Development and validation of experimental modal analysis with fixture-free oblique impact testing based on a vector projection method

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 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.

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.

A new experimental modal analysis method based on double-exponential windowing and application to lightly damped bladed wheels

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).

In this paper, the dynamic behavior of a cantilever beam without and with crack is observed. An elastic Aluminum cantilever beams having surface crack at various crack positions are considered to analyze dynamically. Crack depth, crack length and crack location are the foremost parameters for describing the health condition of beam in terms of modal parameters such as natural frequency, mode shape and damping ratio. It is crucial to study the influence of crack depth and crack location on modal parameters of the beam for the decent performance and its safety. Crack or damage of structure causes a reduction in stiffness, an intrinsic reduction in resonant frequencies, variation of damping ratios and mode shapes. The broad examination of cantilever beam without crack and with crack has been done using Numerical analysis (Ansys18.0) and experimental modal analysis. To observe the exact higher modes of beam, discretize the beam into small elements. An experimental set up was established for cantilever beam having crack and it was excited by an impact hammer and finally the response was obtained using PCB accelerometer with the help sound and vibration toolkit of NI Lab-view. After obtaining the Frequency response functions (FRFs), the natural frequencies of beam are estimated using peak search method. The effectiveness of experimental modal analysis in terms of natural frequency is validated with numerical analysis results. This paper contains the study of free vibration analysis under the influence of crack at different points along the length of the beam.

Frequency response function estimation techniques and the corresponding coherence functions: A review and update

The damage behavior of soda-lime glass was studied due to a steel ball of 1mm and 2mm at oblique impact test. The thickness of glass specimen were 3mm and 5mm and oblique degrees of impact were 90,70 and 50. After the steel ball impact test, the crack patterns were investigated using a stereo-microscope. In addition, the finite element method was performed to analyze the stresses distribution and variation in the oblique impacted glass by steel ball. As a result of the impact test, the crack length of 90impacted glass was the largest and that of 50impacted glass was the smallest. In particular, as the impact velocity and diameter of the steel ball increased, the difference of crack length was prominent. The finite element analysis showed the maximum principle stresses distribution in contact area of glass specimen. The result of analysis was accorded with the crack growth behavior by the oblique impact test.

Viscoelastic materials are used in vibration damping applications as they have the ability to dissipate energy, they are used in machine basis, bridges and many other applications. In this paper four plates with the same thickness but different material lamination are investigated for their modal properties. Namely,natural frequencies, mode shapes and damping loss factors. Experimental modal analysis is carried out using impact hammer for excitation and accelerometer for measurement. Data is processed using computer package to obtain frequency response function (FRF) for each plate and modal parameters are extracted from the plot. Results are compared to finite element model that was created using ANSYS package. It showed very well agreement between experimental and finite element. Damping effect on the shift in natural frequencies was obvious due to the viscoelastic material thickness in the laminated plates. It is concluded that the finite element analysis using ANSYS software is a powerful tool in predicting natural frequencies and mode shapes even in laminated plates with viscoelastic core, it is also confirmed the effect of damping increase due to the use of viscelastic cores on the plate natural modes and vibration behaviour.

This paper presents an application of the Experimental Acoustic Modal Analysis (AMA) on a vintage 10 M Conn tenor saxophone. This technique originates from the traditional Modal Analysis which is commonly adopted to determine the dynamic behaviour of solid structures. The methodology is based on the measurement of Frequency Response Functions (FRFs) as a ratio of the acoustic pressure, measured by means of a set of microphones positioned along the saxophone body, and the volume velocity produced by an acoustic source and measured at the instrument input. The microphones are housed on the stripped saxophone keys by means of tailored three-dimensional printed adapters. The AMA makes use of the FRFs to extract modal parameters, such as resonance frequencies, loss factors, and mode shapes. These parameters pertain to the cavity modes of the saxophone passive resonator. The analysis has been performed for three different notes (B ♭, B, and C) and for two registers of the instrument in order to show the potential of the technique. Moreover, the influence of the mouthpiece volume on the cavity modes has been shown. The information obtained by AMA can find useful application in the validation of analytical or numerical models of this kind of musical instruments.

Experimental Modal Analysis (EMA) is very helpful in engineering design and manufacturing of machine components. In this paper, modal parameters which are natural frequencies, mode shapes and damping ratios are extracted for free-free boundary conditions circular shaft, using EMA, then two disks are added to this shaft as second case study. EMA has been verified as effective and accurate tool, despite of increasing geometrical complexity and nonlinear behaviour of the structure. The two well-known excitation techniques (i.e. impact hammer and shaker) are used for this purpose. For validation, natural frequencies and mode shapes are determined analytically and numerically by Finite Element Modelling (FEM) ANSYS 15 workbench software, and then compared with results obtained experimentally. Noticeable remarks about these approaches are listed. Coherence plots are compared between impact and shaker tests. Digital Signal Processing (DSP) settings like windows type and sample (record) time are compared. The recommended DSP settings mentioned in this work can be used as a general guidance for researchers and people who are working in modal analysis.

The experimental environments for impact tests are simple to construct compared to other vibration tests in experimental modal analysis. However, given that sufficient sampling time is necessary for the response to attenuate, the following two problems arise: The first is that work efficiency is lowered. The second is that the measurement time increases, which makes it more susceptible to noise. To solve these problems, it is common to shorten the sampling time and apply an exponential window to reduce the leakage error of the frequency response function (FRF). Although studies on the influence on the FRF exist, identification accuracy for damping characteristic and the influence on the residue have not discussed. In this study, the influence on the modal properties obtained and the accuracy of the results are clarified using numerical examples based on a circle fit and method using simultaneous equations of the real and imaginary parts of the FRF. Finally, the identification results were compared and made sure that the method using simultaneous equations of the real and imaginary parts of FRF can identify modal properties with high accuracy. This method is effective for improving the working efficiency and reducing the influence of noise.

通过锤击实验，对五层房屋缩尺模型进行了实验模态分析，利用数学软件MATLAB对所得数据进行相关处理得到结构模型的频响函数，运用模态参数识别频域法的相关原理对得到的频响函数进行相关模态参数的识别，获得了结构模型弱轴水平方向的固有频率和模态振型，并将所得结果与ANSYS有限元分析结果进行比较，检验了实验结果的准确性和有效性。 The experimental modal analysis of a five-storey building scale model is performed with the use of hammer test in this paper. After obtaining vibration signal data and processing them by means of mathematical software MATLAB, the FRF (Frequency Response Function) of the model is achieved. Then, the FRF is studied further to obtain the model’s horizontal modal parameters such as modal frequency and modal shape, using relevant modal parameter estimation methods in frequency domain. Furthermore, the results’ validity is examined and testified by means of the comparison between test’s results and that of ANSYS.

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

A longitudinal bar model that includes both stinger elastic and inertia properties is used to analyse the stinger's axial dynamics as well as the mass compensation that is required to obtain accurate input forces when a stinger is installed between the excitation source, force transducer, and the structure under test. Stinger motion transmissibility and force transmissibility, axial resonance and excitation energy transfer problems are discussed in detail;Stinger mass compensation problems occur when the force transducer is mounted on the exciter end of the stinger. These problems are investigated theoretically, numerically, and experimentally. It is found that the measured Frequency Response Function (FRF) can be underestimated if mass compensation is based on the stinger exciter-end acceleration and can be overestimated if the mass compensation is based on the structure-end acceleration due to the stinger's compliance. A new mass compensation method that is based on two accelerations is introduced and is seen to improve the accuracy considerably. The effects of the force transducer's compliance on the mass compensation are also discussed;A theoretical model is developed that describes the measurement system's FRF around a test structure's resonance. This model shows that very large measurement errors occur when there is a small relative phase shift between the force and acceleration measurements. These errors can be in hundreds of percent corresponding to a phase error on the order of one or two degrees. The physical reasons for this unexpected error pattern are explained. This error is currently unknown to the experimental modal analysis community;Two sample structures consisting of a rigid mass and a double cantilever beam are used in the numerical calculations and experiments.