Scaling-factor estimation using an optimized mass-change strategy

The paper presents how to identify natural frequencies and mode shapes of structures by Operational Modal Analysis (OMA) technique, in which the Frequency Domain Decomposition (FDD) method is used. This method is an experimental method only base on the data of measuring the dynamic response of the structures under the excitation due to ambient forces and operational loads to determine the vibration characteristics. Measure vibration (acceleration) and determine spectral density matrix, using the singular values decomposition method of spectral density matrix to determine the natural frequencies and mode shapes of structures. The calculation results show that the natural frequencies, the mode shapes form determined by the OMA technique is consistent with the calculation results according to the theory and show the reliability of the method.KeywordsNatural frequencyMode shapeIdentifyEMAOMAFDD

Modal analysis has developed into a major technology for the study of structural dynamics in the past several decades. Through it, complex structural dynamics phenomena can be represented in terms of structural invariants, i.e., the modal parameters: natural frequencies, damping ratios and mode shapes. Operational Modal Analysis (OMA) deals with the estimation of modal parameters on vibration data measured for operational conditions, when the excitation on the structure is not measured. In this work, OMA is performed on a wind turbine blade undergoing wind tunnel testing. These tests included different wind speeds, pitch angles and also different health conditions of the blade, where masses of different magnitude were fixed to the blade on different locations to emulate damage conditions. In order to monitor the modal parameters across multiple days of varied tests in the wind tunnel, the Polymax modal parameter estimator was implemented, coupled with an Automated Modal Analysis methodology. This methodology included an automatic modal parameter selection technique, using a Machine Learning (ML) clustering algorithm, coupled with a modal tracking procedure which applied statistical thresholds on the modal parameters’ values. The tracking procedure searches for modes similar to the ones calculated for healthy conditions. The results show how the modal parameters of the wind turbine blade vary with the different measured conditions in the wind tunnel. Moreover, a damage detection methodology is implemented to differentiate between the healthy and damaged conditions on the blade, by leveraging an anomaly detection algorithm using the Multivariate Gaussian Distribution (MGD). This algorithm takes as input the modal parameters calculated by the previous Automated Modal Analysis methodology and detects statistical deviations among them which could indicate the presence of damage. All steps of this work contribute to developing an automatic framework able to detect damages on a wind turbine blade, and therefore perform Structural Health Monitoring (SHM) for different operational conditions.

This research investigates the dynamic behavior of a railway bridge using both experimental and numerical methods. Field tests were conducted to capture the bridge response to live loading conditions with acceleration data collected via uniaxial accelerometers placed at critical locations along the structure. The dynamic characteristics, including the natural frequencies and mode shapes, were determined using two analytical techniques: Fast Fourier Transform (FFT) and Operational Modal Analysis (OMA). While FFT provides a frequency domain analysis, OMA enables the estimation of modal parameters, such as natural frequencies, mode shapes, and damping ratios, using the bridge's response to operational forces. The results revealed that the fundamental frequency obtained from the OMA (2.163 Hz) was higher than that obtained from the FFT (1.95 Hz) and the Finite Element Analysis (FEA) model (1.65 Hz). Additionally, the OMA produced mode shapes that were closely aligned with those predicted by the FEA, validating the accuracy of the numerical model. This study highlights the advantages of OMA over FFT, particularly the ability to capture mode shapes, and underscores the importance of integrating OMA with FEA for a comprehensive dynamic assessment of bridge structures. These findings contribute to the growing body of knowledge on structural monitoring and provide practical insights into improving bridge safety and performance.

This article presents a damage identification method based on structural natural frequencies and mode shape points. According to the well-posedness analysis of this method, an algorithm is proposed to find the optimal combination of natural frequencies and mode shape points. Then, an integrated scheme that consists of the optimal point selection, the damage identification and the measurement noise updating is presented. In such a way, the damage identification errors due to measurement noises can be greatly suppressed. Numerical examples demonstrate that although structural damage parameters are very sensitive to the measurement noises, especially the noises in natural frequencies, they can be reliably identified if the natural frequencies and mode shape points are properly selected using the proposed method.

Interval natural frequency and mode shape analysis for truss structures with interval parameters

Machine tool vibrations have great impact on machining process. In this paper the dynamic behavior and modal parameters of surface grinding machine is presented. For this purpose, the CAD (computer aided design) model of the surface grinding machine structure is provided in catia and then Natural frequencies and mode shapes of the machine tool structure are carried out through FEM (finite element method) modal analysis under ansys. The model is evaluated and corrected with experimental results by modal testing on surface grinding machine. Finally, the natural frequencies and mode shapes obtained by both experimental and FEM modal analysis are compared. The results of two methods are in widely agreement.

The rotor is a key element of rotating machinery that can be used in different of mechanical devices such as gas turbines, industrial compressors, motors, and aero engines. The dynamic analysis of a rotor system with active magnetic bearings is presented in this paper. This system consists of a flexible shaft with a rigid disk and flexible bearings. An sys Workbench is used to study a 3D simulation of a finite element model. Correct estimation of the rotor's natural frequencies and mode shapes is required for rotating machinery safety procedures. In order to compute the natural frequencies and mode shapes of this system, in the first case it is assumed a free-free system in which no bearings are used, and the natural frequencies and mode shapes are calculated without rigid body modes. In the second case, the natural frequencies and mode shapes are determined with bearing stiffness. The natural frequencies are also evaluated using finite elements based on matlab code. A comparison between the two methods was carried out.

The accuracy of modal parameter estimates from estimation methods built in the framework of experimental modal analysis (EMA) can be assessed by several methods provided the information of input loadings and output responses. However, a deeper investigation is necessary for estimation methods built in the operational modal analysis (OMA) framework to establish confidence boundaries for the modal parameter estimates. This paper aims to estimate uncertainties of the modal parameter estimates by testing the sensitivity of the damped natural frequencies, damping ratios, and mode shapes to the choice of the estimation method and data acquisition settings used in this method. The uncertainty estimates of the modal parameter estimates are tested for changes in the boundary conditions. The tests provide insights into tendencies for the accuracy of the modal parameter estimates when the boundary conditions provide a different set of “true” modal parameter values. A simple cantilever beam experimental setup is used to obtain benchmark modal parameter estimates from EMA that are used to estimate the accuracy of the modal parameter estimates from OMA. The method’s robustness in estimating uncertainties and accuracies for modal parameter estimates is tested for several independent experiments. The boundary conditions for the cantilever beam are changed to test the influence of altering modal parameter estimates on the estimated uncertainties and accuracies. The boundary conditions are changed using materials with different elastic properties and the connection pressure between the clamping device and beam. A method presented in Paulsen et al. (Proceedings of the 9th International Operational Modal Analysis Conference, IOMAC, 2022) calculates a representative modal parameter estimate from a set of modal parameter estimates based on weightings obtained from the modal assurance criterion. The method’s ability to reduce uncertainties and increase accuracies of the representative estimate is demonstrated by repeating a test setup ten times. The results present simultaneously a reduction of uncertainties and an increase of accuracies for the representative modal parameter when the weighting method is used. An evaluation of dependencies between the estimated uncertainties and accuracies finds a proportional relation for the damped natural frequency when the uncertainties are described as a relative standard deviation. The analysis presents higher accuracy for the damped natural frequency and mode shape estimates compared to the damping factor, and the accuracy of the damping factor is dependent on the actual value of the damping factor. These phenomena for accuracy are well known and indicate that the uncertainties of modal parameter estimates can be assessed through a sensitivity test of estimation methods and data acquisition parameters.

Determination of the natural frequencies and mode shapes for large structures by accelerated Newton-Raphson method

Modal Complexity Factors as indexes for modal parameter identification in Operational Modal Analysis of coupled dynamic systems

The vibrational effect is one of the primary considerations during construction due to the ambient excitation from the surrounding environment. Thus, it is necessary to find the most dependable Finite Element (FE) model for the actual structure to improve its quality and life span on site. In this context, the study included a 3-story building model that was analyzed using finite element analysis to determine its dynamic properties such as natural frequency and mode shape to avoid the resonance effect. It is due to the importance of obtaining a reliable and accurate model by verifying with the results of the Operational Modal Analysis (OMA). In general, the goal of this study is to update the FE model so that it is close to the actual scaled model based on the previous OMA study. As a result, an initial linear FE model of the 3-story building scaled model was created using CAD software based on actual geometry to describe the structure's physical properties. The FE model was then imported into CAE software, where the boundary condition and estimated material properties were assigned to determine the effect of random vibration. Through the pairing of Finite Element Analysis results and previous studies, 9 natural frequencies and 9 mode shapes were extracted. The Modal Assurance Criterion (MAC) was used to compare the mode shape of FE results against the OMA to determine the degree of consistency between paired mode shapes. A model updating process was carried out to reduce the discrepancy between the methods. The uncertainties arising from the initial conditions have been discussed in terms of the stiffness of the material used. The updated model allows for an evaluation of the structure's current actions as well as the development of models for a wide range of potential future research scenarios.

In Operational Modal Analysis, the modal parameters (natural frequencies, damping ratios and mode shapes), obtained from Stochastic System Identification of structures, are subject to statistical uncertainty from ambient vibration measurements. It is hence necessary to evaluate the uncertainty bounds of these obtained results. To obtain vibration measurements at many coordinates of a structure with only a few sensors, it is common practice to use multiple sensor setups for the measurements. Recently, a multi-setup subspace identification algorithm has been proposed that merges the data from different setups first to obtain one set of global modal parameters. This paper proposes an algorithm that efficiently estimates the uncertainty on modal parameters obtained from this multi-setup subspace identification.

One of the important consideration in designing an unmanned aerial vehicle (UAV) is the dynamics characteristic of UAV structure. The dynamics characteristic of UAV structure can be evaluated from its dynamic parameters such as : natural frequencies and mode shape. These parameters play an important role in determining the system’s dynamic response. In general, a low stiffness structure is more sensitive to the dynamic load in comparison with a high stiffness structure. In this research, modification UAV structural stiffness is conducted by varying rib and spar number and configuration on UAV wing. Evaluation of rib and spar number and configuration effect to the natural frequency and mode shape of UAV structure is conducted numerically and experimentally. The simulation results show that the natural frequencies increases with increasing of the number of spar and decreases with decreasing of the number of rib.

A new method for random vibration analysis of stochastic truss structures

Fatigue cracks in steel bridges can lead to catastrophic failure and cause significant risks to public safety. These cracks can grow, propagate, reduce the structure maximum design capacity, and ultimately lead to a sudden failure. Fatigue cracks in steel bridges are primarily induced by the cyclic loading from constant traffic loads over time. Therefore, monitoring fatigue on steel bridges is essential to ensure structural safety. Operational modal analysis (OMA) is a non-destructive testing technique that can be used to monitor fatigue-induced damage through changes in modal parameters. When the fatigue crack grows the stiffness of the beam will reduce. This study implements OMA on a simply supported steel beam with changing stiffness. The natural frequencies and mode shapes of the beam are obtained through OMA, and combined with a model to predict the stress/strains at any point of the structure. The case study shows how maximum stresses and the natural frequencies that are affected by the crack growth are varying due to changes in stiffness. The result demonstrates that by combining OMA with fatigue assessment, the risk of fatigue failure in steel bridges can be significantly reduced.