FRF-based Method Research Articles

Introducing an innovative FRF-based method for identification of an adhesive joint characteristics

An energy harvesting system can be attached to the host structure using adhesive joint with viscoelastic behavior. Adhesive joints having nonlinear properties, significantly alter the dynamics of a piezoelectric energy harvesting system and, as a result, have the potential to dramatically alter the output voltage. In this paper, an innovative FRF-based method is introduced to identify adhesive joint characteristics of a piezoelectric energy harvester in cantilever beam configuration which is jointed to a base structure in root. To this end, a novel viscoelastic model is considered for the adhesive joint, which consists of two longitudinal and torsional springs and two longitudinal and torsional dashpots. Additionally, the system is analytically modeled using Euler-Bernoulli beam theory, strain rate damping and the piezoelectric constitutive relations. The adhesive joint characteristics are identified through Genetic Algorithm method employing experimental tests data and model updating. The identified nonlinear pre-strain-dependent characteristics verify both the proposed analytical model and the joint identification method. Furthermore, the effects of the adhesive joint's thickness and pre-strain loading on its characteristics are investigated.

A two-stage approach to stochastic finite element model updating using FRF data

Stochastic model updating techniques are used to update an FE model of a structure so that the updated model can predict the mean as well as the variability of the structure's dynamic characteristics. Most of the current approaches and studies employ modal data to update the uncertain parameters related to the mass and stiffness matrices. Model updating using FRFs has an advantage over modal data that it avoids modal analysis errors and can be used to update the damping matrix. There is limited work on using FRFs for stochastic model updating and on identifying variability of the damping matrix. The existing methods simultaneously update the parameters related to the mass, stiffness, and damping matrices. These methods may encounter numerical challenges due to large differences in the order of magnitude of these matrices. In some situations, only the mass and stiffness matrices are to be updated to accurately predict the undamped dynamics of the structure and hence the damping identification is not necessary. In these situations, the existing methods cannot be used to update only the mass and stiffness matrices because the modelling and identification of the damping are necessary for updating with FRF-based methods. To address these limitations, this paper proposes a two-stage approach to stochastic model updating using normal FRFs. Normal FRFs represent the estimates of the FRFs, excluding the effect of the damping in the structures. Stage-I updates the mean and variability of the uncertain parameters related to the mass and stiffness matrices using normal FRFs. Stage-II updates the mean and variability of the uncertain parameters related to the damping matrix using the difference between the complex and normal FRFs. Separating updating of the damping matrix from updating of the mass and stiffness matrices improves the conditioning of the sensitivity matrices and eliminates the numerical challenges associated with updating the matrices with different orders of magnitude. For the situations where the variability in the undamped dynamics only needs to be predicted, stage-I of the proposed method can be used. Numerical studies on a damped cantilever beam and an aeroplane model (DLR-AIRMOD structure) are presented to validate the method. Experimental validation of the proposed method is carried out using nominally identical samples of a damped acrylic beam. The performance of the method is also compared with an existing complex FRF based method to highlight the effectiveness of the proposed method.

Direct structural damping identification method using complex FRFs

Most of the identification methods are based only on the viscous damping model and uses modal data. In this paper, a new FRF-based direct structural damping identification method is proposed. The proposed method is a direct method and identifies structural damping matrix explicitly. As the new method is a FRF-based method, it overcomes the problem of closely spaced modes for damping identification. The accuracy of identified structural damping matrix depends upon the accuracy of finite element model. In this paper, FRF-based model updating method is used to obtain accurate mass and stiffness matrices. Thus, the procedure to obtain accurate structural damping matrix is a two-step procedure. In the first step, mass and stiffness matrices are updated and in the second step, structural damping matrix is identified using updated mass and stiffness matrices, which are obtained in the previous step. The effectiveness of the new method is demonstrated by three numerical examples and one experimental example. The numerical studies of lumped mass system, fixed-fixed beam and L-shaped frame structure are carried out. The effects of coordinate incompleteness, ill-conditioning and robustness of method under presence of noise are investigated. The proposed method is able to predict FRFs accurately for the frequency range covering the modes considered. However, beyond the considered modes, the predicted FRFs do not match the experimental FRFs. It is suggested in this work that ill-conditioning problem should be dealt by considering all the modes in the frequency range of interest. The performance of the proposed method is investigated for cases of light, medium and heavily damped structures. The numerical studies are followed by experimental case study of cantilever beam structure. The effectiveness of the proposed method is evaluated by comparing the predicted and the experimental FRFs. The results have shown that the proposed method is able to predict accurately the experimental FRFs with all levels of damping in the system.

Structural model updating using dynamic data

Parameter estimation through model updating is a powerful technique that has gained widespread popularity for condition assessment of aging infrastructure. Among the available techniques, the sensitivity method is perhaps the most popular approach to perform model updating in industrial-scale systems. However, convergence issues are inherent to the method, due to ill-conditioning of the sensitivity matrix and measurement errors. To overcome the afore-mentioned concerns, regularization techniques were successfully applied in simulated and experimental scenarios. Model updating is performed using the University of Central Florida Benchmark Structure which is a laboratory specimen intended to capture the behavior of short to medium span bridges. The finite element model of the Benchmark is updated using (1) a modal parameters-based and (2) a frequency response function (FRF)-based error functions where both methods consider sparse data. In the simulated study, the aim is to evaluate the robustness of both error functions under random noise and ill-conditioning. Finally, the methods are successfully validated using experimentally obtained dynamic data. Based on the obtained results, it is concluded that the FRF-based method is more robust under simulated noise and can handle more unknown parameters in the optimization problem. However, advantages and challenges inherent to each method are presented only in light of those experienced by the authors.

PREDICTION OF DYNAMIC CHARACTERISTICS USING UPDATED FINITE ELEMENT MODELS

Model updating techniques are used to update a finite element model of a structure so that an updated model predicts the dynamics of a structure more accurately. The application of such an updated model in dynamic design demands that it also predict the effects of structural modifications with a reasonable accuracy. This paper deals with updating of a finite element model of a structure and its subsequent use for predicting the effects of structural modifications. Updated models have been obtained by a direct model updating method and by an iterative method of model updating based on the frequency response function (FRF) data. The suitability of updated models for predicting the effect of structural modifications is evaluated by some computer and laboratory experiments. First a study is performed using a simulated fixed–fixed beam. Cases of complete, incomplete and noisy data are considered. Updated models are obtained by the direct and the FRF-based method in each of these cases. These models are then used for predicting the changes in the dynamic characteristics brought about due to a mass and a beam modification. The simulated study is followed by a study involving actual measured data for the case of an F-shape test structure. The updated finite element models for this structure are obtained again by the direct and the FRF-based method. Structural modifications in terms of mass and beam modifications are then introduced to evaluate the updated model for its usefulness in dynamic design. It is found that the predictions based on the iterative method based updated model are reasonably accurate and, therefore, this updated model can be used with reasonable accuracy to perform dynamic design. The predictions on the basis of the direct method based updated model are found to be reasonably accurate in the lower portion of the updating frequency range but the predictions are in a significant error in the remaining portion of the updating frequency range. It is concluded that the updated models that are closer to the structure physically are likely to perform better in predicting the effects of structural modification.