Roadmap for a Highly Improved Modal Test Process

This document addresses enduring challenges encountered in modern experimental modal analysis as well as earlier “resonance testing” associated with measured mode orthogonality requirements. To this end, the document’s goals are (1) retirement of false damping and real mode notions (dating back to Lord Rayleigh, 1877), (2) achievement a community consensus on 85+ years of resonance and modal testing, and (3) establishment of an experimental modal analysis process that is independent of a-priori predictive mathematical models. The above goals are satisfied by addressing six key objectives, namely (a) validation of measured complex experimental modes, (b) empirical isolation of experimental modes (the “Holy Grail” of resonance testing), (c) definition of a state-space orthogonality standard, independent of an approximate reduced-order mass matrix, (d) exploitation of state-space, left-hand eigenvectors and their relationship to modal momentum and kinetic energy distributions, (e) establishment of a universal practice for a broad family of modal testing methods, and (f) application of the above six objectives to ambient (operational modal analysis) methods.

PurposeEnsuring the early detection of structural issues in aircraft is crucial for preserving human lives. One effective approach involves identifying cracks in composite structures. This paper employs experimental modal analysis and a multi-variable Gaussian process regression method to detect and locate cracks in glass fiber composite beams.Design/methodology/approachThe present study proposes Gaussian process regression model trained by the first three natural frequencies determined experimentally using a roving impact hammer method with crystal four-channel analyzer, uniaxial accelerometer and experimental modal analysis software. The first three natural frequencies of the cracked composite beams obtained from experimental modal analysis are used to train a multi-variable Gaussian process regression model for crack localization. Radial basis function is used as a kernel function, and hyperparameters are optimized using the negative log marginal likelihood function. Bayesian conditional probability likelihood function is used to estimate the mean and variance for crack localization in composite structures.FindingsThe efficiency of Gaussian process regression is improved in the present work with the normalization of input data. The fitted Gaussian process regression model validates with experimental modal analysis for crack localization in composite structures. The discrepancy between predicted and measured values is 1.8%, indicating strong agreement between the experimental modal analysis and Gaussian process regression methods. Compared to other recent methods in the literature, this approach significantly improves efficiency and reduces error from 18.4% to 1.8%. Gaussian process regression is an efficient machine learning algorithm for crack localization in composite structures.Originality/valueThe experimental modal analysis results are first utilized for crack localization in cracked composite structures. Additionally, the input data are normalized and employed in a machine learning algorithm, such as the multi-variable Gaussian process regression method, to efficiently determine the crack location in these structures.

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.

Experimental modal analysis and vibro-acoustic testing at leonardo laboratories

Experimental modal analysis has grown steadily in pop ularity since the advent of the digital FFT spectrum analyzer in the early 1970’s. Today, impact testing (or bump testing) has become widespread as a fast and economical means of finding the modes of vibration of a machine or structure. In this paper, we review all of the main topics associated with experimental modal analysis (or modal testing), including making FRF measurements with a FFT analyzer, modal excitation techniques, and modal parameter estimation from a set of FRFs (curve fitting).

As an alternative to operational modal analysis and classical experimental modal analysis (EMA), a novel method was introduced previously, namely impact-synchronous modal analysis (ISMA). The effectiveness ISMA on rotor and structural dynamic systems has been proven in previous literature. More recently, an automated impact device (AID) was introduced which utilized tachometer pulse as initiation signal and its effectiveness on ISMA was proven. An attempt to further enhance this device in term of equipment and cost is then proposed by replacing the tachometer with the in-use tri-axial accelerometer through utilizing the filtered response of cyclic load component as an initiation signal to control the impact device, which is also the primary aim for this study. Prior to modal testing, accuracy of this device is illustrated at desired phase angles of 0 deg, 90 deg, 180 deg, and 270 deg. Subsequently, frequency response function (FRF) estimations obtained for ISMA using enhanced AID has demonstrated the suppression capabilities of this device on disturbances, i.e., reduction of 93.58% at 30 Hz and 57.78% at 60 Hz, resulting in a high correlation for signature assurance criterion (SAC) and cross signature assurance criterion (CSAC). Modal parameters extracted from the EMA and ISMA using impact device are presented and compared, for the first three natural modes of the test rig. It is found that natural frequencies are deviating by less than 6%, whereas modal assurance criterion (MAC) values between the mode shapes of the two tests are found to be above 0.9.

Bicycle frames have to bear variety of loads and it is needed to ensure the frame can withstand dynamic loads to move. This paper focusing on dynamic study for bicycle frame structure with a purpose to avoid the problem regarding loads on the structure and to ensure the structure is safe when multiple loads are applied on it. The main objectives of dynamic study are to find the modal properties using two method; finite element analysis (FEA) and experimental modal analysis (EMA). The correlation between two studies will be obtained using percentage error. Firstly, 3D model of mountain bike frame structure has been draw using computer-aided design (CAD) software and normal mode analysis using MSC Nastran Patran was executed for numerical method meanwhile modal testing using impact hammer was performed for experimental counterpart. From the correlation result, it show that percentage error between FEA and EMA were below 10% due to noise, imperfect experiment setup during perform EMA and imperfect modeling of mountain bike frame structure in CAD software. Small percentage error differences makes both of the method can be applied to obtain the dynamic characteristic of structure. It is essential to determine whether the structure is safe or not. In conclusion, model updating method is required to reduce more percentage error between two results.

By means of ANSYS Workbench, different materials, dimensions and shapes of the Chladni plates are simulated. The natural frequency and Modal are obtained so that the chladni plate is determined and manufactured, that is used in the experimental research. Then, modal analysis test is conducted by Experimental modal analysis, the resonance and modal characteristics of the plate between 1Hz to 1000Hz are identified. Finally, Modal reproduce experiment is conducted under the acoustic excitation. Experimental and analytical results show that the finite element analysis, experimental modal analysis and Modal reproduce experiment basically have the same results.

Accurate representation of bolted joints in the finite element (FE) model of a built-up structure is a crucial factor in ensuring the accuracy and reliability of the dynamic behaviour prediction of the structure. Modelling of bolted joints in industrial structures has not been widely and thoroughly studied, especially in the dynamic response of the bolted joint itself. The aim of this work is to investigate several flexibility formulae for the calculation of the stiffnesses of CBUSH elements for the modelling of the bolted joints. The flexibility formulae used in this work are attributed to Huth, Tate & Rosenfeld, Boeing, Swift and Grumman. The results of the normal modes analysis of the FE models with different flexibility formulae were compared with those obtained from the experimental modal analysis (EMA). EMA was performed to measure the natural frequencies and mode shapes of the structure with bolted joints. The total errors calculated from the comparisons between FE and EMA were recorded for all flexibility formulae. The results of the investigation demonstrated that there are noticeable variations in the total errors recorded using different flexibility formulas for the CBUSH element representing the bolts in the FE model of the structure with bolted joints. It was found that the Swift’s flexibility formula is the most appropriate for the prediction of the natural frequencies of the structure with bolted joints.Accurate representation of bolted joints in the finite element (FE) model of a built-up structure is a crucial factor in ensuring the accuracy and reliability of the dynamic behaviour prediction of the structure. Modelling of bolted joints in industrial structures has not been widely and thoroughly studied, especially in the dynamic response of the bolted joint itself. The aim of this work is to investigate several flexibility formulae for the calculation of the stiffnesses of CBUSH elements for the modelling of the bolted joints. The flexibility formulae used in this work are attributed to Huth, Tate & Rosenfeld, Boeing, Swift and Grumman. The results of the normal modes analysis of the FE models with different flexibility formulae were compared with those obtained from the experimental modal analysis (EMA). EMA was performed to measure the natural frequencies and mode shapes of the structure with bolted joints. The total errors calculated from the comparisons between FE and EMA were recorded for all fle...

<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>

This study investigated the dynamic properties of a spherical sandwich composite structure made of carbon fiber face sheets and a Nomex honeycomb core. The structure was produced using the hand lay-up method. The results from Experimental Modal Analysis (EMA) and the numerical model created in ANSYS showed high consistency. The natural frequency difference was only 0.73% for the second mode, with the largest discrepancy of 6.5% was observed in the first mode. These differences are thought to be related to structural variations from the manufacturing process, such as resin distribution, carbon fiber fabric stacking, and air voids and the experimental challenges such as double hit errors, measurement resolutions related to force sensor and accelerometer and environmental noise. The vibration damping capability of the sandwich structure was investigated. Some modes exhibited high damping, while others had relatively lower values. The highest and the lowest damping ratios were obtained as 0.83% for the third mode and 0.23% for the fourth mode. A numerical equivalent model of the structure was created in ANSYS to determine its natural frequencies and vibration modes, confirming its effectiveness in modeling complex structures.

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.

<p>This report consists of experimental and Finite element-based numerical modal analysis of a 3D printed PLA cantilever beam with a nonuniform delamination of 0.5mm, carried out as part of an MEng project. Experimental modal analysis is performed on four different samples of different delamination thicknesses, including the one with a delamination of 0.5mm, to obtain the system's bending fundamental frequency. Numerical analysis, however, is focused and conducted on only the defective specimen with a non-uniform delamination of 0.5mm. In this case, the delamination is sketched with the help of an electronic microscope which takes the images of the delamination zone. These images are then used to plot the non-uniform delamination on the 3D model, focusing on obtaining the model that is as close as possible to the manufactured specimen. The experimental frequencies are subsequently compared with the numerical values obtained from the Finite Element Analysis (FEA) of the 3D model. In numerical analysis, a progressive approach was used to create two sophisticated models referred to as refined and further refined models. The numerical fundamental frequency obtained from these last models are compared with that of the PLA beam with uniform delamination of 0.5mm. It is observed that by applying progressive refinement in the FEM model, the numerical fundamental bending frequency increasingly converges to the experimental one. Appendix A consists of the images taken by the microscope, which show the non-uniform geometry of the delamination zone.</p>

This paper presents an experimental and numerical modal analysis for an external gear pump considering its mounting on a test rig in a laboratory setting. Most of the previous studies on experimental modal analysis (EMA) of hydraulic pumps focused on the modal frequencies to allow model validation. However, the mode shapes of pump bodies have not extensively been discussed. Furthermore, the nature of the pump components assembly and mounting poses some modeling challenges, such as the uncertain material properties of each component, the behavior of the bolted joints, and some critical modeling boundary conditions related to pump mounting. In this regard, the experimentally obtained vibration modes of a reference pump using the least-square complex exponential (LSCE) method are analyzed with an emphasis on the characteristics of the mode shapes. Then, simple modeling strategies are proposed and validated by performing the analysis from the component level to the full assembly. As a result, the mode shapes are categorized depending on the type of motions that the modes exhibit. It is observed that the pump casing does not show any substantial deformation but is close to the rigid body motion. Moreover, without considerably increasing model complexities, the proposed numerical approach provides reasonable accuracy with average errors in modal frequencies of 6%, as well as good agreement in terms of mode shapes. The vibration reduction strategy is briefly discussed based on the measured mode shapes, and the proposed modeling approaches can be useful to study external gear pumps with minimal model complexities yet allowing reasonable result accuracy.

An experimental and numerical modal analysis was performed on an 8 m2 T-shaped heliostat structure at different elevation angles. The experimental results were used to validate a finite element (FE) model by comparing natural frequencies and mode shapes. The agreement between experiments and simulations is good in all operating points investigated. In addition, damping coefficients were determined experimentally for each mode, in order to provide all necessary information for the development of a dynamic model. Furthermore, potentially critical operating conditions caused by vortex shedding were identified using a simple approach.