Continuous Scanning Laser Doppler Vibrometry Research Articles

Operational Deflection Shape Measurements on Bladed Disks with Continuous Scanning Laser Doppler Vibrometry.

The continuous scanning laser Doppler vibrometry (CSLDV) technique is usually used to evaluate the vibration operational deflection shapes (ODSs) of structures with continuous surfaces. In this paper, an extended CSLDV is demonstrated to measure the non-continuous surface of the bladed disk and to obtain the ODS efficiently. For a bladed disk, the blades are uniformly distributed on a given disk. Although the ODS of each blade can be derived from its response data along the scanning path with CSLDV, the relative vibration direction between different blades cannot be determined from those data. Therefore, it is difficult to reconstruct the complete vibration mode of the whole blade disk. In order to measure the complete ODS of the bladed disk, a method based on ODS frequency response functions (ODS FRFs) has been proposed. While the ODS of each blade is measured by designing the suitable scanning paths in CSLDV, an additional response signal is obtained at a fixed point as the reference signal to identify the relative vibration phase between the blade and the blade of the bladed disk. Finally, a measurement is performed with a simple bladed disk and the results demonstrate the feasibility and effectiveness of the proposed extended CSLDV method.

A novel mirror-assisted method for full-field vibration measurement of a hollow cylinder using a three-dimensional continuously scanning laser Doppler vibrometer system

A novel general-purpose three-dimensional (3D) continuously scanning laser Doppler vibrometer (CSLDV) system was recently developed by the authors to measure 3D vibration of a structure with a curved surface. As a non-contact system, it can avoid the mass-loading problem in 3D vibration measurement using triaxial accelerometers. In previous studies, the 3D CSLDV system was used to measure 3D full-field vibration of a turbine blade with a curved surface and identify its operating deflection shapes (ODSs) and mode shapes. The 3D CSLDV system had the same level of accuracy as that with a commercial 3D scanning laser Doppler vibrometer system, but can measure many more points in much less time than the latter. However, the 3D CSLDV system can be limited by its field of view, which is a common problem for optical-based measurement devices. Moving the 3D CSLDV system to different positions to measure different parts of a test structure is not practical during 3D CSLDV measurement, since the system has to be re-calibrated once it has been moved, which can be time-consuming and introduce measurement errors. This work proposes a novel mirror-assisted testing methodology for 3D CSLDV measurement that aims to measure vibration of difficult-to-access areas of a structure without moving the 3D CSLDV system during the test, and stitch ODSs of its different parts together to obtain its panoramic 3D ODSs. The proposed methodology includes a novel scan trajectory design method that uses virtual areas of the structure behind the mirror to conduct continuous and synchronous scanning of three laser spots, and a novel velocity transformation method that uses virtual positions of three laser heads behind the mirror to stitch ODSs of different parts of the structure together. To demonstrate the proposed methodology, 3D CSLDV measurement is conducted on an aluminum hollow cylinder specimen, which has difficult-to-access areas such as its side and back surfaces, with the assistance of the mirror to obtain its panoramic 3D ODSs corresponding to its first two modes. Comparison between identified ODSs of the hollow cylinder specimen from the experiment and mode shapes from its finite element model is made and modal assurance criterion values are larger than 0.98.

Application of Time Synchronous Averaging in Mitigating UAV Noise and Signal Loss for Continuous Scanning Laser Doppler Vibrometry

The laser Doppler vibrometer (LDV) has been shown to be effective for a wide application of vibration assessments that are well accepted. One of the new avenues for exploring alternative measurement scenarios, mounting LDVs on unmanned aerial vehicles (UAVs) is emerging as a potential avenue for remote and harsh environment measurements. Such configurations grapple with the challenge of the LDV sensor head being sensitive to UAV vibration during flight and signal loss due to tracking error. This study investigates the effectiveness of several Time Synchronous Averaging (TSA) techniques to circumvent these obstacles. Through comprehensive evaluations, all three TSA techniques under investigation demonstrated significant potential in suppressing UAV-induced noise and minimising the effects of signal dropout. Traditional TSA showcased a remarkable sixfold enhancement in signal quality when analysed via the mean square error. However, the study also highlighted that while TSA and Multi-Cycle Time Synchronous Average (MCTSA) elevated signal clarity, there is a trade-off between noise suppression and signal duration. Additionally, the findings emphasise the importance of synchronisation between scanning and target vibration. To achieve optimal results in Continuous Scanning Laser Doppler Vibrometer measurements, there is a need for advanced algorithms capable of estimating target vibration and synchronising scanning in real-time. As the study was rooted in steady-state vibrations, future research should explore transient vibration scenarios, thereby broadening the application scope of TSA techniques in UAV-mounted LDV systems.

A novel demodulation method with a reference signal for operational modal analysis and baseline-free damage detection of a beam under random excitation

A novel demodulation method with a reference signal is developed for operational modal analysis and damage detection of a beam structure under random excitation. The novel demodulation method can process measurements of the beam by a continuously scanning laser Doppler vibrometer (CSLDV) system and measurements of a reference point on the beam by a single-point laser Doppler vibrometer to estimate its modal parameters, such as damped natural frequencies and undamped mode shapes. Damped natural frequencies of the beam are estimated from fast Fourier transforms of measurements of the CSLDV system. A cross-correlation function between a measurement of the CSLDV system and a measurement of a single-point laser Doppler vibrometer is calculated, and the cross-correlation function is multiplied by a sinusoidal signal whose frequency is an estimated damped natural frequency of the beam. The processed cross-correlation function is filtered by a low-pass filter to obtain the undamped mode shape of the beam that corresponds to the estimated damped natural frequency of the beam. Smooth polynomials are used to fit estimated undamped mode shapes, which can be considered as undamped mode shapes of an undamaged beam. Curvatures of estimated undamped mode shapes and polynomials are compared by curvature damage indices to determine the location of a damage in the beam. The novel demodulation method with a reference signal is investigated for baseline-free damage detection from both finite element simulation and experiment. Modal parameters of a finite element model of the damaged beam and a damaged beam specimen, which are under random excitation, are successfully estimated, and locations of damages in the beam model and beam specimen are accurately determined.

Interpretation of bimodal interference in and optimized operational modal analysis for long-range continuously scanning laser Doppler vibrometer measurements with a beam under white noise excitation

This paper explains the phenomenon of a dominant frequency in the spectrum of a raw response measured by a long-range continuously scanning laser Doppler vibrometer (LCSLDV) system being symmetrically shifted into two sharp peaks. This phenomenon is referred to as bimodal interference in this work, which gradually becomes obvious when the scanning length is greater than 0.5 m. Bimodal interference is significant because it makes natural frequencies unable to be estimated in LCSLDV measurements and this paper analyzes its nature. Natural frequencies and mode shapes of a structure under white noise excitation can be estimated by analysis of its responses measured by the LCSLDV system. The effect of bimodal interference has been ignored in previous LCSLDV and continuously scanning laser Doppler vibrometer (CLSDV) measurement studies, but its appearance makes the value of the dominant frequency not to be accurately identified. By deducing mathematical interpretation of bimodal interference with analysis of incidence and reflection of a continuously scanning laser beam in a tiny time interval and comparing experimental results with 21 groups of different conditions, it is concluded that bimodal interference is caused by signal coupling between the scanning frequency of the mirror and the vibration frequency of the measured structure. There is a positive correlation between the scanning frequency and the magnitude of the symmetric frequency shifts centered at the dominant frequency generated by bimodal interference. In experimental results of LCSLDV measurements with a distance of 60 m, the frequency shift ratio compared to the dominant frequency can be reduced to 0.06% when the scanning frequency is lower than 0.01 Hz. In this case, bimodal interference is not noticeable in the spectrum. The experiment was carried out on a cantilever beam machined based on a prescribed design. Modal parameters of the cantilever beam estimated by white noise excitation were successfully estimated by the LCSLDV system with a distance of 60 m. The maximum difference between the first four natural frequencies of the cantilever beam from the finite element model and the LCSLDV system was 2.97% and the minimum difference was 1.1%.

A novel robust edge detection method for full-field modal parameter estimation using an image-based tracking continuously scanning laser Doppler vibrometer system

A novel robust edge detection method is developed for an image-based tracking continuously scanning laser Doppler vibrometer (CSLDV) system to track a rotating structure without attaching any encoder or mark to it and scan its whole surface. The robust edge detection method can extract edges of the rotating structure from its complex background by processing grayscale images of the rotating structure. Once edges of the rotating structure are clearly shown in the processed image, their positions can be easily determined. To track a rotating structure like a rotating blade of a wind turbine with multiple blades, a distance condition is used to determine the position of an edge of the structure that needs to be tracked and estimate its real-time rotation speed. Once the position of the edge of the rotating structure is determined, the image-based tracking CSLDV system can scan the whole surface of the rotating structure via a two-dimensional scan scheme. An improved demodulation method is used to process measured data of response of the rotating structure subject to random excitation and estimate its modal parameters including damped natural frequencies and full-field undamped mode shapes. The robust edge detection method is investigated by tracking and scanning a rotating fan blade subject to random excitation with a complex background using the image-based tracking CSLDV system, and estimating modal parameters of the rotating fan blade with different constant speeds.

Identification of modal parameters of a model turbine blade with a curved surface under random excitation with a three-dimensional continuously scanning laser Doppler vibrometer system

Modal parameters of a model turbine blade with a curved surface excited by white noise are identified by a novel general-purpose 3D continuously scanning laser Doppler vibrometer (CSLDV) system via an extended demodulation method (EDM). The proposed general-purpose system is calibrated to synchronously and continuously move three laser spots on the curved surface of the blade along the same scan trajectory and capture its 3D vibrations. The EDM is used to estimate its damped natural frequencies (DNFs) and 3D full-field undamped mode shapes. Identified modal parameters are compared with those from a commercial 3D scanning laser Doppler vibrometer (SLDV) system. Differences between their first six DNFs are less than 1.5%; their first six mode shapes are highly correlated as their modal assurance criterion values all exceed 95%. However, the 3D CSLDV system has much higher efficiency in obtaining 3D mode shapes of the blade than the 3D SLDV system.

Complete operating deflection shapes and model updating for an excited structure in thermal environments via an optimized continuously scanning laser Doppler vibrometer with a two-dimension scan scheme

In order to improve the efficiency and accuracy of operational modal analysis (OMA) and model updating with structures in thermal environments, an optimized continuously scanning laser Doppler vibrometer (CSLDV) with a two-dimension scan (2D-S) scheme (CSLDV 2D-S) system was first utilized to estimate modal parameters for complete operating deflection shapes (ODSs). The experiment was carried out on a free-hanging plate made of aluminum. Before this work, the manual-moving laser Doppler vibrometer as a non-contact measurement method replaced heat resistant accelerometers and was used in thermal vibrational measurements to extract only a few dozens of measured points across the grid. The CSLDV is capable of efficient and spatially dense vibration measurements by sweeping its laser spot along a scan path on the surface of a structure. Compared with a manual-moving laser Doppler vibrometer in thermal vibrational measurements, an optimized CSLDV 2D-S system is able to measure thousands of vibration points in a few seconds and reconstitute precise multi-ODSs through the demodulation method and arranging each single ODS according to the position of scan paths on the measured structure. Hence, the complete ODSs can be meshed after interpolation, instead of rough mode shapes formed by the LDV. In terms of model updating considering thermal environments (MUCTE), the target responses composed of measured natural frequencies and selected complete ODSs, which are more physical and correspond to the FE model nodes one by one, replace the past practice, whose ODSs are inaccurate and extracted by frequency response function and commercial software. Even simplifying the cumbersome process of reconstructing a model from response data, the selected complete ODSs are capable of improving model accuracy by a factor of twenty. The model updating based on sensitivity analysis is implemented with the parameter choice of Young's and shear moduli. After MUCTE, the difference between updated and measured natural frequencies is reduced three times as much as those with the past method. The updated target parameters accord with the physical properties of the material in thermal environments and the updated FE model is capable of predicting the first twelve modes of the structure in a uniform 300 °C field.

A novel general-purpose three-dimensional continuously scanning laser Doppler vibrometer system for full-field vibration measurement of a structure with a curved surface

Three-dimensional (3D) full-field vibration measurement is significant to structures, especially those with curved surfaces. A triaxial accelerometer and a commercial non-contact 3D scanning laser Doppler vibrometer (SLDV) system are usually used in 3D vibration measurement of a structure. However, the triaxial accelerometer can lead to the mass-loading problem for a light-weight structure, and the 3D SLDV system can take a long time to complete scanning of a structure with a large surface in a step-wise scanning mode. This study proposes a novel general-purpose 3D continuously scanning laser Doppler vibrometer (CSLDV) system to measure 3D full-field vibration of a structure with a curved surface in a non-contact and fast way. The proposed 3D CSLDV system consists of three CSLDVs, a profile scanner, and an external controller, and is experimentally validated by measuring 3D full-field vibration of a turbine blade with a curved surface under sinusoidal excitation and identifying its operating deflection shapes (ODSs). A 3D zig-zag scan path is proposed for scanning the curved surface of the blade based on results from the profile scanner, and scan angles of mirrors in CSLDVs are adjusted based on relations among their laser beams to focus three laser spots at one location, and direct them to continuously and synchronously scan the proposed 3D scan path. A signal processing method that is referred to as the demodulation method is used to identify 3D ODSs of the blade. The first six ODSs from 3D CSLDV measurement have good agreement with those from a commercial 3D SLDV system with modal assurance criterion values larger than 95%. In the experiment, it took the 3D SLDV system about 900 s to scan 85 measurement points, and the 3D CSLDV system 115.5 s to scan 132,000 points, indicating that the 3D CSLDV system proposed in this study is much more efficient than the 3D SLDV system for measuring 3D full-field vibration of a structure with a curved surface.

Selection of optimal exciting frequency and Lamb wave mode for detecting wall-thinning in plates using scanning laser Doppler vibrometer

The continuous excitation-based scanning laser Doppler vibrometer (SLDV) has been gaining prominence as a defect-detecting tool because of its superior performance in discovering faults, such as thinning of structures, compared to conventional non-destructive evaluation methods. To date, the optimal test mode and frequency for interdigital transducers have been heuristically selected. Although this approach is effective for problems involving a small number of modes, heuristic algorithms have limitations with respect to problems involving multiple complex modes. Therefore, in this study, the determination of the inspection mode and frequency is formulated as an optimization problem, and the effective wavenumber and bandwidth of the high-pass and bandpass filters in signal processing are also considered. Numerical optimization examples show that the proposed method is effective and robust. An experiment with a thick plate with shallow defects was performed, and the quantitative images obtained showed the correct location of the defects with the proposed numerical optimal solution.

Operational modal analysis of a rotating structure using image-based tracking continuously scanning laser Doppler vibrometry via a novel edge detection method

A novel edge detection method is developed for an image-based tracking continuously scanning laser Doppler vibrometer (CSLDV) system to track a rotating structure without attaching any encoder or mark to it. The edge detection method can determine real-time positions of points on edges of the rotating structure by processing images captured by a camera in the tracking CSLDV system. Once a point on an edge of a rotating structure is determined, the position of the rotating structure is determined. The tracking CSLDV system can generate a scan path on the rotating structure and control its laser spot to sweep along the scan path. A newly developed improved demodulation method is used to process measured data of response of the rotating structure under random excitation and estimate its modal parameters including damped natural frequencies and undamped mode shapes. Damped natural frequencies of the rotating structure are estimated from fast Fourier transforms of measured data. Undamped mode shapes are estimated by multiplying measured data by sinusoidal signals whose frequencies are estimated damped natural frequencies and applying low pass filters to measured data multiplied by the sinusoidal signals. Experimental investigation of the edge detection method is conducted by using the tracking CSLDV system to track and scan a rotating fan blade. Modal parameters of the rotating fan blade under random excitation with different constant speeds and its instantaneous undamped mode shapes with a non-constant speed are estimated.

Full-field mode shape estimation of a rotating structure subject to random excitation using a tracking continuously scanning laser Doppler vibrometer via a two-dimensional scan scheme

A two-dimensional (2D) scan scheme is developed for a tracking continuously scanning laser Doppler vibrometer (CSLDV) system to scan the whole surface of a rotating structure subject to random excitation. A tracking CSLDV system is developed to track a rotating structure and sweep its laser spot on its surface. The measured response of the structure using the 2D scan scheme of the tracking CSLDV system is considered as the response of the whole surface of the structure subject to random excitation. The measured response can be processed by an operational modal analysis (OMA) method called the improved demodulation method based on a rigorous nonuniform rotating plate model to obtain modal parameters of the rotating structure, such as damped natural frequencies and undamped full-field mode shapes. Damped natural frequencies of the rotating structure are estimated from the fast Fourier transform of the measured response. Undamped full-field mode shapes are estimated by multiplying the measured response by sinusoids whose frequencies are estimated damped natural frequencies. Experimental investigation of the 2D scan scheme of the tracking CSLDV system and OMA method is conducted, and damped natural frequencies and undamped full-field mode shapes of a rotating fan blade with different constant speeds are estimated. It is theoretically and experimentally shown that damped natural frequencies of the rotating fan blade increases with its rotation speed.

The CSLDV Technique for Vibration Measurement of a Plate Structure with Arbitrary Rectangular Holes

The Continuous Scanning Laser Doppler Vibrometry (CSLDV) developed on the base of the galvanometer scanner system has made it possible to quickly obtain the full-field vibration responses within an intact structure without any hole. In order to make CSLDV also suitable for testing structures with arbitrary rectangular holes, a novel method of area-partitioned continuous scanning test and mode reconstruction is further proposed in this paper. In the first step, the surface of a flat plate structure with arbitrary rectangular holes is divided into several rectangular sub regions by an appropriate area-partitioned method, and the operational deflection shape(ODS) of each sub region is obtained by a continuous scanning at constant speed. Then, considering that the ODSs of all sub regions are spliced and the relative phases among them are different, the operational deflection shape of the whole structure is reconstructed based on linear function and other process. Finally, a plate structure with two arbitrary rectangular holes was taken as an example for modal test using the proposed method. At the same time, a validated experiment was performed using the SLDV measurement. The results show the mode shapes derived from the extended CSLDV are in agreement with those from SLDV and the Modal Assurance Criterion (MAC) between the two are all greater than 0.95. This method has great potential in practical engineering applications with the advantages of high efficiency and the full-field measurement.

Operational Modal Analysis of a Rotating Structure Subject to Random Excitation Using a Tracking Continuously Scanning Laser Doppler Vibrometer via an Improved Demodulation Method

Abstract A new operational modal analysis (OMA) method is developed for estimation of modal parameters (MPs) of a rotating structure (RS) subject to random excitation using a nonuniform rotating beam model, an image processing method, and an improved demodulation method. The solution to the governing equation of a nonuniform rotating beam is derived, which can be considered as the response of the beam measured by a continuously scanning laser Doppler vibrometer (CSLDV) system. A recently developed tracking CSLDV system can track and scan the RS. The image processing method determines the angular position of the RS so that the tracking CSLDV system can sweep its laser spot along a time-varying path on it. The improved demodulation method obtains undamped mode shapes (UMSs) of the RS by multiplying its measured response by sinusoids whose frequencies are its damped natural frequencies (DNFs) that are obtained from the fast Fourier transform (FFT) of the measured response. Experimental investigation of the OMA method using the tracking CSLDV system is conducted, and MPs of a rotating fan blade (RFB), including DNFs and UMSs, with different constant speeds and its instantaneous MPs with a nonconstant speed are estimated. Estimated first DNFs and UMSs of the stationary fan blade and RFB are compared with those from the lifting method that was previously developed by the authors.

Estimation of modal parameters of a beam under random excitation using a novel 3D continuously scanning laser Doppler vibrometer system and an extended demodulation method

A novel three-dimensional (3D) continuously scanning laser Doppler vibrometer (CSLDV) system that contains three CSLDVs and an external controller is developed to measure 3D vibration of a structure under random excitation, and a new operational modal analysis method is proposed to estimate its 3D modal parameters, including damped natural frequencies and undamped end-to-end mode shapes, by extending the conventional demodulation method. Calibration among three CSLDVs in the 3D CSLDV system based on the geometrical model of its scan mirrors is conducted to adjust their rotational angles and ensure that three laser spots can continuously and synchronously move along the same scan path on the structure. The extended demodulation method can estimate undamped mode shapes of the structure under random excitation by filtering raw response with a bandpass filter and multiplying the filtered response by sinusoidal signals with its damped natural frequencies obtained from the fast Fourier transform of raw response. Experimental investigation on one-dimensional (1D) and 3D CSLDV measurements for modal parameter estimation is conducted on a beam under white-noise excitation to validate the extended demodulation method and examine the accuracy of the 3D CSLDV system. Modal assurance criterion (MAC) values between the first four undamped mode shapes of the beam from 1D CSLDV measurement and corresponding damped mode shapes from 1D step-wise scanning measurement are larger than 95%. MAC values between the first four undamped mode shapes of the beam from 3D CSLDV measurement and corresponding damped mode shapes from 3D step-wise scanning measurement are larger than 90% in all the three directions of a specified measurement coordinate system.

Operational modal analysis of a rotating structure under ambient excitation using a tracking continuously scanning laser Doppler vibrometer system

A continuously scanning laser Doppler vibrometer (CSLDV) system is capable of rapidly obtaining spatially dense vibration measurement by continuously sweeping its laser spot along a path on a structure surface. This paper presents a new operational modal analysis (OMA) method for a rotating structure based on a rigorous rotating beam vibration theory, an image processing method, and a data processing method called the lifting method. A novel tracking CSLDV (TCSLDV) system was developed in this work to track and scan a rotating structure, and the real-time position of the rotating structure can be determined by image processing so that the TCSLDV system is capable of tracking a time-varying scan path on the rotating structure. The lifting method can transform raw TCSLDV measurement into measurements at multiple virtual measurement points as if they were measured by transducers attached to these measurement points. Modal parameters of the rotating structure with a constant speed, including damped natural frequencies, undamped mode shapes, and modal damping ratios, and operating deflection shapes (ODSs) of the structure with a constant or prescribed time-varying rotation speed can be determined by calculating and analyzing correlation functions with non-negative time delays among measurements at virtual measurement points. Experimental investigation is conducted using the TCSLDV system to study the OMA method with which modal parameters and ODSs of a rotating fan blade with different constant speeds, as well as an ODS of the rotating fan blade with a non-constant speed, are successfully estimated.

Diagnostics Based on Continuous Scanning LDV Measurements and RASTAR Analysis Method

This paper presents a technique for rapid diagnostics of structural integrity that exploits spectral sidebands measured by the continuous scanning LDV (CSLDV) measurement method. Structural integrity can be monitored by Operational Deflection Shapes ODSs, which can be quickly measurable at any excitation frequency when a laser continuously scans a vibrating surface. The LDV output time series is an amplitude modulated signal, and its spectral lines are used for recovering polynomial coefficients which build a polynomial function describing a deflection shape. The process of conversion from the time series to a polynomial function can be biased by measurement and analysis uncertainty which eventually will affect the quality of recovered ODS. This paper will show that an effective, rapid and straightforward diagnostics can be yielded by direct analysis of the spectral sidebands without the need to be transformed into polynomial coefficients. The Relative Amplitude of the Sidebands to the Total Amplitude Reference (RASTAR) method is an indicator that exploits the relative amplitude of the sidebands against a datum reference. The relative magnitudes of the sidebands will not change in the absence of any the structural change, and it is independent of the vibration response amplitudes set for the measurements. Such diagnostic method suits maintenance operations of structures which could be quickly scanned by an SLDV system providing an indicative level of structural integrity over the number of duty cycles.

Modal parameter estimation using free response measured by a continuously scanning laser Doppler vibrometer system with application to structural damage identification

Spatially dense vibration measurement can be obtained by use of a continuously scanning laser Doppler vibrometer (CSLDV) system that sweeps its laser spot along a scan path. For a linear, time-invariant, viscously damped structure undergoing free vibration, a type of vibration shapes called free response shapes was defined and obtained by the authors using a CSLDV system with the demodulation method. To date, application of free response shapes is limited to structural damage identification, and they cannot be directly used for model validation while mode shapes can be. This paper extends the concept of free response shapes by proposing a new modal parameter estimation (MPE) method using a CSLDV system to estimate modal parameters of the structure undergoing free vibration, including natural frequencies, modal damping ratios, and mode shapes; the MPE method is applicable to linear structures without repeated and closely spaced modes. Advantages of the proposed method are: (1) modal damping ratios and mode shapes can be accurately estimated from obtained free response shapes in the least-square sense, (2) the scanning frequency of the CSLDV system can be relatively low, and (3) estimated mode shapes can be used for structural damage identification as if they were measured by stepped scanning of a scanning laser Doppler vibrometer. A baseline-free method is applied to identify structural damage using mode shapes estimated by the proposed MPE method. The method does not require any baseline information of an undamaged structure, such as its complete geometry, material properties, boundary conditions, modal parameters, and operating deflection shapes. In the proposed MPE method, natural frequencies of the structure are identified from free response of certain fixed points on the structure; its modal damping ratios and mode shapes are simultaneously estimated using free response shapes measured by a CSLDV system. Both numerical and experimental investigations are conducted to study the MPE method and its application to baseline-free damage identification with mode shapes estimated by the MPE method.

Extension of continuous scanning laser Doppler vibrometry measurement for complex structures with curved surfaces

The continuous Scanning Laser Doppler Vibrometry (SLDV) developed on the base of the galvanometer scanner system has made it possible to quickly obtain the full field vibration responses within a rectangular area of the structure. In this paper, an arbitrary continuous scanning path generating method for Continuous Scanning Laser Doppler Vibometry (CSLDV) is further put forward in order to allow the CSLDV suitable for testing structures featured by complex shapes not just for regular areas. In the first step, the relationship between position of laser spot and the driving voltages of galvanometer scanner system has been described by a mathematical modeling. Then, a novel arbitrary scanning path generating strategy based on CSLDV is presented by deforming a normalization rectangular scanning path to an arbitrary continuous scanning path. The mapping relation between the normalization rectangular scanning path and arbitrary continuous scanning path is established using the reference points. In the second step, a compressor blade with curved surface was taken as an example for modal test using the proposed method. At the same time, a validated experiment was performed in SLDV. The results show the mode shapes derived from the extended CSLDV are in agreement with those from SLDV and the Modal Assurance Criterion (MAC) between the two are all greater than 0.96. They also demonstrate the feasibility and effectiveness of the proposed method for CSLDV test and show strong potential on further practical engineering applications.

Fast modal rotation measurement using a dual sinusoidal-scan continuously scanning laser Doppler vibrometer

Rotational degrees of freedom (DOF) are usually indirectly derived from the measured translational DOF in structural dynamic tests by using the finite difference method. However, the noise of translational DOF measurement is easily propagated and further amplified when the finite difference method is employed to obtain the rotational DOF. Therefore, the accuracy of the obtained rotational DOF was rather poor. In order to overcome this disadvantage, a novel approach of using a dual sinusoidal-scan continuously scanning laser Doppler vibrometer (CSLDV) with the objective of obtaining the structural modal rotational DOFs is put forward in this paper. For plate structures, the operational deformation shape of the normal translational DOFs can be measured and described with polynomial functions through the modulation of CSLDV output signals. Then, rotational out-of-plane DOFs can be achieved with respect to the first derivatives of the polynomial functions along orthogonal directions. In such a way, the measurement noise that considerably affects the rotational out-of-plane DOFs derived from normal translational DOF can be significantly eliminated. The approach is validated experimentally with a cantilever plate structure, and a comparison with the results obtained from discrete point measurement is given. The results demonstrate the noticeable improvement in accuracy and spatial resolution of the proposed technique.