Operational Deflection Shapes Research Articles

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.

Bridge damage detection using operating deflection shape ratios obtained from a passing vehicle

Large scale monitoring of bridge structures poses a significant challenge for infrastructure managers. This challenge could be overcome by using passing vehicles to monitor bridge condition. The operating deflection shapes of a bridge can theoretically be detected from in-vehicle measurements. This paper proposes a novel approach which introduces the concept of operating deflection shape ratios (ODSRs) from the responses measured on two following axles on a bridge. Unlike operating deflection shapes derived from drive-by measurements, ODSRs are non-dimensional values and are not a function of the bridge excitation level. This means that ODSRs are always constant for various vehicles passages. It is theoretically demonstrated in this study that ODSRs corresponding to each mode of bridge vibration can be approximately extracted from the responses of two following axles. Finite element modelling is employed to validate the feasibility of using ODSRs for bridge monitoring. The sensitivity of the ODSRs to damage is demonstrated numerically for damage at various locations, different vehicle speeds and different pavement roughness values. Laboratory experiments are then used to verify the theory in a practical environment. It is confirmed that the ODSR can be calculated from in-vehicle vibration measurements and can be used to detect changes in the structural behaviour of the bridge. The results of the study indicate that the ODSR represents a useful feature for drive-by bridge monitoring.

Idle Vibration Reduction of a Diesel Sport Utility Vehicle

This paper presents a study on the idle vibration reduction of a diesel sport utility vehicle (SUV). To reduce idle vibration, the transmission paths of vibration from the engine to the driver seat floor were investigated with the vehicle components related to idle vibration. Furthermore, operational deflection shape (ODS) tests were conducted to visualize the vibration shapes during engine idling. Experimental modal analyses were performed to obtain the natural frequencies and mode shapes. Through the ODS and modal tests, the vibration characteristics of the diesel SUV during idling were identified. Considering these vibration characteristics, a multi-body dynamic model for the diesel SUV described by differential equations of motion was established to evaluate the idle vibration. To implement the dynamic model effectively, the equivalent stiffnesses and damping coefficients included in the model were determined experimentally or analytically. The established dynamic model was verified by comparing the natural frequencies and idle vibration levels between simulations. Using this dynamic model, we analyzed the effects of various design variables on idle vibration and obtained an optimal design for reducing the idle vibration level. Finally, we present a design guide to reduce the idle vibration for diesel SUVs.

Advancements on bifurcation behavior and operational deflection shapes of disk brake creep groan

Disk brake creep groan vibrations are friction-induced stick–slip vibrations. Their impulse-like excitation, caused by the physical properties of the frictional contacts, leads to strongly nonlinear vibrations of brake system, axle and also chassis parts. As with many nonlinear phenomena, theoretical and experimental investigations on the bifurcation behavior were already done. So-far performed experiments used either strongly reduced setups or were limited in the controllability of testing, leading to certain deviations and a reduced complexity compared to the real-world behavior of the full vehicle. In this work, an approach based on half-axle tests is presented. Here, tire and rim are part of the system. By running drum-driven test matrices, extended stability maps of the rest position were created. An operational deflection shape (ODS) analysis over all 72 operating points of the test matrix was performed. Together with the relative speeds in the friction contact, a novel classification of creep groan phenomena is presented. These results prove an interaction between longitudinal and rotational axle displacements during creep groan, which was already assumed in corresponding vehicle tests. The insights enable a clearer distinction of creep groan, which is necessary for the accurate objective rating of creep groan phenomena in industry. Furthermore, the ODS results suggest the structure for a sufficient minimal model.

Streamlined particle filtering of phase-based magnified videos for quantified operational deflection shapes

Non-contact optical measurements are commonly used in industrial and research domains to obtain displacement measurements. This can be attributed to their noninvasive advantages over traditional instrumentation approaches. Phase-based motion estimation (PME) and magnification (PMM) are targetless methods that have been utilized recently to extract qualitative data from structures via experimental modal analysis (EMA) and operational modal analysis (OMA). Transforming the motion-magnified sequence of images into quantified operating deflection shape (ODS) vectors is currently being conducted via edge detection. Although effective, these methods require human supervision and interference; such that, accurate characteristics of the structure are guaranteed. Within this study, a new hybrid computer vision approach is introduced to extract the quantified ODS vectors from motion-magnified images with minimal human supervision. The particle filter (PF) point tracking method is utilized to track the desired feature points in the motion-magnified sequence of images. Moreover, the k-means clustering method is employed as an unsupervised learning approach to perform the segmentation of the particles and assign them to specific feature points in the motion-magnified sequence of images. Total variation denoising is used to smooth the motion-magnified artifacts, which improves ODS vector extraction and provides a robust outlier removal. The results show that the cluster centers can be applied to estimate the ODS vectors, and the performance of the proposed methodology is evaluated experimentally on a lab-scale cantilever beam.

Exploiting phase-based motion magnification for the measurement of subtle 3D deformation maps with FP + 2D-DIC

Phase-Based Motion Magnification (PBMM) is an effective methodology to visualise imperceptible phenomena based on magnifying periodic subtle movements on image sequences. Moreover, the integration of the optical techniques Fringe Projection and 2D Digital Image Correlation (FP + 2D-DIC) make it possible to obtain 3D displacement maps employing a single camera.In this study, the integration of PBMM with FP + 2D-DIC is exploited for the determination of subtle 3D displacements. An initial solid-rigid test validates of the combination of those techniques. A later test, employing a cantilever beam, demonstrates its correct performing in the determining of Operational Deflection Shapes. In both cases, the results are compared with those obtained with 3D-DIC and Scanning Laser Doppler Vibrometer (SLDV) to evaluate the relation between the magnification factor and the result obtained. Finally, the potential of the proposed integration for the determination of complex mode shapes is demonstrated by obtaining the ODSs of an industrial component.

Vibration reduction of cables with pendulum-type elastic metamaterials

Elastic metamaterials (EMMs) have been used to reduce the vibration of various mechanical structures. Recent studies have proposed methods to reduce the vibration of cables and space tethers by introducing pendulum-type EMMs. However, the vibration absorption characteristics in the bandgaps of pendulum-type EMMs need to be investigated in relation to the local resonances of the unit cell structure because only beams among the unit cell structure were considered. Furthermore, it is necessary to improve the vibration reduction performance of the pendulum-type EMMs by allocating as many bandgaps as possible in the frequency range of interest. In this study, the effect of the dynamic characteristics of the coupled structure with the same configuration as the unit cell structure including the ring or annular plate as well as the beam were investigated in depth. Further, based on these results, an improved pendulum-type EMM with multiple bandgaps in the frequency range of interest was developed, which is well suited for most practical applications in mechanical systems where the influence of low vibration modes is dominant. The vibration reduction performance and the effect of the bandgaps of the pendulum-type EMM with an annular plate were verified through comparison between the experimental and simulation results. The frequency response experiments and simulation results were consistent in terms of the resonant peak frequencies outside the bandgaps and the low response amplitude within the bandgaps. Moreover, the experimentally visualized and simulated operational deflection shapes showed that the cable hardly vibrates at the frequency within the bandgap; at this frequency, the operational deflection shape of the annular plate is very similar to the mode shape of the vibration mode of the coupled structure.

3D intra-cellular wave dynamics in a phononic plate with ultra-wide bandgap: attenuation, resonance and mode conversion

The intra-cellular wave dynamics of a water jetted phononic plate are experimentally investigated by means of high-resolution three-dimensional (3D) scanning laser Doppler vibrometry. The study is focused on the vibrational behavior around the ultra-wide bandgap of the plate (with a relative bandgap width of 0.89), as the critical frequency range of its phononic functionality. Broadband vibrational excitations are applied using a piezoelectric transducer and both in-plane and out-of-plane operational deflection shapes of the unit-cells are analyzed with respect to mode shapes calculated by finite element (FE) simulation. Attenuation and resonance of both symmetric and antisymmetric wave modes are validated, and it is shown that despite the absence of in-plane wave energy actuation, the symmetric modes are effectively excited in the phononic lattice, due to mode conversion from co-existing antisymmetric modes. Supported by FE modal analysis, this mode conversion observation is explained by the slight through-the-thickness asymmetry introduced during manufacturing of the phononic plate which leads to coupling of modes with different symmetry. The results confirm the potential of such detailed 3D inspection of phononic crystals (and in general acoustic metamaterials) in gaining full insight about their intracellular dynamics, which can also illuminate discrepancies with respect to idealized numerical models that might be due to manufacturing imperfections.

In-plane Operating Deflection Shape Measurement of an Aluminum Plate Using a Three-dimensional Continuously Scanning Laser Doppler Vibrometer System

In-plane Operating Deflection Shape Measurement of an Aluminum Plate Using a Three-dimensional Continuously Scanning Laser Doppler Vibrometer System

Identification of Internal Damage in Circular Cylinders through Laser Scanning of Vibrating Surfaces

With the aid of non-contact measurements of vibrating surfaces through laser scanning, operating deflection shapes (ODSs) with high spatial resolutions can be used to graphically characterize damage in plane structures. Although numerous damage identification approaches relying on laser-measured ODSs have been developed for plate-type structures, they cannot be directly applied to circular cylinders due to the gap between equations of motions of plates and circular cylinders. To fill this gap, a novel approach is proposed in this study for damage identification of circular cylinders. Damage-induced discontinuities of the derivatives of ODSs can be used to graphically manifest the occurrence of the damage, and characterize the location and size of the damage. The approach is experimentally validated on a specimen of the circular cylinder component, whose out-of-plane ODSs in an inspection region are acquired through laser scanning using a scanning laser vibrometer. The results suggest that the occurrence, location, and size of the internal damage of the circular cylinder can be identified.

Vibration Mode Contribution to Refrigerator’s Door and the Vibration Reduction

In this study, we investigated contribution of several vibration modes on refrigerator vibration at low compressor speed and attempted to decrease the refrigerator’s door vibration. At first, we measured the door vibration in the operational condition and large vibration was found at low speed. We then analyzed the main factor increasing the vibration through operational deflection shape (ODS) and vibration modes of the refrigerator. From these result, it was found that rigid vibration mode along front-back direction affected significantly to the door vibration at the operational condition. Finally, rubber mats were installed at front-bottom side of the refrigerator to decrease natural frequency of the rigid mode and the result showed that the vibration could be decreased largely.

A Multi-step Interpolated-FFT procedure for full-field nonlinear modal testing of turbomachinery components

Model updating for lightweight structures featuring geometrical nonlinearities has long been a goal in the aerospace industry, which requires spatially detailed measurement of the structure vibrating at large amplitudes. Performing such a measurement for lightweight structure is an extremely challenging task due to its low mass-to-area ratio, complex spatial deformation shapes, and geometrically nonlinear behaviours. Indeed, the current full-field measurements of nonlinear structural dynamics are mostly limited to flat, small-scale, academic structures such as beams or plates. To enable full-field measurement of nonlinear responses of large-scale industrial structures, a procedure based on the Three-Dimensional Scanning Laser Doppler Vibrometry (3D SLDV) is developed in this paper, in which full-field, multi-harmonic operating deflection shapes are measured when the structure is vibrating at its resonance. More specifically, a super-short sampling interval is used for each scan point to achieve a significant reduction in measurement duration. A novel Multi-step Interpolated-Fast Fourier Transform (Multi-step Interpolated-FFT) procedure is proposed to refine the coarse frequency resolution and suppress the severe spectral leakage of the signal spectra. In the procedure, the instantaneous driving frequency is first interpolated using the force signal and then used to perform a fixed-frequency interpolation for each harmonic of the response signals. In such a way, it allows accurate estimations of the frequencies, magnitudes and phase lags of the constituent harmonics in the measured signal sets. Numerical validations of the proposed procedure are carried out to investigate its accuracy and robustness with regard to different signal frequencies and noise levels before it is applied to experimental data of an industrial-scale fan blade. Results have shown that it allows, for the first time, to capture full-field, multi-harmonic operating deflection shapes of a large-scale, geometrically-nonlinear structure vibrating at its resonance. These spatially-detailed operating deflection shapes are advantages in describing local deformation patterns of a nonlinear structure, allowing essential ingredients in model updating algorithms, such as the Modal Assurance Criterion (MAC) values, to be correlated with exceptionally high quality.

A novel unknown-input and single-output approach to extract vibration patterns via a roving continuous random excitation

Operating deflection shape analysis allows investigating the dynamic behaviour of a structure during operation. It normally requires simultaneous, multi-point measurements to capture the response from an unknown excitation source (unknown-input and multiple-output), which can complicate its usage for structures without ease of access. A novel vibration pattern testing method is proposed based on a roving continuous random excitation employing a small robotic Hexbug device and a single-point measurement. The Hexbug introduces a random excitation in consecutive locations while roaming over the structure. The resulting multi-modal, time and location dependent response of the system is captured in a single location, and then analysed with a newly developed method based on empirical wavelet transform, multiscale morphological filtering and optimization to extract the excited vibration patterns. The efficiency of the proposed method is experimentally demonstrated on a free–free and a cantilevered beam with comparison to mode shapes extracted by hammer test. The validation highlights its ability to extract several vibration patterns from a long slender structure with good accuracy and robustness, with the general ability to expand the usability of an operating deflecting shape analysis.

Operational Deflection Shapes Magnification and Visualization Using Optical-Flow-Based Image Processing.

Much information can be derived from operational deflection shapes of vibrating structures and the magnification of their motion. However, the acquisition of deflection shapes usually requires a manual definition of an object’s points of interest, while general motion magnification is computationally inefficient. We propose easy extraction of operational deflection shapes straight from vision data by analyzing and processing optical flow information from the video and then, based on these graphs, morphing source data to magnify the shape of deflection. We introduce several processing routines for automatic masking of the optical flow data and frame-wise information fusion. The method is tested based on data acquired both in numerical simulations and real-life experiments in which cantilever beams were subjected to excitation around their natural frequencies.

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.

Ultrasonic Vibration-Assisted Ball Burnishing Tool for a Lathe Characterized by Acoustic Emission and Vibratory Measurements.

This paper focuses on a resonant system used to induce a low-amplitude movement and ultrasonic frequency to complement a ball burnishing process on a lathe. The system was characterized through the combination of different techniques. A full vibratory characterization of this process was undertaken with the purpose of demonstrating that the mechanical system—composed of the tool and the machine—does not present resonance phenomena during the execution of the operation that could lead to eventual failure. This dynamic analysis validates the adequateness of the tool when attached to an NC lathe, which is important to guarantee its future implementation in actual manufacturing contexts. A further aim was to confirm that the system succeeds in transmitting an oscillating signal throughout the material lattice. To this end, different static and dynamic techniques that measure different vibration ranges—including impact tests, acoustic emission measurement, and vibration measurement—were combined. An operational deflection shape model was also constructed. Results demonstrate that the only high frequency appearing in the process originated in the tool. The process was not affected by the presence of vibration assistance, nor by the burnishing preload or feed levels. Furthermore, the frequency of the assisting ultrasonic vibration was characterized and no signal due to possible damage in the material of the specimens was detected. These results demonstrate the suitability of the new tool in the vibration-assisted ball burnishing process.

LDV-induced stroboscopic digital image correlation for high spatial resolution vibration measurement.

Vibration measurement, particularly mode shape measurement, is an important aspect of structural dynamic analysis since it can validate finite element or analytical vibration models. Scanning laser Doppler vibrometry (LDV) and high-speed digital image correlation have become dominant methods for experimental mode shape measurement. However, these methods have high equipment costs and several disadvantages regarding spatial or temporal performance. This paper proposes a laser Doppler vibrometer induced stroboscopic digital image correction for non-contact mode shape and operational deflection shape measurement. Our results verify that single-point LDV and normal rate cameras can be used obtain high spatial resolution mode shape and operational deflection shape. Measurement frequency range is much higher than the camera capturing rate. We also show that the proposed approach coincides well with time-averaged electronic speckle pattern interferometry.

Application to visualize simultaneous vibrations of plates and ribs in a violin.

A code was written to explore, in real-time, experimental operational deflection shapes up to 5 kHz of a violin soundbox. The animations can be rotated and zoomed using the mouse, while the developed graphical user interface (GUI) allows controlling the frequency, amplitude, and frame-per-second rate. Also, some parts of the model can be hidden to improve the visualization of specific details of interest. The measurements-performed by students as laboratory exercise-include the ribs and not only the plates as it is traditionally done, thus the vibrations of the soundbox can be analyzed as a whole. Since the GUI was developed under a cross-platform open-source software (scilab), it can be easily installed and used as an educational tool for traditional in-person learning or online learning.

Phase-based displacement measurement on a straight edge using an optimal complex Gabor filter

In recent years, a number of phase-based motion processing techniques have been developed, and these allow for motion signals to be extracted from the local phase. The phase is generated by applying a pair of even- and odd-symmetric filters, and it is more robust to the intensity change. However, the phase can be unstable in certain areas where it is not linearly correlated with motion. This paper proposes an accurate and robust displacement measurement technique using an optimal complex Gabor filter and phase-based optical flow (POF) to measure the vibration response of a straight edge with the generated linear phase. The causes of nonlinear phase are discussed, and the nonlinearity of phase is used as an indicator of the measurement accuracy. Three types of nonlinear phase caused by noise background and inappropriate filter parameters for a straight edge are presented, along with solutions that optimize the parameters of the complex Gabor filter to obtain the phase with low nonlinearity. A numerical experiment is conducted on artificially created patterns to demonstrate the correlation between the proposed phase nonlinearity and the measurement accuracy. The validation experiments are carried out on a 5-story structure using a Laser Doppler Vibrometer (LDV) and a camera to demonstrate the accuracy and robustness of the proposed technique using the phase with low nonlinearity. The results show that the proposed technique can measure the vibration at 0.01-pixel scale. In addition, the robustness of the proposed technique is validated by performing experiments under different illumination conditions. The vibration responses of the 5-story structure with noisy background are measured using both accelerometers and a camera to perform the output-only modal identification. The results confirm that the proposed method can accurately identify modal frequencies, damping ratios, and high-resolution operational deflection shapes (ODS) requiring no pure background.

Baseline-Free Damage Identification Method for Lattice Sandwich Structures Based on Operational Deflection Shapes

ABSTRACT A novel baseline-free damage identification method based on high frequency operational deflection shapes (ODSs) is presented for debonding detection in lattice sandwich structures (LSSs). Two numerical models with different unit cells are constructed to analyze the vibration characteristics of a structure with debonded defect in the high-frequency band. The mode shapes and ODSs are computed numerically to investigate the local defect vibration effects. The results show that there will be obvious local vibration at the damaged location at a certain and appropriate frequency band. A baseline-free damage index calculated from ODSs is originally proposed for damage imaging. For experimental validation, we suggested an intermittent periodic excitation signal for vibration actuating, which may excite multiple ODSs at different frequencies using one measurement that significantly improve the detection efficiency. The experimental results also indicated that the proposed damage identification method is effective to locate the debonding damage in LSSs. The conclusions derived from this study are expected to provide an efficient vibration measurement technique and a practical damage detection method for LSSs, as well as other plate-like structures.