the rotor by comparing the calculated and measured free-free natural frequencies and mode shapes. This work presents additional tools for the verification of analytical models against experimental data. These tools use models of the rotor constructed from the measured data and the analytical model. A comparison of the first six calculated and measured free-free natural frequencies and mode shapes for a multi-mass flexible rotor is presented. The natural frequencies compare within 1.8%. The calculated and measured mode shapes were used to construct independent reduced order models of the rotor. These models were used to perform forced response and stability analyses. Forced response functions are presented comparing the forced response characteristics obtained from the two models. This provides a comparison between the measured and calculated forced response functions for the same number of modes. For the stability analysis, identical bearing models were added to both reduced order models. The eigenvalues were calculated using both models for a range of bearing stiffness and damping coefficients and were plotted for comparison.

scholarly journals High-Fidelity Sensitivity Analysis of Modal Properties of Mistuned Bladed Disks Regarding Material Anisotropy

2018 ◽  
Author(s):  
Adam Koscso ◽  
Guido Dhondt ◽  
E. P. Petrov
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Finite Element Models ◽  
Coordinate Systems ◽  
Bladed Disks ◽  
Bladed Disk ◽  
Material Orientation

A new method has been developed for sensitivity calculations of modal characteristics of bladed disks made of anisotropic materials. The method allows the determination of the sensitivity of the natural frequencies and mode shapes of mistuned bladed disks with respect to anisotropy angles that define the crystal orientation of the monocrystalline blades using full-scale finite element models. An enhanced method is proposed to provide high accuracy for the sensitivity analysis of mode shapes. An approach has also been developed for transforming the modal sensitivities to coordinate systems used in industry for description of the blade anisotropy orientations. The capabilities of the developed methods are demonstrated on examples of a single blade and a mistuned realistic bladed disk finite element models. The modal sensitivity of mistuned bladed disks to anisotropic material orientation is thoroughly studied.

scholarly journals Stochastic Modal Models of Slender Uncertain Curved Beams Preloaded Through Clamping

2012 ◽  
Author(s):  
Javier Avalos ◽  
Lanae A. Richter ◽  
X. Q. Wang ◽  
Raghavendra Murthy ◽  
Marc P. Mignolet
Keyword(s):  
Stochastic Model ◽  
Stiffness Matrix ◽  
Natural Frequencies ◽  
Simulated Data ◽  
Mode Shapes ◽  
Curved Beams ◽  
Shape Information ◽  
Final Shape ◽  
Modal Model ◽  
Clamped Beams

This paper addresses the stochastic modeling of the stiffness matrix of slender uncertain curved beams that are forced fit into a clamped-clamped fixture designed for straight beams. Because of the misfit with the clamps, the final shape of the clamped-clamped beams is not straight and they are subjected to an axial preload. Both of these features are uncertain given the uncertainty on the initial, undeformed shape of the beams and affect significantly the stiffness matrix associated with small motions around the clamped-clamped configuration. A modal model using linear modes of the straight clamped-clamped beam with a randomized stiffness matrix is employed to characterize the linear dynamic behavior of the uncertain beams. This stiffness matrix is modeled using a mixed nonparametric-parametric stochastic model in which the nonparametric (maximum entropy) component is used to model the uncertainty in final shape while the preload is explicitly, parametrically included in the stiffness matrix representation. Finally, a maximum likelihood framework is proposed for the identification of the parameters associated with the uncertainty level and the mean model, or part thereof, using either natural frequencies only or natural frequencies and mode shape information of the beams around their final clamped-clamped state. To validate these concepts, a simulated, computational experiment was conducted within Nastran to produce a population of natural frequencies and mode shapes of uncertain slender curved beams after clamping. The application of the above concepts to this simulated data led to a very good to excellent matching of the probability density functions of the natural frequencies and the modal components, even though this information was not used in the identification process. These results strongly suggest the applicability of the proposed stochastic model.

Updating of Non-Conservative Systems Using Inverse Methods

1997 ◽  
Author(s):  
Ladislav Starek ◽  
Milos Musil ◽  
Daniel J. Inman
Keyword(s):  
Analytical Model ◽  
Degrees Of Freedom ◽  
Ad Hoc ◽  
Natural Frequencies ◽  
Eigenvalue Problems ◽  
Model Updating ◽  
Analytical Models ◽  
Mode Shapes ◽  
Element Analysis ◽  
Modal Data

Abstract Several incompatibilities exist between analytical models and experimentally obtained data for many systems. In particular finite element analysis (FEA) modeling often produces analytical modal data that does not agree with measured modal data from experimental modal analysis (EMA). These two methods account for the majority of activity in vibration modeling used in industry. The existence of these discrepancies has spanned the discipline of model updating as summarized in the review articles by Inman (1990), Imregun (1991), and Friswell (1995). In this situation the analytical model is characterized by a large number of degrees of freedom (and hence modes), ad hoc damping mechanisms and real eigenvectors (mode shapes). The FEM model produces a mass, damping and stiffness matrix which is numerically solved for modal data consisting of natural frequencies, mode shapes and damping ratios. Common practice is to compare this analytically generated modal data with natural frequencies, mode shapes and damping ratios obtained from EMA. The EMA data is characterized by a small number of modes, incomplete and complex mode shapes and non proportional damping. It is very common in practice for this experimentally obtained modal data to be in minor disagreement with the analytically derived modal data. The point of view taken is that the analytical model is in error and must be refined or corrected based on experimented data. The approach proposed here is to use the results of inverse eigenvalue problems to develop methods for model updating for damped systems. The inverse problem has been addressed by Lancaster and Maroulas (1987), Starek and Inman (1992,1993,1994,1997) and is summarized for undamped systems in the text by Gladwell (1986). There are many sophisticated model updating methods available. The purpose of this paper is to introduce using inverse eigenvalues calculated as a possible approach to solving the model updating problem. The approach is new and as such many of the practical and important issues of noise, incomplete data, etc. are not yet resolved. Hence, the method introduced here is only useful for low order lumped parameter models of the type used for machines rather than structures. In particular, it will be assumed that the entries and geometry of the lumped components is also known.

Accuracies of Reduced Order Models of a Bladed Rotor With Geometric Mistuning

2013 ◽  
Vol 136 (7) ◽  
Author(s):  
Yasharth Bhartiya ◽  
Alok Sinha
Keyword(s):  
Natural Frequencies ◽  
Domain Analysis ◽  
Forced Response ◽  
Reduced Order Model ◽  
Mode Shapes ◽  
Reduced Order Models ◽  
Order Model ◽  
Reduced Order ◽  
Model Based ◽  
Bladed Rotor

The results from a reduced order model based on frequency mistuning are compared with those from recently developed modified modal domain analysis (MMDA). For the academic bladed rotor considered in this paper, the frequency mistuning analysis is unable to capture the effects of geometric mistuning, whereas MMDA provides accurate estimates of natural frequencies, mode shapes, and forced response.

Modified Modal Domain Analysis of a Bladed Rotor Using Coordinate Measurement Machine Data on Geometric Mistuning

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Vinod Vishwakarma ◽  
Alok Sinha ◽  
Yasharth Bhartiya ◽  
Jeffery M. Brown
Keyword(s):  
Natural Frequencies ◽  
Domain Analysis ◽  
Reduced Order Modeling ◽  
Forced Response ◽  
Mode Shapes ◽  
Reduced Order ◽  
Coordinate Measurement ◽  
Coordinate Measurement Machine ◽  
Bladed Rotor ◽  
Proper Orthogonal

Modified modal domain analysis (MMDA), a reduced order modeling technique, is applied to a geometrically mistuned integrally bladed rotor to obtain its natural frequencies, mode shapes, and forced response. The geometric mistuning of blades is described in terms of proper orthogonal decomposition (POD) of the coordinate measurement machine (CMM) data. Results from MMDA are compared to those from the full (360 deg) rotor Ansys model. It is found that the MMDA can accurately predict natural frequencies, mode shapes, and forced response. The effects of the number of POD features and the number of tuned modes used as bases for model reduction are examined. Results from frequency mistuning approaches, fundamental mistuning model (FMM) and subset of nominal modes (SNM), are also generated and compared to those from full (360 deg) rotor Ansys model. It is clearly seen that FMM and SNM are unable to yield accurate results whereas MMDA yields highly accurate results.

A Reduced-Order Model for Evaluating the Effect of Rotational Speed on the Natural Frequencies and Mode Shapes of Blades

2003 ◽  
Vol 125 (3) ◽  
pp. 772-776 ◽  
Author(s):  
P. Marugabandhu ◽  
J. H. Griffin
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Reduced Order Model ◽  
Mode Shapes ◽  
Finite Element Analyses ◽  
Order Model ◽  
Reduced Order ◽  
Low Aspect Ratio ◽  
Centrifugal Stiffening ◽  
Fan Blade

A reduced-order model has been developed that can be used to accurately and quickly calculate the changes in the natural frequencies and mode shapes of a blade that are caused by centrifugal stiffening. It has been corroborated by comparisons with finite element analyses of a cantilevered tapered plate and with frequencies from a low aspect ratio fan blade.

Extending Blind Modal Identification to the Underdetermined Case for Ambient Vibration

2012 ◽  
Author(s):  
Scot McNeill
Keyword(s):  
Natural Frequencies ◽  
Second Order ◽  
Modal Identification ◽  
Ambient Vibration ◽  
Mode Shapes ◽  
Frequency Domain Method ◽  
Blind Identification ◽  
Vibration Data ◽  
Modal Damping ◽  
Six Dof

The modal identification framework known as Blind Modal Identification (BMID) has recently been developed, drawing on techniques from Blind Source Separation (BSS). Therein, a BSS algorithm known as Second Order Blind Identification (SOBI) was adapted to solve the Modal IDentification (MID) problem. One of the drawbacks of the technique is that the number of modes identified must be less than the number of sensors used to measure the vibration of the equipment or structure. In this paper, an extension of the BMID method is presented for the underdetermined case, where the number of sensors is less than the number of modes to be identified. The analytic signal formed from measured vibration data is formed and the Second Order Blind Identification of Underdetermined Mixtures (SOBIUM) algorithm is applied to estimate the complex-valued modes and modal response autocorrelation functions. The natural frequencies and modal damping ratios are then estimated from the corresponding modal auto spectral density functions using a simple Single Degree Of Freedom (SDOF), frequency-domain method. Theoretical limitations on the number of modes identified given the number of sensors are provided. The method is demonstrated using a simulated six DOF mass-spring-dashpot system excited by white noise, where displacement at four of the six DOF is measured. All six modes are successfully identified using data from only four sensors. The method is also applied to a more realistic simulation of ambient building vibration. Seven modes in the bandwidth of interest are successfully identified using acceleration data from only five DOF. In both examples, the identified modal parameters (natural frequencies, mode shapes, modal damping ratios) are compared to the analytical parameters and are demonstrated to be of good quality.

scholarly journals Dynamic Response Of Tower Structures

2015 ◽  
Vol 2 ◽  
pp. 85
Author(s):  
Liga Gaile ◽  
Ivars Radinsh
Keyword(s):  
Finite Element ◽  
Structural Changes ◽  
Natural Frequencies ◽  
Resonance Effect ◽  
Dynamic Loads ◽  
Mode Shapes ◽  
Finite Element Models ◽  
Dynamic Parameters ◽  
Vibration Level ◽  
Tower Structure

The present study focuses on the tower type structures response to the dynamic loads. The study analyzes the possible mode shapes regarding to tower structure. The estimation of mode shapes and their dependence from structural changes was made for an existing tower structure. To get an acceptable tower’s vibration level and avoid possibility of resonance effect from usual serviceability loads it was evaluated options to change natural frequencies of the structure. It is performed existing 36m high sightseeing tower dynamic analysis and proposed potential solutions to increase critical natural frequencies of the structure. In this study to obtain dynamic parameters of the sightseeing tower structure have been used finite element models and calculation techniques.

On Frequency-Domain System Identification

1997 ◽  
Author(s):  
Eric L. Blades ◽  
Roy R. Craig
Keyword(s):  
System Identification ◽  
Frequency Domain ◽  
Mode Shapes ◽  
Finite Element Models ◽  
Identification Algorithm ◽  
Parameter System ◽  
Modal Damping ◽  
Stiffness Matrices ◽  
Modal Model ◽  
Vibration Tests

Abstract Over the past three decades vibration tests have frequently been conducted on structures and machines for the purpose of validating (updating) finite element models. Such testing is usually referred to as experimental modal analysis. The results of the vibration test are generally presented as a modal model consisting of natural frequencies, mode shapes, and modal damping factors, and the algorithms most frequently used to reduce the test data to modal-model form are time-domain algorithms. Alternatively, direct-parameter system identification may be performed, in which case the direct-parameter model consists of system mass, damping, and stiffness matrices. This paper discusses several features of a new frequency-domain direct-parameter system identification algorithm. Simulations based on a 52-DOF “payload simulator” are used to illustrate the performance of this algorithm.

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