| 1. |
- Abrahamsson, Thomas, 1956, et al.
(author)
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Calibration and cross-validation of a car component using frequency response functions and a damping equalization technique
- 2014
-
In: 26th International Conference on Noise and Vibration Engineering, ISMA 2014, Including the 5th International Conference on Uncertainty in Structural Dynamics, USD 2014. - 9789073802919 ; , s. 2625-2640
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Conference paper (peer-reviewed)abstract
- The calibration of an FE model of a car subframe is reported. In this calibration the minimum deviation between finite element model data and experimental data is searched for. The outcome of the calibrated model and cross-validation results are compared with results of testing being made on an ensemble of seemingly identical subframes. The subframe model has 250,440 degrees-of-freedom and the calibration is made for 16 uncertain model parameters. The efficiency of the calibration procedure under these conditions is reported. With model calibration being a cornerstone of the finite element validation procedure, the calibration problem is normally characterized as being a large scale optimization problem with many model parameters to solve for and with deviation metric that are nonlinear in these parameters. The calibrated parameters need to be found by iterative procedures, starting from initial estimates of parameter values. Sometimes these procedures get trapped in local deviation function minima and do not converge to the globally optimal calibration solution that is searched for. Here, a calibration formulation which gives a smooth deviation metric with a large radius of convergence to the global minimum is used. A method that utilizes damping equalization is used to avoid the mode correlation and mode pairing problem that need to be solved in various other model updating procedures. The method is combined with model reduction for increased speed and employs the Levenberg-Marquardt minimizer with randomized starts to achieve the calibration solution. The MATLAB-based open-domain software tool FEMcali has been used for calibration, validation and cross-validation.
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| 2. |
- Abrahamsson, Thomas, 1956, et al.
(author)
-
FEM calibration with FRF damping equalization
- 2014
-
In: Conference Proceedings of the Society for Experimental Mechanics Series. - Cham : Springer International Publishing. - 2191-5644 .- 2191-5652. - 9783319007670 ; 3, s. 265-278
-
Conference paper (peer-reviewed)abstract
- A finite element model calibration procedure that uses frequency response function data and relies on damping equalization is presented. In this, the dampings of the finite element model and the corresponding experimental model are set equal before calibration. The damping equalization is made to avoid the mode pairing problem that normally needs to be solved in other model updating procedures. It is demonstrated that one particular use of frequency response data gives a calibration deviation metric that is smooth in the variation of model parameters and give a large radius of convergence to the calibration minimum. The method is combined with model reduction for increased speed and employs a minimizing procedure that employs randomized multiple starting points in the parameter space to get to the calibration solution. The performance of the calibration procedure is demonstrated by two numerical examples. © The Society for Experimental Mechanics, Inc. 2014.
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| 3. |
- Chen, Yousheng, 1985-, et al.
(author)
-
Frequency Response Calculations of a Nonlinear Structure a Comparison of Numerical Methods
- 2014
-
In: Nonlinear Dynamics, Volume 2. - Cham : Springer. - 9783319045221 - 9783319045221 ; 2, s. 35-44
-
Conference paper (peer-reviewed)abstract
- Mechanical systems having presence of nonlinearities are often represented by nonlinear ordinary differential 5 equations. For most of such equations, exact analytic solutions are not found; thus numerical techniques have to be used. 6 In many applications, among which model calibration can be one, steady-state frequency response functions are the desired 7 quantities to calculate. 8 The objective of this paper is to compare the performance of computations of nonlinear frequency response functions 9 (FRFs) calculated directly within the frequency domain, using the Multi-Harmonic Balance method, with the time-domain 10 methods Runge–Kutta, Newmark and Pseudo Force in State Space (PFSS). The PFSS method is a recently developed state- 11 space based force feedback method that is shown to give efficient solutions. 12 The accuracy and efficiency of the methods are studied and compared using a model of a cantilever beam connected to a 13 non-linear spring at its free end.
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| 4. |
- Chen, Yousheng, 1985-, et al.
(author)
-
Model Calibration of a Locally Non-linear Structure Utilizing Multi Harmonic Response Data
- 2014
-
In: Nonlinear Dynamics, Volume 2. - Cham : Springer. - 2191-5644 .- 2191-5652. - 9783319045221 - 9783319045214 ; , s. 97-109
-
Conference paper (peer-reviewed)abstract
- Model correlation and model calibration using test data are natural ingredients in the process of validating computational models. Here, model calibration for the important sub-class of non-linear systems consisting of structures dominated by linear behavior having presence of local non-linear effects is studied. The focus is on the selection of uncertain model parameters together with the forming of the objective function to be used for calibration. To give precise estimation of parameters in the presence of measurement noise, the objective function data have to be informative with respect to the parameters chosen. Also, to get useful data the excitation force is here designed to be multi-harmonic since steady-state responses at the side frequencies are shown to contain valuable information for the calibration process. In this paper, test data from a replica of the Ecole Centrale de Lyon (ECL) nonlinear benchmark together with steady-state solutions stemming from calculations using the Multi-Harmonic Balancing method are used for illustration of the proposed model calibration procedure.
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| 5. |
- Chen, Yousheng, 1985-, et al.
(author)
-
Model calibration of locally nonlinear structures using information from sub and super harmonic responses
- 2012
-
In: International Conference on Noise and Vibration Engineering 2012 (ISMA 2012). - Leuven : Katholieke Universiteit Leuven, Department of Mechanical Engineering. - 9781622768257 ; , s. 2451-2464
-
Conference paper (other academic/artistic)abstract
- Large linear finite element models are commonly used in industry to represent global structural behavior and such models are often validated by use of data from vibrational tests. The validated models serve to predict the structural responses due to dynamic loads. Hence, it is important to have models that are able to represent the structural dynamics within the given operating envelope. When test data show proof of non linear behavior, a linear model may not be able to represent the dynamics well enough and thus a modification of the model is required. The main part of the structure may have a linear characteristic whereas localized physical processes can be sources of the observed nonlinearities. Model calibration of such locally nonlinear structures is studied in this paper. Specifically, the calibration process including the selection of appropriate data to be used for calibration of the model parameters chosen is treated. Here, synthetic test data stemming from a model of the Ecole Centrale de Lyon (ECL) nonlinear benchmark are used.
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| 6. |
- Gibanica, Mladen, 1988, et al.
(author)
-
Experimental-Analytical Dynamic Substructuring of Ampair Testbed: A State-Space Approach
- 2014
-
In: Conference Proceedings of the Society for Experimental Mechanics Series. - Cham : Springer International Publishing. - 2191-5644 .- 2191-5652. ; 1, s. 1-14
-
Conference paper (peer-reviewed)abstract
- The Society for Experimental Mechanics (SEM) Substructuring Focus Group has initiated a research project in experimental dynamic substructuring using the Ampair 600W wind turbine as a testbed. In this paper, experimental as well as analytical models of the blades of said wind turbine are coupled to analytical models of its brackets. The focus is on a state-space based substructuring method designed specifically for experimental-analytical dynamic substructuring. It is shown a) theoretically that the state-space method gives equivalent results to the second order methods under certain conditions, b) that the state-space method numerically produces results equivalent to those of a well-known frequency-based substructuring technique when the same experimental models are used for the two methods and c) that the state-space synthesis procedure can be translated to the general framework given by De Klerk et al.
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| 7. |
- Gibanica, Mladen, 1988, et al.
(author)
-
Spread in Modal Data Obtained From Wind Turbine Blade Testing
- 2014
-
In: Topics in Experimental Dynamic Substructuring, Conference Proceedings of the Society for Experimental Mechanics Series. - New York, NY : Springer New York. - 9781461465409 ; 2, s. 207-215
-
Conference paper (peer-reviewed)abstract
- This paper presents a pre-study for an on-going research project in experimental dynamic substructuring, initiated by the SEM Substructures Focus Group. The focus group has selected a small wind turbine, the Ampair 600W, to serve as test bed for the studies. The turbine blades are considered in this study. A total of twelve blades have been tested for modal properties in a free-free configuration. The data has been acquired and analysed by students participating in the undergraduate course ”Structural Dynamics - Model Validation” at Chalmers University of Technology. Each blade was tested by different students as part of their required course work to account for spread in modal properties between the blades. A subset of the blades weretested independently multiple times to account for variability in the test setup. Furthermore, correlation analysis of test data was made with Finite Element model eigensolution data of the blade.
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| 8. |
- Johansson, Anders, 1982, et al.
(author)
-
An experimental approach to improve controllability in test rigs using passive components
- 2012
-
In: Proceedings, International Conference on Noise and Vibration Engineering, ISMA2012; International Conference on Uncertainty in Structural Dynamics, USD2012. Editors : P. Sas, D. Moens, S. Jonckheere. KU Leuven (Belgium), 17 - 19 September 2012. - 9789073802896 ; 3, s. 2367-2381
-
Conference paper (peer-reviewed)abstract
- The first step in successful vibration testing is to calculate input signals such that the test rig accuratelyreplicates the reference signal. The Time Waveform Replication (TWR) method, or augmentations of it, isoften used to this end. TWR and similar methods most often result in a test output which closely replicates,or tracks, the reference signal; however, if there are eigenmodes of the test specimen in the desired frequencyrange of the test which are uncontrollable, it can be shown that the output error cannot be removed beyond theuncontrollable state’s contribution to the reference trajectory. For those specific cases, a method to improvetracking by the use of passive control components designed using a validated finite element (FE) model of thetest specimen has been previously proposed by the authors. In this article we propose instead an experimentalapproach, based on state-space substructure synthesis, to passive control components design for improvedtracking in controllability-lacking test rigs.
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| 9. |
- Johansson, Anders, 1982, et al.
(author)
-
Improving test rig performance using passive components
- 2012
-
In: Conference Proceedings of the Society for Experimental Mechanics Series. - New York, NY : Springer New York. - 2191-5644 .- 2191-5652. - 9781461424185 ; 6, s. 437-442
-
Conference paper (peer-reviewed)abstract
- The Time Waveform Replication (TWR) algorithm is presently used in industry for calculating the input force needed to replicate reference sensor outputs in a dynamic test rig. The feasible range of that input force is restricted by power supply and forcing rate limitations. If the force transfer paths of the reference test cannot be replicated in the test rig, lack of state controllability may cause unnecessarily large input forces and an increased remaining output error. We advocate the use of passive components to improve output tracking and limit input force demands of dynamic test rigs in the case that controllability is lacking. A method for introducing such passive components is described in this paper. It uses a virtual testing model of the test system with genetic algorithm optimization and TWR in the loop to calculate the position and dynamic properties of the proposed passive component.
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| 10. |
- Johansson, Anders, 1982, et al.
(author)
-
Improving the TWR algorithm using passive control components
- 2011
-
In: Svenska Mekanikdagar 13-15 juni 2011 Chalmers Göteborg (T. Abrahmsson, A. Boström, L. Davidson, W. Kropp, H. Nilsson, K. Runesson, U. Stigh, eds.). ; , s. 11-
-
Conference paper (other academic/artistic)
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| 11. |
- Johansson, Anders, 1982, et al.
(author)
-
Model calibration and uncertainty of A600 wind turbine blades
- 2014
-
In: Model Validation and Uncertainty Quantification, Volume 3. - Cham : Springer. - 2191-5644 .- 2191-5652. - 9783319045511 ; , s. 215-227
-
Conference paper (peer-reviewed)abstract
- Recently, a lot of work has been made on modeling, testing and calibrating Ampair 600W wind turbine blades, owing to the use of that turbine as a test bed structure for the Dynamic Substructuring Focus Group within the Society of Experimental Mechanics. In Sweden alone, more than 20 blades have been tested for dynamical properties, geometrical differences and material properties as was presented in several papers at IMAC XXXI. The quantity of blades, originating from different manufacturing batches, makes them ideal for investigations of component variability.In this paper, measurement variability predominantly stemming from the difference between individual blades is propagated backwards to model parameters, using model calibration techniques, in an effort to quantify their uncertainties. The coupling between spread in structural properties such as mass, center of gravity together with blade twist angles and spread in the resulting blade dynamics is shown.
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| 12. |
- Johansson, Anders, 1982, et al.
(author)
-
Modeling and Calibration of Small-scale Wind Turbine Blade
- 2014
-
In: Topics in Experimental Dynamic Substructuring, Volume 2, Proceedings of the 31st IMAC, A Conference on Structural Dynamics, 2013. - New York, NY : Springer New York. - 2191-5644. ; 36:2, s. 51-58
-
Conference paper (peer-reviewed)abstract
- The SEM Substructuring Focus Group has chosen an Ampair 600W wind turbine to be used as a test bed in the continued efforts to further experimental and experimental-analytical substructure coupling techniques. To assess such coupling techniques, validated models of the parts, the substructures considered, play a crucial role. This paper describes the modeling, calibration and validation of a Finite Element (FE) model of a blade for the test bed turbine. State-of-the-art composite material modeling is used to set up the model, which is calibrated and validated based on results from an ambitious measurement campaign including both nondestructive testing for dynamic properties and dedicated destructive tests for deduction of material properties. The measurement campaign is carefully described in the paper.
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| 13. |
- Johansson, Anders, 1982, et al.
(author)
-
Selecting Appropriate Analytical Mode Basis for SEREP-expansion of Experimental Modes
- 2011
-
In: Proceedings of the 29th IMAC, A Conference on Structural Dynamics, 2011. - 2191-5644. - 9781441992987 ; 3
-
Conference paper (other academic/artistic)abstract
- Since being introduced in 1986, the System Equivalent Reduction ExpansionProcess (SEREP) has been used to expand experimental eigenvector elementsto the number of degrees-of-freedom of an associated FE-model. In fact, expansionfor interpolation and extrapolation was its original purpose. Since then, studies ofSEREP and other reduction/expansion methods have been abundant. A remarkablenumber of these have concentrated on the selection of master degrees of freedomfor model reduction. Few have however considered the modal basis best used whenSEREP is used for expansion.Expanded experimental modes are expected to correlate well with their analyticalsiblings. However, we argue that the degree of global correlation should only be inparity with the local correlation between the analytical and experimental modes atlocations where measurements are made. Since SEREP is a method which basicallyapproximates a measured mode by a linear combination of analytical modes, perfectagreement between the expanded experimental and analytical modes is easilyachieved, e.g. by simply using only one single mode for expansion. Of course, inthis way the expanded mode normally has very little in common with the measuredmode. On the other hand, using too many modes may result in something similarto the well known problem of fitting a high-order polynomial to noisy data: Perfectagreement at measurement locations is achieved at the expense of unrealisticdeviations and large curvatures between these. To make sure that the experimentalmode has been expanded in a manner faithful to the actual measurements, it is thereforereasonable to use a correlation based criterion in the selection of the expansionbasis. Such a criterion is presented in the present paper.
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| 14. |
- Khorsand Vakilzadeh, Majid, 1984, et al.
(author)
-
An improved modal approach for model reduction based on input-output relation
- 2012
-
In: International Conference on Noise and Vibration Engineering (ISMA) / International Conference on Uncertainty in Structural Dynamics (USD). KU Leuven, Dept Mech Engn, Leuven, BELGIUM. SEP 17-19, 2012. - 9789073802896 ; 5, s. 3451-3459
-
Conference paper (peer-reviewed)abstract
- An approximated model of a large scale dynamical system captures its main features by a proper selection of its dominant modes. In this paper, a new metric is presented for modal dominancy analysis. This metric is an explicit formulation for evaluating the participation of each mode, independent from the other modes, into the output. Only eigensolutions with a large contribution to this metric, the dominant eigensolutions, will be retained in the approximating lower order model. The modal truncation technique which includes the proposed dominancy analysis not only has a metric for error estimation, but is able to automatically detect and eliminate unobservable and uncontrollable modes. An example from finite element analysis of an aluminum plate illustrates the approach and shows that the proposed method is very efficient in respect to computational time.
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| 15. |
- Khorsand Vakilzadeh, Majid, 1984, et al.
(author)
-
Development of simplified models for wind turbine blades with application to NREL 5MW offshore research wind turbine
- 2014
-
In: Conference Proceedings of the Society for Experimental Mechanics Series. - Cham : Springer International Publishing. - 2191-5644 .- 2191-5652. - 9783319007700 ; 1, s. 389-402
-
Conference paper (peer-reviewed)abstract
- Integration of complex models of wind turbine blades in aeroelastic simulations places an untenable demand on computational resources and, hence, means of speed-up become necessary. This paper considers the process of producing simplified rotor blade models which accurately approximate the dynamics of interest. The novelty, besides applying an efficient model updating procedure to the wind turbine blade, is to challenge the conventional beam element formulation utilized in the majority of aeroelastic codes. First, a 61.5 m blade, previously reported by the National Renewable Energy Laboratory, is selected as a case study and a verified industry-standard three dimensional shell model is developed based on its actual geometry. Next, given the reported spanwise cross sectional properties of the blade, a calibrated beam model is developed, using an efficient model updating process, that shows an excellent agreement to the low frequency dynamics of the baseline model in terms of mode shapes, resonance frequency and frequency response function. The simulation study provides evidence that a beam model cannot capture all the important features found in a large-scale 3D blade. This motivates a departure from conventional beam element formulation and suggests addressing the problem of producing simplified models in the framework of model reduction techniques. A modified modal truncation algorithm is applied to the baseline model to produce a simpler model which accurately approximates its input-output behavior in a given frequency range. It is concluded that besides the computational efficiency of the reduction algorithm, the resulting approximation error is guaranteed to be bounded and the yielded low-order model can, in turn, be served in wind turbine design codes.
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| 16. |
- Khorsand Vakilzadeh, Majid, 1984, et al.
(author)
-
Manifold Metropolis adjusted Langevin algorithm for high-dimensional Bayesian FE
- 2014
-
In: Proceedings of the International Conference on Structural Dynamic , EURODYN. - 2311-9020. - 9789727521654 ; 2014-January, s. 3029-3036
-
Conference paper (peer-reviewed)abstract
- Bayesian finite element model updating provides a rigorous framework to take various sources of uncertainty, such as uncertainties in observation, modeling and prior knowledge, into account when characterizing uncertainty in model parameters, through updates of their joint probability density function. The Markov chain Monte Carlo methods are currently the most popular simulation techniques for producing samples from the posterior probability density functions of the uncertain parameters. However, the effectiveness of these approaches is adversely affected by the dimension and correlation structure of the model parameter space. This paper presents the application of a manifold based Metropolis adjusted Langevin algorithm forsolving high-dimensional model updating problems in structural dynamics. It exploits the Riemannian geometry of the model parameters to help construct proposal densities which closely approximate the target density. Thus, the Markov chain explores the target density faster. Practical issues for applicability of the proposed algorithm for the Bayesian FE model updating problem are illustrated using simulated data for a six degrees of freedom mass-spring model with up to 16 parameters to be calibrated.
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| 17. |
- Khorsand Vakilzadeh, Majid, 1984, et al.
(author)
-
Modal Reduction Based on Accurate Input-Output Relation Preservation
- 2014
-
In: Conference Proceedings of the Society for Experimental Mechanics Series. - New York, NY : Springer New York. - 2191-5644 .- 2191-5652. - 9781461465843 ; 45:7, s. 333-342
-
Conference paper (peer-reviewed)abstract
- An eigenmode based model reduction technique is proposed to obtain low-order models which contain the dominanteigenvalue subspace of the full system. A frequency-limited interval dominancy is introduced to this technique to measure the output deviation caused by deflation of eigenvalues from the original system in the frequency range of interest. Thus, the dominant eigensolutions with effective contribution can be identified and retained in the reduced-order model. This metric is an explicit formula in terms of the corresponding eigensolution. Hence, the reduction can be made at a low computational cost. In addition, the retained low-order model does not contain any uncontrollable and unobservable eigensolutions. The performance of the created reduced-order models, in regard to the approximation error, is examined by applying three different input signals; unit-impulse, unit-step and linear chirp.
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| 18. |
- Liljerehn, A., et al.
(author)
-
Dynamic sub-structuring with passive state-space components
- 2014
-
In: 26th International Conference on Noise and Vibration Engineering, ISMA 2014, Including the 5th International Conference on Uncertainty in Structural Dynamics, USD 2014; Leuven; Belgium; 15 September 2014 through 17 September 2014. - 9789073802919 ; , s. 3879-3890
-
Conference paper (peer-reviewed)abstract
- Component synthesis regards modeling of complex dynamic structures by decomposing the structure into smaller simpler components, modeling each component or sub-structure individually and then assemble the components to construct the complete dynamic structure model. The methodology allows for a mixture of experimental and analytical models of sub-structures to be assembled into a coupled system model. There are a number of component synthesis methods that stands at disposal. In this paper we use state-space component synthesis to assemble two state-space sub-components of a test rig. One sub-component model is based on measured frequency response data and the other is based on a Finite Element (FE) modeled component and the coupled structure is validated against reference measurements. The paper also investigates and shows the necessity of physically consistent experimentally derived sub-system models in component synthesis and presents a new methodology for passivity enforcement on state-space models.
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| 19. |
- Liljerehn, Anders, 1979, et al.
(author)
-
Dynamic substructuring in metal cutting machine chatter
- 2010
-
In: Proceedings of ISMA2010 International Conference on Noise and Vibration Engineering Including USD2010, Leuven, 20-22 September 2010. - 9789073802872
-
Conference paper (peer-reviewed)abstract
- In metal cutting, spindle speed optimization for process stability is one example of action that may reduceproduction time and increase process reliability. For process stability, it is crucial to avoid regenerativevibrations and thereby enable larger cutting depth, with higher material removal rate as benefit. A spindlespeed optimization is usually based on the machine tool and cutting tool assembly’s frequency response atthe tool-tip. This is normally obtained by dynamic testing of the full assembly. In this paper we use areceptance coupling technique to reduce testing time by synthesizing the frequency response displacementfunction of the system. The method utilizes test data of the machine tool with an inserted blank tooltogether with a finite element representation of the real cutting tool. The coupling is made via a state spacecoupling technique. Comparisons are made with data from full system tests and a stability prediction isdemonstrated.
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| 20. |
- Liljerehn, A., et al.
(author)
-
Experimental-analytical substructure model sensitivity analysis for cutting machine chatter prediction
- 2012
-
In: Conference Proceedings of the Society for Experimental Mechanics Series. - New York, NY : Springer New York. - 2191-5644 .- 2191-5652. - 9781461424215 ; 2, s. 11-20
-
Conference paper (peer-reviewed)abstract
- Process reliability and dynamic stability is a growing customer demand in the metal machining industry. A limiting factor in process stability is regenerative vibrations which may damage the machined component, the cutting tool and even the machine tool. Spindle speed optimization to ensure process stability and enable larger cutting depths is based on the machine tool and cutting tool assembly's frequency response at the tool-tip. The traditional procedure to retrieve the tool-tip frequency response is to conduct dynamic testing of each machine tool mounted cutting tool. This methodology is normally very time-consuming. In an attempt to reduce testing time, receptance coupling substructure analysis (RCSA) has been proposed by a number of researchers. The objective with this approach is to measure the machine tool structure once and then couple a finite element based substructure representation of the cutting tool of interest. The accuracy of the predicted tool-tip frequency response is then dependent on the quality of measured data. This paper details the state-space based sub-structure coupling technique that is used and presents a sensitivity analysis. This analysis distinguishes key considerations for the machine tool component test and it quantifies the parameter influence on the process stability predictions of the coupled system.
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| 21. |
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| 22. |
- Linderholt, Andreas, 1974, et al.
(author)
-
Finding local non-linearities using error localization from model updating theory
- 2012
-
In: Conference Proceedings of the Society for Experimental Mechanics Series. - New York, NY : Springer New York. - 2191-5644 .- 2191-5652. - 9781461424154 ; 3, s. 323-334
-
Conference paper (peer-reviewed)abstract
- Within the aerospace industry, linear finite element models are traditionally used to describe the global structural dynamics of an aircraft. Ground vibration test data serve to facilitate the validation of models which are then used to characterize the aeroelastic behavior of the aircraft and to predict the responses due to dynamic loads. Thus, it is vital that the models contain the essential dynamics of the aircraft. Observed nonlinearities are judged to be local in nature whereas the main part of the structure behaves linearly under normal loading. In this work we focus on the identification of nonlinear effects and do that based on model updating theory. That includes methods for error localization with proper selection of candidate error parameters. The nonlinearities are treated as local modeling errors not considered in the linear system model. The error localization behavior is studied using synthetic test data from a simple system, known as the ECL Benchmark, with known nonlinear properties.
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| 23. |
- Rahrovani, Sadegh, 1981, et al.
(author)
-
A Metric for Modal Truncation in Model Reduction Problems Part 1: Performance and Error Analysis
- 2014
-
In: Conference Proceedings of the Society for Experimental Mechanics Series. - New York, NY : Springer New York. - 2191-5644 .- 2191-5652. - 9781461465843 ; 7:7, s. 781-788
-
Conference paper (peer-reviewed)abstract
- The strength of the modal based reduction approach resides in its simplicity, applicability to treat moderate-size systems and also in the fact that it preserves the original system pole locations. However, the main restriction has been in the lack of reliable techniques for identifying the modes that dominate the input-output relationship. To address this problem, an enhanced modal dominancy approach for reduction of second-order systems is presented. Briefly stated, a modal reduction approach is combined with optimality considerations such that the difference between the frequency response function of the full and reduced modal model is minimized in H2 sense. A modal ranking process is performed without solving Lyapunov equations. In the first part of this study, a literature survey on different model reduction approaches and a theoretical investigation of the modified modal approach is presented. The error analysis of the proposed dominancymetric is carried out. Furthermore, the performance of the method is validated for a lightly damped structure and the results are compared with other dominancy metrics. Finally the optimality of the obtained reduced model is discussed and the results are compared with the optimum solution.
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| 24. |
- Rahrovani, Sadegh, 1981, et al.
(author)
-
A Metric for Modal Truncation in Model Reduction Problems Part 2: Extension to Systems with High-Dimensional Input Space
- 2014
-
In: Conference Proceedings of the Society for Experimental Mechanics Series. - New York, NY : Springer New York. - 2191-5644 .- 2191-5652. - 9781461465843 ; 7:7, s. 789-796
-
Conference paper (peer-reviewed)abstract
- In the first part of this study, a theoretical investigation of an improved modal approach and a complete error analysis of the proposed modal dominancy metric were presented. In this part the problem of metric non-uniqueness for systems with multiple eigenvalues is described and a method to circumvent this problem based on spatial distribution of either the sensors or the actuators is proposed. This technique is implemented using QR factorization without solving Lyapunov equations. Moreover, the method is improved such that it is able to use the information extracted from spectral properties of the input. Also in order to make the method more effective, information extracted from the input internal structure is incorporated in the modal ranking process. It is shown that this improvement is particularly effective in problems with high-dimensional input and/or output space such as in distributed loading and moving load problems. Finally the performance of the method is validated for a high order system subjected to a high-dimensional input force. That originates from a railway track moving load problem.
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| 25. |
- Rahrovani, Sadegh, 1981, et al.
(author)
-
A new parameter perturbation method suitable for reliability analysis of large dynamic systems
- 2013
-
In: Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures - Proceedings of the 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013. - 9781138000865 ; , s. 5343-5349
-
Conference paper (peer-reviewed)abstract
- To decrease the computational efforts needed for reliability analysis of large-scale finite element (FE) models, fast simulation is a necessity. To achieve this, model reduction approach offers a systematic way to capture the main input-output behaviour of the original dynamic model with a simpler one. However to be useful for reliability analysis, the approximant must provide a good accuracy for a range of stochastic parameters variation. This problem is addressed by introducing a reduced modal basis based on a reference Linear Time Invariant (LTI) FE model.Amethod is employed that uses an iterative algorithm to obtain perturbed solutions that are due to the effects of parameter variation. The main idea is to iteratively approximate the perturbed solution in the space spanned by reduced basis. This technique is used to develop an adaptive reliability method. In a numerical example, this approach is applied to a railway track problem.
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| 26. |
- Rahrovani, Sadegh, 1981, et al.
(author)
-
An Efficient Exponential Integrator for Large Nonlinear Stiff Systems Part 1: Theoretical Investigation
- 2014
-
In: Conference Proceedings of the Society for Experimental Mechanics Series. - Cham : Springer International Publishing. - 2191-5644 .- 2191-5652. - 9783319045214 ; 2, s. 259-268
-
Conference paper (peer-reviewed)abstract
- In the first part of this study an exponential integration scheme for computing solutions of large stiff systems isintroduced. It is claimed that the integrator is particularly effective in large-scale problems with localized nonlinearity when compared with the general purpose methods. A brief literature review of different integration schemes is presented and theoretical aspect of the proposed method is discussed in detail. Computational efficiency concerns that arise in simulation of large-scale systems are treated by using an approximation of the Jacobian matrix. This is achieved by combining theproposed integration scheme with the developed methods for model reduction, in order to treat the large nonlinear problems.In the second part, geometric and structural properties of the presented integrator are examined and the preservation of these properties such as area in the phase plane and also energy consistency are investigated. The error analysis is given through small scale examples and the efficiency and accuracy of the proposed exponential integrator is investigated through a large-scale size problem that originates from a moving load problem in railway mechanics. The superiority of the proposedmethod in sense of computational efficiency, for large-scale problems particularly system with localized nonlinearity, has been demonstrated, comparing the results with classical Runge–Kutta approach.
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| 27. |
- Rahrovani, Sadegh, 1981, et al.
(author)
-
An Efficient Exponential Integrator for Large Nonlinear Stiff Systems Part 2: Symplecticity and Global Error Analysis
- 2014
-
In: Conference Proceedings of the Society for Experimental Mechanics Series. - Cham : Springer International Publishing. - 2191-5644 .- 2191-5652. - 9783319045214 ; 2, s. 269-280
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Conference paper (peer-reviewed)abstract
- In the first part of this study an exponential integration scheme for computing solutions of large stiff systems was presented. It was claimed that the integrator is particularly efficient in large-scale problems with localized nonlinearity when compared to general-purpose methods. Theoretical aspects of the proposed method were investigated. The method computational efficiency was increased by using an approximation of the Jacobian matrix. This was achieved by combining the proposed integration scheme with the developed methods for model reduction, in order to treat the large nonlinear problems. In this second part geometric and structural properties of the presented integration algorithm are examined and preservation of these properties such as area in the phase plane and also energy consistency are investigated. The error analysis is given through small scale examples and the efficiency and accuracy of the proposed exponential integrator is investigated through a large-scale size problem that originates from a moving load problem in railway mechanics. The superiority of the proposed method in sense of computational efficiency, for large-scale problems particularly system with localized nonlinearity, has been demonstrated, comparing the results with classical Runge–Kutta approach.
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| 28. |
- Rahrovani, Sadegh, 1981, et al.
(author)
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Integration of Hamiltonian systems with a structure preserving algorithm
- 2014
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In: 26th International Conference on Noise and Vibration Engineering, ISMA 2014, Including the 5th International Conference on Uncertainty in Structural Dynamics, USD 2014; Leuven; Belgium; 15 September 2014 through 17 September 2014. - 9789073802919 ; , s. 2915-2929
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Conference paper (peer-reviewed)abstract
- The disability of classical general-purpose integrators, such as the Runge-Kutta integrators, to exploit/preserve the structure of the analytical system and the failure of traditional structure-preserving geometric integrators, such as the leapfrog method, in treating highly oscillatory problems has been the main motivation for development of a recently proposed symplectic exponential integrator. Here, the capability of the method in robust simulation of Hamiltonian systems with complex dynamical behaviour, such as the elastic pendulum benchmark, is studied. The method exactly conserves the motion invariants, such as the angular momentum, while approximately conserves the Hamiltonian function. Furthermore, the method performance has been validated for systems with highly oscillatory behavior. These advantages are of particular interest for a variety of problems encountered in mechanical engineering applications, such as simulation of spacecraft structures, rotor blades, and similar systems.
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| 29. |
- Rahrovani, Sadegh, 1981, et al.
(author)
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Modal Dominancy Analysis Based on Modal Contribution to Frequency Response Function ℋ2-Norm
- 2014
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In: Mechanical Systems and Signal Processing. - : Elsevier BV. - 0888-3270 .- 1096-1216. ; 48:1-2, s. 218-231
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Journal article (peer-reviewed)abstract
- A main restriction in the general applicability of modal reduction techniques has been the lack of a proper dominancy analysis as well as the lack of a guaranteed bound for the approximation error. In this study, a modal dominancy approach for reduction of dynamical systems is presented. A quadratic-metric, introduced based on modal contribution to the ℋ2ℋ2-norm of the frequency response function matrix, is given in closed-form formulation. Briefly stated, a performance and error analysis of the proposed modal dominancy procedure is carried out, the problem of metric non-uniqueness as well as the treatment of structural non-minimality for a class of systems with multiple eigenvalues is described, and a method to circumvent this problem is proposed. In treating problems with high-dimensional input space, such as in moving and/or distributed loading problems, the presented method is an improvement as it incorporates information extracted from the structural and spectral properties of the input force in the modal dominancy analysis. In addition, the method׳s performance is validated for reduction of a large-scale finite element model, originated from a moving load problem in railway mechanics, and the results are compared with the balancing approach.
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| 30. |
- Rahrovani, Sadegh, 1981, et al.
(author)
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On Gramian-Based Techniques for Minimal Realization of Large-Scale Mechanical Systems
- 2014
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In: Conference Proceedings of the Society for Experimental Mechanics Series. - New York, NY : Springer New York. - 2191-5644 .- 2191-5652. - 9781461465843 ; 45:7, s. 797-805
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Conference paper (peer-reviewed)abstract
- Abstract In this paper, a review of Gramian-based minimal realization algorithms is presented, several comments regarding their properties are given and the ill-condition and efficiency that arise in balancing of large-scale realizations is being addressed. A new algorithm to treat non-minimal realization of very large second-order systems with dense clusters of close eigenvalues is proposed. The method benefits the effectiveness of balancing techniques in treating of non-minimal realizations in combination with the computational efficiency of modal techniques to treat large-scale problems.
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| 31. |
- Rahrovani, Sadegh, 1981, et al.
(author)
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On Grammian-based reduction methods for moderate size systems
- 2012
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In: 19th International Congress on Sound and Vibration 2012, ICSV 2012. - 9781622764655 ; 1, s. 73-80
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Conference paper (peer-reviewed)abstract
- Over the last decades, there has been a constantly increasing interest in the compact reduced dynamical models. The central idea of model reduction is to systematically capture the main input-output properties by a much simpler model than needed for describing the entire states of the system. Among the most popular model reduction approaches, particularly in systems in the order of a couple of thousands, singular value decomposition based are most common model reduction schemes. In this note, a survey of Grammian-based model reduction techniques for moderate size systems is presented. Comments regarding their properties and discussion about their computational issues are given. Computational efforts needed in reduction methods based on Sylvester and Lyapunov equation are being compared. This investigation is followed by a numerical moderate-size example with dense clusters of close eigenvalues. Finally, results of the competing reduction approaches are compared with respect to computational cost and approximation error for same size approximants.
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| 32. |
- Yaghoubi Nasrabadi, Vahid, 1985, et al.
(author)
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An efficient simulation method for structures with local nonlinearity
- 2014
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In: Conference Proceedings of the Society for Experimental Mechanics Series. - Cham : Springer International Publishing. - 2191-5644 .- 2191-5652. - 9783319045214 ; 2, s. 141-149
-
Conference paper (peer-reviewed)abstract
- In general, simulating the nonlinear behavior of systems needs a lot of computational effort. Since researchers in different fields are increasingly targeting nonlinear systems, attempts toward fast nonlinear simulation have attracted much interest in recent years. Examples of such fields are system identification and system reliability. In addition to efficiency, the algorithmic stability and accuracy need to be addressed in the development of new simulation procedures. In this paper, we propose a method to treat localized nonlinearity in a structure in an efficient way. The system will be separated by a linearized part and a nonlinear part that is considered as external pseudo forces that act on the linearized system. The response of the system is obtained by iterations in which the pseudo forces are updated. Since the method is presented in linear state space model form, all manipulations that are made on these, like similarity transformations and model reduction, can easily be exploited. To do numerical integration, time-stepping schemes like the triangular hold interpolation can be used to the advantage. We demonstrate the efficiency, stability and accuracy of the method on numerical examples.
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| 33. |
- Yaghoubi Nasrabadi, Vahid, 1985, et al.
(author)
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Application of an automated modal analysis based on frequency response function estimates
- 2012
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In: 25th International Conference on Noise and Vibration engineering, ISMA2012 in conjunction with the 4th International Conference on Uncertainty in Structural Dynamics, USD 2012; Leuven; Belgium; 17 September 2012 through 19 September 2012. - 9789073802896 ; 3, s. 2145-2155
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Conference paper (peer-reviewed)abstract
- Given measured data as estimated frequency responses of a quasi-linear system, there is a variety of system identification methods that identify a state-space model that gives good correlation to the data. Such methods are the N4SID and the PolyMAX methods. Using these methods, a key problem is to select the proper model order. An Automated Modal Analysis was developed in our group to find the proper model order. This method is based on the statistical evaluation of an ensemble of state-space models all identified from the same basic set of frequency response functions, but with different realizations based on a bootstrapping scheme. In this work, we made that method more robust and applied it to two real test data sets.
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| 34. |
- Yaghoubi Nasrabadi, Vahid, 1985, et al.
(author)
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Automated modal analysis based on frequency response function estimates
- 2012
-
In: Conference Proceedings of the Society for Experimental Mechanics Series. - New York, NY : Springer New York. - 2191-5644 .- 2191-5652. - 9781461424246 ; 5, s. 9-18
-
Conference paper (peer-reviewed)abstract
- Given measured data as estimated frequency responses of a quasi-linear system, there is a variety of system identification methods that identify a state-space model that gives good correlation to the data. Such methods are the N4SID and the PolyMAX methods. Using these methods, a key problem is to select the proper model order. In this work we investigate a method for the automatic detection of proper model order. The method is based on the statistical evaluation of an ensemble of state-space models all identified from the same basic set of frequency response functions, but with different realizations based on a bootstrapping scheme. We apply the method to real test data.
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| 35. |
- Yaghoubi Nasrabadi, Vahid, 1985, et al.
(author)
-
Automated Modal Analysis Based on Statistical Evaluation of Frequency Responses
- 2014
-
In: Conference Proceedings of the Society for Experimental Mechanics Series. - New York, NY : Springer New York. - 2191-5644 .- 2191-5652. - 9781461465843 ; 45:7, s. 479-486
-
Conference paper (peer-reviewed)abstract
- This paper presents a newly developed method for obtaining the modal model with a proper model order from experimental frequency response functions (FRF). The method is a multi-step procedure which commences with the identification of a high-order state-space model, Exhaustive Model (EM), using the full FRF data set. Then, modal states that give small contribution to the output, quantified by a metric associated to the observability grammian, are rejected from the EM resulting in a Reference Model (RM). Competing models, with the same model order as the RM, are then found by bootstrapping realization using same-size fractions of the full FRF. Eigensolutions of the Bootstrapping Models (BMs) are then paired by the eigensolutions of the RM based on high Modal Observability Correlation (MOC) indices. In a second reduction stage, the modal states with low MOC index are rejected from the BMs. Final model is found by an averaging through BMs. Only one threshold quantity, related to observability grammians need to be set by the user. The method thus requires very little user interaction. The method is applied to experimental data used in a previous IMAC Round Robin exercise for experimental modal analysis evaluation. © The Society for Experimental Mechanics 2014.
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| 36. |
- Yaghoubi Nasrabadi, Vahid, 1985, et al.
(author)
-
Efficient simulation method for nonlinear structures: methodology and stability consideration
- 2014
-
In: Proceedings of the International Conference on Structural Dynamic , EURODYN. - 2311-9020. - 9789727521654 ; 2014-January, s. 1853-1858
-
Conference paper (peer-reviewed)abstract
- In general, simulating the nonlinear behavior of systems needs a lot of computational effort. Since researchers in different fields are increasingly targeting nonlinear systems, attempts toward fast nonlinear simulation have attracted much interest in recent years. Examples of such fields are system identification and system reliability. In addition to efficiency, the algorithmic stability and accuracy need to be addressed in the development of new simulation procedures. In this paper, we propose a method to treat localized nonlinearity in a structure in an efficient and accurate way. The method is conditionally stable. The system will be separated by a linearized part and a nonlinear part that is considered as external pseudo forces that act on the linearized system. The response of the system is obtained by iterations in which the pseudo forces are updated. Since the method is presented in linear state space model form, all manipulations that are made on these, like similarity transformations and model reduction, can easily be exploited. To do numerical integration, time-stepping schemes like the triangular hold interpolation can be used to the advantage. To increase the accuracy and stability of the method, second-order hold equivalent is derived and implemented. We demonstrate the efficiency, stability and accuracy of the method on numerical examples.
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| 37. |
- Yaghoubi Nasrabadi, Vahid, 1985, et al.
(author)
-
Locally Non-Linear Model Calibration Using Multi Harmonic Responses : Applied on Ecole de Lyon Non-Linear Benchmark Structure
- 2013
-
In: Topics in Nonlinear Dynamics, Volume 1. - New York, NY : Springer. - 9781461465690 ; 1, s. 113-123
-
Conference paper (other academic/artistic)abstract
- In industry, linear FE-models commonly serve to represent global structural behavior. However, when test data are availa-ble they may show evidence of nonlinear dynamic characteristics. In such a case, an initial linear model may be judged being insufficient in representing the dynamics of the structure. The causes of the non-linear characteristics may be local in nature whereas the major part of the structure is satisfactorily represented by linear descriptions. Although the initial model then can serve as a good foundation, the parameters needed to substantially increase the model’s capability of representing the real structure are most likely not included in the initial model. Therefore, a set of candidate parameters controlling nonlinear effects, opposite to what is used within the vast majority of model calibration exercises, have to be added. The selection of the candidates is a delicate task which must be based on engineering insight into the structure at hand.The focus here is on the selection of the model parameters and the data forming the objective function for calibration. An over parameterized model for calibration render in indefinite parameter value estimates. This is coupled to the test data that should be chosen such that the expected estimate variances of the chosen parameters are made small. Since the amount of information depends on the raw data available and the usage of them, one possibility to increase the estimate precision is to process the test data differently before calibration. A tempting solution may be to simply add more test data but, as shown in this paper, the opposite could be an alternative; disregarding low excessive data may make the remaining data better to dis-criminate between different parameter settings.Since pure mono-harmonic excitation during test is an abnormality, the excitation force is here designed to contain sub and super harmonics besides the fundamental one. Further, the steady-state responses at the side frequencies are here shown to contain most valuable information for the calibration process of models of locally nonlinear structures.Here, synthetic test data stemming from a model representing the Ecole Centrale de Lyon (ECL) nonlinear benchmark are used for illustration. The nonlinear steady state solutions are found using iterative linear reverse path state space calculations. The model calibration is here based on nonlinear programming utilizing several parametric starting points. Candidates for starting points are found by the Latin Hypercube sampling method. The best candidates are selected as starting points for optimization.
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| 38. |
- Yaghoubi Nasrabadi, Vahid, 1985, et al.
(author)
-
The Modal Observability Correlation as a Modal Correlation Metric
- 2014
-
In: Conference Proceedings of the Society for Experimental Mechanics Series. - New York, NY : Springer New York. - 2191-5644 .- 2191-5652. - 9781461465843 ; 45:7, s. 487-494
-
Conference paper (peer-reviewed)abstract
- The historical development of the Modal Assurance Criterion (MAC) originated from the need of a correlation metric for comparingexperimental modal vectors, estimated from measured data, to eigenvectors that have been determined from finite element calculation. For systems with well separated eigenvalues with many system degrees-of-freedom (DOF) represented in the eigenvectors it is normally easy to distinguish eigenvectors associated to different eigenvalues by low MAC correlation numbers. However, for eigenvectors with a sparse DOF sampling it may be hard to distinguish between vectors by MAC correlation numbers. To reduce the problem of distinguishing between eigensolutions, this paper advocates the use of a new correlation metric based on the observability matrix of the diagonal state-space realization. This is instead of using a metric based on the eigenvectors only. © The Society for Experimental Mechanics 2014.
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