Phase correction for frequency response function measurements

In modal testing, an impulse is often used to excite the structure and a linear transducer is used to measure the response. For these impact tests, two signals are measured: the impulsive force and the vibration response. Any lack of synchronization in the time domain acquisition of the two signals results in a frequency-dependent phase error in the frequency response function, or FRF. However, knowledge of the time delay may be used to correct the corresponding phase error. In this research, tests were conducted to measure the frequency-dependent phase error for a capacitive sensor and a frequency domain technique is proposed to correct the FRF. The method was validated using an FRF measurement of a cylindrical artifact mounted in a milling machine spindle.     

A firmware system for phase measurements in extremely low and ultralow frequency ranges

In experimental investigations of artificial and natural signals in extremely-low frequency (ELF) and ultra-low frequency (ULF) ranges, it is necessary to measure amplitudes and relative phases of the electromagnetic field components in a network of stations. The phase measurement includes accurate synchronization of data with the universal time. In this work, the geophysical data acquisition system, which allows one to synchronize measurement results and the coordinated universal time with an accuracy of a few microseconds, is described. Methods for processing the electromagnetic field components of the harmonic signal source, recorded by this data acquisition system, are proposed.     

Identification of damage on a substructure with measured frequency response functions

Recently the authors tried to find damage position only using measured frequency response functions. According to their work, it seems that the algorithm is very practical since it needs only measured frequency responses while other methods require exact analytic model. But when applying the method to a real structure, it requires lots of experiment. The authors, in this time, propose a method to reduce its experimental load by detecting damage within a substructure. This method searches damages not within an entire structure but within substructures. In addition, damage severity was treated in this paper since it is worthy to know damage severity. Optimization technique is used to estimate damage level using measured responses and damage model. Two test examples, a plate and a jointed structure, are chosen to verify the suggesting method.     

Experimental issues related to frequency response function measurements for frequency-based substructuring

Frequency-based substructuring is a very popular approach for the generation of system models from component measured data. Analytically the approach has been shown to produce accurate results. However, implementation with actual test data can cause difficulties and cause problems with the system response prediction. In order to produce good results, extreme care is needed in the measurement of the drive point and transfer impedances of the structure as well as observe all the conditions for a linear time invariant system.Several studies have been conducted to show the sensitivity of the technique to small variations that often occur during typical testing of structures. These variations have been observed in actual tested configurations and have been substantiated with analytical models to replicate the problems typically encountered. The use of analytically simulated issues helps to clearly see the effects of typical measurement difficulties often observed in test data.This paper presents some of these common problems observed and provides guidance and recommendations for data to be used for this modeling approach.     

A frequency response function-based damage identification method for cylindrical shell structures

In this paper, a structural damage identification method (SDIM) is developed for cylindrical shells and the numerically simulated damage identification tests are conducted to study the feasibility of the proposed SDIM. The SDIM is derived from the frequency response function solved from the structural dynamic equations of damaged cylindrical shells. A damage distribution function is used to represent the distribution and magnitudes of the local damages within a cylindrical shell. In contrast with most existing modal parameters-based SDIMs which require the modal parameters measured in both intact and damaged states, the present SDIM requires only the FRF-data measured in the damaged state. By virtue of utilizing FRF-data, one is able to make the inverse problem of damage identification well-posed by choosing as many sets of excitation frequency and FRF measurement point as needed to obtain a sufficient number of equations.     

A frequency response based structural damage localization method using independent component analysis

Vibration-based structural damage detection has been the focus of attention by many researchers over the last few decades. However, most methods proposed for this purpose utilize extracted modal parameters or some indices constructed on the basis these parameters. Our literature review revealed that few papers have employed frequency response functions (FRFs) for detecting structural damage. In this paper, a technique is presented for damage detection which is based on measured FRFs. Independent component analysis (ICA) has been implemented on the spatiotemporal responses in each frequency in order to reduce the dimension of the data. This is based on the concept that the forced harmonic response of a linear vibrating system can be fully captured utilizing a single ICA mode. A different approach is also presented in which ICA is applied to the frequency domain data. Operational deflection shapes (ODSs) have been decomposed using ICA to localize the damage. The efficiency of both methods is demonstrated through some numerical and experimental case studies.     

Differentiating damage effects in a structural component from the time response

This paper proposes an approach to differentiate the effect of local anomalies on the different load-resisting capacities of a structural component made of elastic isotropic material. The sensitivities of structural dynamic response with respect to different damage indices are derived. They are then used in a time-domain sensitivity-based algorithm for model updating using a gradient-based approach. A planar frame structure is studied in the numerical simulation. Results show that the proposed method can effectively locate and quantify the different types of damage effects, and the proposed method is insensitive to measurement noise. Laboratory verification was performed with a three-dimensional truss structure with the identified results clearly showing how much a local physical damage can change the different physical parameters that lead to the load-resisting capacities of a structural component.     

Time dependant measurements of cavitation damage

Due to the extremely long length of experiments, in most studies of cavitation erosion only damage in the incubation period is measured and the final damage (mass loss rate) is then predicted by extrapolation. The methods of extrapolation are usually very basic since there were almost no in depth time dependant measurements of cavitation erosion performed in the past. A rotating disc test rig that generates a very aggressive cavitation and pure copper specimens, as erosion sensors, were used to investigate the correlation between the damage within the incubation period and final mass loss. The damage was measured optically three times during the incubation period and by weighing the specimen during the rest of the experiment.The results confirmed that the same clear relationship between the damage in the incubation period and the final mass loss rate exists, what means, that the mass loss rate can indeed be qualitatively predicted on the basis of measurements performed within the incubation period. This is a good basis for developing laws of extrapolation from a short time scale (laboratory measurement within the incubation period) to the real time scale (machine operation).     

Analysis of jitter influence in fast frequency measurements

This paper presents a theoretical analysis of possible jitter impact in application of numeric criterion for fast measurement of frequency by coincidence principle. The primary goal is the generation of a signal containing a known amount of each jitter components. This signal was used for testing signals with regular pulse trains. Initially, jitter components are analyzed and modeled individually. Next, sequences for combining different kinds of jitter are modeled, simulated and evaluated. Jitter model simulation in Matlab is utilized to show the independence of frequency measurement results on the total jitter present in the reference and desired pulse trains independently. A good agreement between previously introduced theory of fast measurement of frequency and simulation in jitter presence is verified; these results allows to engineers use the numeric criterion for fast measurement of frequency in spite to interactions among jitter components in various applications for frequency domain sensors.     

相轨迹电涡流无损检测方法及频率响应特性研究

基于电磁涡流检测的变压器等效理论,研究了激励频率对电涡流等效变压器模型中各参数的影响。对不同频率正弦激励下空间磁通密度法相分量B_z信号进行相敏解调,并绘制其相轨迹图。仿真及实验结果表明,在不同频率的电流激励下,B_z的相轨迹最大值点所处位置相同.在该最大值点处,单一频率激励下B_z的相轨迹均呈现较好的线性度。而当激励频率变化时,相轨迹的斜率k_B呈现出高维度的变化规律,利用多项式拟合方法对k_B=f(ω)进行最小二乘拟合后发现,被测材料表面及内部缺陷均会对k_B=f(ω)的模型产生影响,表面缺陷对高频部分影响更明显,而内部缺陷使低频部分的变化更大。利用这一结论可有效识别缺陷深度,且该方法实现了对提离噪声的抑制。     

Parametric identification of structural nonlinearities from measured frequency response data

Structural nonlinearity is a common phenomenon encountered in engineering structures under dynamic loading. In several cases, linear theory can suffice to analyze nonlinear systems to some extent. However, there are cases where nonlinear effects and therefore nonlinear analysis become unavoidable. In most of the engineering applications it is usually very difficult if not impossible to model nonlinearity theoretically, especially for nonlinear effects stemming from structural connections. Then it becomes necessary to detect, localize and parametrically identify nonlinear elements from measured vibration data. In this study, two different methods, one being a method suggested recently by two of the authors of this paper, and the other being again a method developed in an earlier work, are implemented on a test rig containing a nonlinear element. Both methods are capable of parametrically identifying nonlinearities from measured frequency response functions. It is aimed in this paper to asses the validity of each method by applying them to a real test structure and thus parametrically identifying the nonlinear element in the system to obtain a mathematical model, and then employing the model in harmonic response analysis of the system in order to compare predicted responses with measured ones.     

High-pressure apparatus for dielectric measurements in high frequency

The present article describes an experimental apparatus for the measurement of low-loss dielectric material under conditions of high pressures (maximum pressure 1500 bars) and high frequencies (1-15 MHz.) The measurements of these losses are based on the classical method of the Q-meter with a general Radio type 1690-A sample holder, located in a high-pressure bomb. All the manual operations made on the holder during the measurements are controlled by dc motors. The first results have shown that the dielectric losses of polyethylene (PE) vary with the pressure. This apparatus will later be used in the measurement of the dielectric losses of the insulating materials used for submarine telecommunication cables.     

Matrix of the covariance of covariance of acceleration responses for damage detection from ambient vibration measurements

A new matrix on the covariance of covariance is formed from the auto/cross-correlation function of acceleration responses of a structure under white noise ambient excitation. The components of the covariance matrix are proved to be function of the modal parameters (modal frequency, mode shape, and damping parameter) of the structure. Information from all the vibration modes of the structure limited by the sampling frequency contributes to these components. The formulated covariance matrix contains more information on the vibration modes of the structure that cannot be obtained by the general methods for extracting modal parameters. When the component of the covariance matrix is used for damage detection, it is found more sensitive to local stiffness reduction than the first few modal frequencies and mode shapes obtained from ambient excitation. A simply supported 31 bar plane truss structure is studied numerically where a multiple damage scenario with different noise levels is identified with satisfactory results.     

Uncertainty analysis of high frequency image-based vibration measurements

Image-based vibration measurement techniques allow to remotely measuring the displacement of multiple targets in the field of view, without the need to mount anything on the measurand. In this paper the uncertainty budget of vision systems has been performed in order to both optimize the measurement procedure and identify the potential application fields. Two different types of camera are used in this work, both of them equipped with a 1280 × 1024 px sensor but with two different maximum frame rates at full resolution: 25fps and 2000fps respectively. The uncertainty analysis proposed here is based on a careful identification of the uncertainty sources and on experimental tests on an electro-magnetic shaker, where the displacement measured with the cameras are calibrated by means of the reference measurements provided by state-of-the-art traditional techniques.     

Reduction of frequency noise and frequency shift by phase shifting elements in frequency modulation atomic force microscopy

We recently reported the analysis of the frequency noise in the frequency modulation atomic force microscopy (FM-AFM) both in high-Q and low-Q environments [Rev. Sci. Instrum. 80, 043708 (2009)]. We showed in the paper that the oscillator noise, the frequency fluctuation of the oscillator, becomes prominent in the modulation frequency lower than f(0)∕2Q, where f(0) and Q are the resonance frequency and Q-factor. The magnitude of the oscillator noise is determined by the slope of the phase versus frequency curve of the cantilever at f(0). However, in actual FM-AFM in liquids, the phase versus frequency curve may not be always ideal because of the existence of various phase shifting elements (PSEs). For example, the spurious resonance peaks caused by the acoustic excitation and a band-pass filter in the self-oscillation loop increase the slope of the phase versus frequency curve. Due to those PSEs, the effective Q-factor is often increased from the intrinsic Q-factor of the cantilever. In this article, the frequency noise in the FM-AFM system with the PSEs in the self-oscillation loop is analyzed to show that the oscillator noise is reduced by the increase of the effective Q-factor. It is also shown that the oscillation frequency deviates from the resonance frequency due to the increase of the effective Q-factor, thereby causing the reduction in the frequency shift signal with the same factor. Therefore the increase of the effective Q-factor does not affect the signal-to-noise ratio in the frequency shift measurement, but it does affect the quantitativeness of the measured force in the FM-AFM. Furthermore, the reduction of the frequency noise and frequency shift by the increase of the effective Q-factor were confirmed by the experiments.     

Identifying and quantifying structural nonlinearities in engineering applications from measured frequency response functions

Engineering structures seldom behave linearly and, as a result, linearity checks are common practice in the testing of critical structures exposed to dynamic loading to define the boundary of validity of the linear regime. However, in large scale industrial applications, there is no general methodology for dynamicists to extract nonlinear parameters from measured vibration data so that these can be then included in the associated numerical models. In this paper, a simple method based on the information contained in the frequency response function (FRF) properties of a structure is studied. This technique falls within the category of single-degree-of-freedom (SDOF) modal analysis methods. The principle upon which it is based is effectively a linearisation whereby it is assumed that at given amplitude of displacement response the system responds at the same frequency as the excitation and that stiffness and damping are constants. In so doing, by extracting this information at different amplitudes of vibration response, it is possible to estimate the amplitude-dependent ‘natural’ frequency and modal loss factor. Because of its mathematical simplicity and practical implementation during standard vibration testing, this method is particularly suitable for practical applications. In this paper, the method is illustrated and new analyses are carried out to validate its performance on numerical simulations before applying it to data measured on a complex aerospace test structure as well as a full-scale helicopter.     

晶体倍频中光波折射对相位匹配的影响

晶体倍频中当晶体表面法线与相位匹配方向不一致时 ,需调整入射光方向使相位失配最小。讨论了光波折射对相位匹配的影响 ,提出了精确确定入射光方向的方法 ,此方法既可用于单轴晶体 ,也可用于双轴晶体。     

晶体倍频中光波折射对相位匹配的影响

晶体倍频中当晶体表面法线与相位匹配方向不一致时,需调整入射光方向使相位失配最小.讨论了光波折射对相位匹配的影响,提出了精确确定入射光方向的方法,此方法既可用于单轴晶体,也可用于双轴晶体.     

晶体倍频中光波折射对相位匹配的影响

晶体倍频中当晶体表面法线与相位匹配方向不一致时,需调整入射光方向使相位失配最小.讨论了光波折射对相位匹配的影响,提出了精确确定入射光方向的方法,此方法既可用于单轴晶体,也可用于双轴晶体.