A Performance Study of Controlled Impact Timing on Harmonics Reduction in Operational Modal Testing

In experimental modal analysis, the use of characterized excitation and the choice of window functions are fundamental to the estimation of system frequency response function (FRF) data. It greatly influences the quality of the resulting FRF measurements. Discussed are combination methods of several commonly-used excitation signals with window function, which is relative to lightly damped systems. Study shows that burst random signal with Rectangular works well for lightly damped structures, and pure random with Hanning will bring about higher error. A modal testing of white car body was done. Experimental parameters analysis are given to demonstrate the study result presented above. So it poses a practicable method for improving the accuracy of frequency response function (FRF) measurements of lightly damped structure by using proper excitation signal with appropriate window function.

The paper deals with an experimental and a numerical investigation of dynamic properties of the structure. Object of interest is a steel rod with circle section. The modal parameters, such as mode shapes and natural frequencies, are obtained by two different ways: experimentally by using experimental modal analysis and numerically by finite element analysis which were computed in NX Nastran solver. The results from both methods are compared in NX through the correlation function. A relation between measured mode shapes and computed mode shapes is expressed by Modal Assurance Criterion. This process of comparing is appropriate for verification of experimental approaches.

Experimental modal analysis (EMA) with oblique excitation (i.e. oblique impact testing) is useful in improving the long test time problem of conventional EMA with normal excitation (i.e. triaxial normal impact testing), in order to extract all the important dynamic characteristics of a 3D complex structure. In this study, a new methodology involving a vector projection method is introduced to find the driving point frequency response function (FRF) in the oblique direction, without the need for a special fixture with an obliquely oriented impedance head. Hence, this presents a low cost and practical solution for scaling the mode shape, as compared to the traditional approach. Moreover, the concurrent forces characteristic of oblique excitation are used in the development of the theoretical relationship between FRFs with oblique excitation and those with normal excitation. This is important for the validation of the oblique impact testing result, such as the FRF and modal parameter estimations. The experimental results show that oblique impact testing has reliable and effective results, as compared with the triaxial normal impact testing, in terms of the FRF correlation, natural frequency discrepancy, modal damping ratio error and modal assurance criterion of the unit modal mass mode shape.

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.

This paper adopts composite structure system analysis method to perform modal analysis of high-speed face milling cutter which is mounted on the machine tool through FEM modal analysis. The key problem of this method is to obtain joint surface parameters between the machine tool spindle and face milling cutter through experimental modal analysis and MATLAB software. The joint surface parameters consist of linear stiffness, linear damping, rotation stiffness and rotation damping. After getting the frequency response function (FRF) at the tool tip of the face milling system through experimental modal analysis, the contact surface parameters can be used to eliminate the influence of the machine tool to get modal parameters of the face-milling cutter itself. Based on the finite element model of face milling cutter, composite structure system analysis method can be used easily to acquire the dynamic performance of the face milling system through FEM modal analysis, greatly to improve the reliability of modal analysis, and is helpful to the dynamic design and the structure improvement of high speed face milling cutter.

In this paper, we identified the material constitutive parameters of the human skull from reported tensile test results. Initially, we applied both linear-elastic and Mooney–Rivlin nonlinear hyperelastic constitutive models to the available tensile test data at different strain rates of 0.005, 0.10, 10, and 150 1/sec. It was shown that the suggested hyperelastic model fitted the test results with higher accuracy in comparison with the linear-elastic model. In the next step, the experimental modal analysis was carried out through roving hammer-impact tests on a dried human skull. The first four natural frequencies of the skull were measured to be 496, 543, 1250, and 1287 Hz, and these values were verified by the modal assurance criterion. Then, a 3D finite element (FE) model of that human skull was created by a 3D scanner and discretized to carry out a computational modal analysis. The performance of the determined material properties for the human skull from both linear and hyperelastic material models was evaluated using FE modal analysis. The calculated modal frequencies were then compared to the experimentally measured frequencies. It was shown that the material parameters from both the linear and hyperelastic constitutive models obtained at a strain rate of 0.10 1/sec, provided the best performance in computational modal analysis with minimum deviations relative to the experimental results. These results confer a better understanding of the human skull behavior among different strain rates, which could increase the accuracy of nonlinearity dynamic simulations on the skull.

A damage identification scheme combining impact-synchronous modal analysis (ISMA) and artificial neural network is developed in this study. The ISMA de-noising method makes it feasible to detect and classify the damage states with high accuracy when the machine is under operation. The feed-forward backprop network was utilized in this study. The input feature vector of the network consisted of the FRF changes in a selected vibrational mode frequency interval at several measurement points. The scheme was tested on a rectangular Perspex plate. It is proved that the trained network can successfully identify damage locations with the testing data collected by ISMA, which allows the damage detection to be carried out without shutting down the tested machine. For the plate structure in this study, an overall accuracy reached 100% when all five measurement points were used. With the input features optimized by mode shape assessment, 100% accuracy was also achieved with only two measurement points.

This study carried out an experimental and numerical modal analysis of the Turkish traditional instrument 'Bendir' by an acoustical excitation source. In experimental modal analysis, Bendir was excited acoustically for specified frequencies and elastic deformations of different areas of Bendir due to the excitation were observed with a laser vibrometer. Using the Fourier series handled gained data, modal analysis was done. The first six natural frequencies obtained experimentally and numerically were compared. In addition, other hits in Bendir, symbolizing three fundamental voices such as 'dum', 'te', 'ke' were used to excite the instrument. As a result, time dependent deformation & velocity data were determined and different responses of Bendir were compared.

Rotational FRFs have not been measured in experimental modal analysis even though the importance of rotational FRFs have been recognized recently. Consequently it is difficult to utilize the FRFs on the basis of vibration testing for the structure modification analysis. The authors have proposed an estimation of the auto FRFs in rotation of structures. In the method a T-shaped rigid block whose inertia properties were known was attached to the measurement point on the structure. The estimation of three-degree-of-freedom (3-DOF) FRFs (one DOF in rotation and two DOFs in translation) of the beam structure using the T-shaped rigid block was demonstrated. The effect of estimated rotational FRFs against the random noise of measured FRFs were evaluated as a Reliability Factor. In this paper the estimation method of the cross FRFs in rotation and the reliability of the estimated FRFs are presented. A new rigid block whose overview is the cross-shape is designed for measuring 6-DOF FRFs. The 6-DOF FRFs of the beam structure is estimated. The structure modification analysis of 3D-rahmen structure based on experimental data is carried out.

An alternative approach to measure similarity between two deterministic transient signals

Application of Sherman–Morrison–Woodbury formulas in instantaneous dynamic of peripheral milling for thin-walled component

Modal analysis based structural health monitoring (SHM) is required now more than ever due to many factors such as aging infrastructure, loading incidents likely earthquakes, over loading etc. Although the continuous monitoring of structures is a full-fledged commercial sector, its high cost makes it infeasible for large structures as the number of sensors required is large. Accelerometers, widely used as sensors in SHM, in addition to high cost, possess some other challenges such as damage vulnerability in environmental and operational conditions. In this research, low cost lead-zirconate-zitanate (PZT) sensors are proposed as replacement of costly and fragile accelerometers as sensors for SHM. PZT patches, which cost less than one-tenth of the accelerometers, can also be embedded in the reinforced concrete structures to protect from the harsh operational conditions. In this paper, PZT patches are studied by technique of experimental modal analysis (EMA) on a steel beam specimen and the results are compared with the traditionally used accelerometers. Single input single output (SISO) approach is adopted for EMA of the rectangular steel beam. PZT sensors are able to capture modal data in terms of natural frequencies and mode shapes in good agreement with accelerometer. The fundamental natural frequency of the beam is obtained with the error of less than 1 % as compared to the accelerometer. The signal to noise ratio is of same order as accelerometer. The strain mode shape from the PZT sensors is well correlated to displacement mode shapes from the accelerometer by a modal assurance criteria (MAC) values greater than 0.9 for observed experimentally.

As all experimental procedures, Experimental Modal Analysis (EMA) is subject to a wide range of potential testing and processing errors. The modal identification methods are sensitive to these errors, yielding modal results which are uncertain up to certain error bounds. The question hence is what these error bounds on test data and modal parameters are. In this paper, the studied source of uncertainty is related to the variance (noise) on the Frequency Response Function (FRF) measurements. Under the H1 assumptions and in single-input cases, the FRF variances can be computed from the coherences and the FRFs. In multiple-input cases, some more measurement functions are required. Advanced system identification methods like the Maximum Likelihood Estimator (MLE) and PolyMAX Plus have the possibility to take the uncertainty on the measurement data into account and to propagate the data uncertainty to (modal) parameter uncertainty. This paper will review FRF variance estimation techniques, including some pragmatic approaches. The basic concepts of Maximum Likelihood Estimation and the calculation of confidence bounds will be discussed. Some typical structural testing and modal analysis cases will be used as illustration of the discussed concepts.

MODAL ANALYSIS OF A LIGHTWEIGHT STRUCTURE—INVESTIGATION OF THE EFFECTS OF THE SUPPORTS ON THE STRUCTURAL DYNAMICS

<div class="htmlview paragraph">Traditionally, vibration analysis in operating conditions (on the road or on a bench) had to be combined with experimental modal analysis in controlled laboratory conditions in order to understand the modal behaviour of the structure. This requires additional measurements, costs and time. However, in many applications, the real operating conditions may differ significantly from those applied during the modal test and hence the vibration modes from the modal test might not be representative for the active modes in operation conditions. The need for a capability of doing a modal analysis on data from operating conditions is obvious.</div> <div class="htmlview paragraph">Over the last years, several modal parameter estimation techniques have been proposed and studied for modal parameter extraction from output-only data. Each method needs to make a number of assumptions and has some limitations. In this paper, the capabilities and limitations of the Least Squares Complex Exponential and two subspace techniques, referred to as the Balanced Realization (BR) and the Canonical Variate Analysis, are evaluated for its applicability to industrial cases.</div>