The Improved Frequency Response Function and its Effect on Modal Circle Fits

1984 ◽  
Vol 51 (3) ◽  
pp. 657-663 ◽  
Author(s):  
K. B. Elliott ◽  
L. D. Mitchell
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Frequency Response Function ◽  
System Analysis ◽  
Resonance Region ◽  
Random Excitation ◽  
Structural Parameter ◽  
Parameter Estimates ◽  
Average Percentage ◽  
Fitting Error

When structures are excited by random force excitation the circle fits of the data around resonance are usually poor. The structural parameter estimates, which result from this fit, are usually erroneous. No matter how elegant the circle or the multimodal fit, the results will be poor if the frequency response function (FRF) is a poor representation of the actual structural response. In general for the random excitation case, this is the case. The conventional fast Fourier transform (FFT) method which is used to estimate the frequency response function, is given by H1 (f) = Gxy/Gxx. This produces poor results when the coherence of the data falls in the resonance region. A drop in the coherence usually indicates noise at the input of the structure for this case. H1 (f) is quite sensitive to such noise giving erroneous estimates. This paper investigates an alternative method for computing the frequency response function, H2 (f) = Gyy/Gyx, and its impact on the accuracy of the circle fit procedure used in modal analysis. This new estimator is not sensitive to input noise like the currently used H1 (f). H2(f) provides the best estimate at or around resonance even in the presence of noise on the input signal. If one defines the average percentage fit error in the circle fit operation as 100 times the average radial deviation of the data points from the radius of the statistically fit circle divided by the fit circle radius, one can compute the circle fit accuracy for each of the proposed methods of data treatment. Typically, the percentage fitting error for H1 (f) might be 10 percent while the fitting error for H2 (f) using exactly the same data will be 0.5 percent. Thus, the proposed method eliminates long-standing system analysis errors through the use of a simple revision of the way the data are treated in the FFT processor around the resonance regions.

Characterization of Electro-Active Paper Vibration Sensor by Impact Testing and Random Excitation

2015 ◽  
Vol 07 (04) ◽  
pp. 1550065 ◽  
Author(s):  
Zafar Abas ◽  
Dong Ho Yang ◽  
Heung Soo Kim ◽  
Moon Kyu Kwak ◽  
Jaehwan Kim
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Polyvinylidene Fluoride ◽  
Frequency Response Function ◽  
Low Frequency ◽  
Random Excitation ◽  
Impact Testing ◽  
Vibration Sensor ◽  
Dynamic Strain ◽  
The Time Domain

We characterized a vibration sensor made of piezoelectric paper by measuring the frequency response function of an aluminum cantilever that was subjected to impulse loading and random excitation. The dynamic characteristics of the device were measured by recording the transient response of the smart cantilever beam with a pair of electro-active paper (EAPap) and polyvinylidene fluoride (PVDF) sensors located at a 5 mm distance from the clamped end as well as from a second pair of piezoelectric sensors located at a distance of 140 mm. The responses were measured by impacting the cantilever at its tip and at its mid-point. A fast Fourier transform was applied on the time domain data to measure the resonant frequencies of the vibrating structure. Both the EAPap and the PVDF sensors were observed to be very sensitive to varying levels of dynamic strain. The EAPap sensor showed a low strain sensitivity that was found to be desirable due to the inherent piezoelectricity and eco-friendly behavior of the material. The results revealed that the dynamic sensing ability of the EAPap at a low frequency range was quite comparable to that of PVDF when monitoring structural vibrations. The frequency response function was also measured via random excitation, piezoelectricity of the EAPap sensor shows potential for sensing vibrations with a dynamic response.

Rapid Measurement of Modal Properties Using FFT Analyzers With Random Excitation

1986 ◽  
Vol 108 (4) ◽  
pp. 394-398 ◽  
Author(s):  
P. Cawley ◽  
L. G. Rigner
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Frequency Response Function ◽  
Random Excitation ◽  
Nyquist Plot ◽  
Frequency Resolution ◽  
Testing Time ◽  
Rapid Measurement ◽  
Modal Amplitude ◽  
Time Required

The use of a Nyquist plot of the H2 (Syy/Sxy*) frequency response function estimates produced by an FFT based spectrum analyzer with random excitation to obtain modal amplitudes and hence modal constants has been investigated. It has been proved that, irrespective of the frequency resolution used, the H2 estimates always lie on the true modal circle so even at coarse frequency resolution, a circle fitted to these points gives accurate values of modal amplitude. The conventional H1 (Sxy/Sxx) estimates lie inside the true modal circle. Use of the H2 technique results in major savings in the testing time required for a modal survey, particularly when measurements are to be taken at many points on the test structure.

The Accuracy of Frequency Response Function Measurements Using FFT-Based Analyzers With Transient Excitation

1986 ◽  
Vol 108 (1) ◽  
pp. 44-49 ◽  
Author(s):  
P. Cawley
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Frequency Response Function ◽  
Random Excitation ◽  
Frequency Resolution ◽  
Impact Excitation ◽  
Analogue Computer ◽  
Bias Error ◽  
Response Measurement ◽  
Theoretical Predictions

The accuracy of the frequency response measurement obtained using impact excitation and a Fast Fourier Transform based spectrum analyzer has been investigated. It has been shown that with impact excitation, provided the impacts are reproducible and the extraneous noise level is low, the coherence estimates obtained from the analyzer are unity, irrespective of the frequency resolution employed. Hence the H1 (Sxy/Sxx) and H2 (Syy/Sxy*) frequency response function estimates are identical. However, these frequency response function estimates are affected by a bias error caused by inadequate frequency resolution so unity coherence does not necessarily imply accurate results. The results with impact excitation are compared with those obtained using random excitation where both the coherence and frequency response function estimates are affected by bias error. The bias error in the frequency response function estimates with impact excitation is intermediate between that in the H1 and H2 estimates when random excitation is used. The theoretical predictions have been verified by tests on an analogue computer and on a built-up structure.

scholarly journals Road Roughness Estimation Based on the Vehicle Frequency Response Function

Actuators ◽  
2021 ◽  
Vol 10 (5) ◽  
pp. 89
Author(s):  
Qingxia Zhang ◽  
Jilin Hou ◽  
Zhongdong Duan ◽  
Łukasz Jankowski ◽  
Xiaoyang Hu
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Frequency Response Function ◽  
Gaussian White Noise ◽  
Estimation Method ◽  
Time Shift ◽  
Ride Quality ◽  
The Road ◽  
Road Roughness ◽  
Measured Response

Road roughness is an important factor in road network maintenance and ride quality. This paper proposes a road-roughness estimation method using the frequency response function (FRF) of a vehicle. First, based on the motion equation of the vehicle and the time shift property of the Fourier transform, the vehicle FRF with respect to the displacements of vehicle–road contact points, which describes the relationship between the measured response and road roughness, is deduced and simplified. The key to road roughness estimation is the vehicle FRF, which can be estimated directly using the measured response and the designed shape of the road based on the least-squares method. To eliminate the singular data in the estimated FRF, the shape function method was employed to improve the local curve of the FRF. Moreover, the road roughness can be estimated online by combining the estimated roughness in the overlapping time periods. Finally, a half-car model was used to numerically validate the proposed methods of road roughness estimation. Driving tests of a vehicle passing over a known-sized hump were designed to estimate the vehicle FRF, and the simulated vehicle accelerations were taken as the measured responses considering a 5% Gaussian white noise. Based on the directly estimated vehicle FRF and updated FRF, the road roughness estimation, which considers the influence of the sensors and quantity of measured data at different vehicle speeds, is discussed and compared. The results show that road roughness can be estimated using the proposed method with acceptable accuracy and robustness.

scholarly journals Predicting Dam Flood Discharge Induced Ground Vibration with Modified Frequency Response Function

Water ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 144
Author(s):  
Yan Zhang ◽  
Jijian Lian ◽  
Songhui Li ◽  
Yanbing Zhao ◽  
Guoxin Zhang ◽  
...  
Keyword(s):  
Frequency Response ◽  
Frequency Distribution ◽  
Response Function ◽  
Frequency Response Function ◽  
Ground Vibration ◽  
Vibration Source ◽  
Ground Vibrations ◽  
High Energies ◽  
Flood Discharge ◽  
Opening Method

Ground vibrations induced by large flood discharge from a dam can damage surrounding buildings and impact the quality of life of local residents. If ground vibrations could be predicted during flood discharge, the ground vibration intensity could be mitigated by controlling or tuning the discharge conditions by, for example, changing the flow rate, changing the opening method of the orifice, and changing the upstream or downstream water level, thereby effectively preventing damage. This study proposes a prediction method with a modified frequency response function (FRF) and applies it to the in situ measured data of Xiangjiaba Dam. A multiple averaged power spectrum FRF (MP-FRF) is derived by analyzing four major factors when the FRF is used: noise, system nonlinearity, spectral leakages, and signal latency. The effects of the two types of vibration source as input are quantified. The impact of noise on the predicted amplitude is corrected based on the characteristics of the measured signal. The proposed method involves four steps: signal denoising, MP-FRF estimation, vibration prediction, and noise correction. The results show that when the vibration source and ground vibrations are broadband signals and two or more bands with relative high energies, the frequency distribution of ground vibration can be predicted with MP-FRF by filtering both the input and output. The amplitude prediction loss caused by filtering can be corrected by adding a constructed white noise signal to the prediction result. Compared with using the signal at multiple vibration sources after superimposed as input, using the main source as input improves the accuracy of the predicted frequency distribution. The proposed method can predict the dominant frequency and the frequency bands with relative high energies of the ground vibration downstream of Xiangjiaba Dam. The predicted amplitude error is 9.26%.

Response Prediction and Dynamic Substructuring for Coupled Structures in the Frequency Domain

2020 ◽  
Vol 36 (6) ◽  
pp. 867-879
Author(s):  
X. H. Liao ◽  
W. F. Wu ◽  
H. D. Meng ◽  
J. B. Zhao
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Frequency Response Function ◽  
Dynamic Properties ◽  
Main Idea ◽  
Prediction Method ◽  
Response Prediction ◽  
Synthesis Methods ◽  
Dynamic Substructuring ◽  
Coupled Structures

ABSTRACTTo evaluate the dynamic properties of a coupled structure based on the dynamic properties of its substructures, this paper investigates the dynamic substructuring issue from the perspective of response prediction. The main idea is that the connecting forces at the interface of substructures can be expressed by the unknown coupled structural responses, and the responses can be solved rather easily. Not only rigidly coupled structures but also resiliently coupled structures are investigated. In order to further comprehend and visualize the nature of coupling problems, the Neumann series expansion for a matrix describing the relation between the coupled and uncoupled substructures is also introduced in this paper. Compared with existing response prediction methods, the proposed method does not have to measure any forces, which makes it easier to apply than the others. Clearly, the frequency response function matrix of coupled structures can be derived directly based on the response prediction method. Compared with existing frequency response function synthesis methods, it is more straightforward and comprehensible. Through demonstration of two examples, it is concluded that the proposed method can deal with structural coupling problems very well.

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