Scanning Laser Doppler Vibrometer System Research Articles

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.

Delamination imaging in composites using cross-correlation method by non-contact air-coupled Lamb waves

This paper presents a cross-correlation damage detection technique using damage scattered waves of all directions cross-correlate with the incident waves for delamination imaging in carbon fiber reinforced polymer (CFRP) composite plate. The presented imaging can not only detect the delamination but also precisely quantify the damage with locations and sizes. First, a CFRP composite sample with interlaminar delamination by inserting the Teflon layer is designed and manufactured in house using the hot-press machine. And a three-dimensional model of composite sample is simulated using the finite element method. Next, the cross-correlation imaging algorithm is introduced in detail, and the cross-correlation imaging proof-of-concept study is conducted with the simulated Lamb waves in the composite sample. Finally, a fully non-contact air-coupled transducer and scanning laser Doppler vibrometer system with a single-mode Lamb wave method is established to actuate and sense the interrogating Lamb waves in the structure. The imaging method is experimentally implemented for the one delamination and two delaminations imaging and quantification.

Wave Attenuation in Additively Manufactured Polymer Acoustic Black Hole Structures Considering the Viscoelastic Effect.

The acoustic black hole (ABH) is a feature commonly found in thin-walled structures that is characterized by a diminishing thickness and damping layer with an efficient wave energy dissipation effect, which has been extensively studied. The additive manufacture of polymer ABH structures has shown promise as a low-cost method to manufacture ABHs with complex geometries, exhibiting even more effective dissipation. However, the commonly used elastic model with viscous damping for both the damping layer and polymer ignores the viscoelastic changes that occur due to variations in frequency. To address this, we used Prony exponential series expansion to describe the viscoelastic behavior of the material, where the modulus is represented by a summation of decaying exponential functions. The parameters of the Prony model were obtained through experimental dynamic mechanical analysis and applied to finite element models to simulate wave attenuation characteristics in polymer ABH structures. The numerical results were validated by experiments, where the out-of-plane displacement response under a tone burst excitation was measured by a scanning laser doppler vibrometer system. The experimental results illustrated good consistency with the simulations, demonstrating the effectiveness of the Prony series model in predicting wave attenuation in polymer ABH structures. Finally, the effect of loading frequency on wave attenuation was studied. The findings of this study have implications for the design of ABH structures with improved wave attenuation characteristics.

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.

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.

Modeling Full-Field Transient Flexural Waves on Damaged Plates with Arbitrary Excitations Using Temporal Vibration Characteristics.

We propose an efficient semi-analytical method capable of modeling the propagation of flexural waves on cracked plate structures with any forms of excitations, based on the same group of vibration characteristics and validated by a non-contact scanning Laser Doppler Vibrometer (LDV) system. The proposed modeling method is based on the superposition of the vibrational normal modes of the detected structure, which can be applied to analyze long-time and full-field transient wave propagations. By connecting the vibration-based transient model to a power flow analysis technique, we further analyze the transient waves on a cracked plate subjected to different excitation sources and show the influence of the damage event on the path of the propagating waves. The experimental results indicate that the proposed semi-analytical method can model the flexural waves, and through that, the crack information can be revealed.

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

A combined global-local approach for delamination assessment of composites using vibrational frequencies and FBGs

In this paper, a combined global-local strategy was developed for structural health monitoring (SHM) of fiber reinforced polymer (FRP) composites to assess the internal delamination damage, which has combined vibrational frequency shifts as the global index and the fiber Bragg grating (FBG) wavelength shifts as the local index. The delamination detection was carried out in two steps. The first step was based on the global damage index, which is the changes in multiple modes of frequencies measured by a non-contact scanning laser Doppler vibrometer (SLDV) system. Machine learning (ML) algorithms including support vector machine (SVM) and extreme learning machine (ELM) algorithms were used to initially predict the delamination interface, location, and size through frequency shifts. Numerical and experimental verification results show that SVM has a higher prediction accuracy than ELM when only a small number of samples exist, and the classification of SVM is better than its regression function to be used in the prediction of discrete delamination interfaces. To verify the damaged area predicted by frequency changes and further update the delamination edges with better accuracy, the second step has taken the changes in the wavelength of multiple FBG sensors as the local damage index. Multistage loads were applied at equidistant positions of the FRP specimens to induce deformations and the wavelength shifts in FBGs were used to determine the boundary of delamination. The results showed that delamination in FRP composites can be assessed more precisely using the global-local two-step SHM strategy, which can compensate for the shortcomings of only using vibration-based or FBG-based monitoring techniques. Besides, the SVM algorithm showed excellent predictive performance in both steps and had great potential in delamination damage monitoring.

State-of-charge and state-of-health estimation for lithium-ion battery using the direct wave signals of guided wave

With the development of new energy technology, lithium-ion battery, as a common energy storage and driving structure, has been widely used in many fields. It is significant to accurately monitor and evaluate the state of charge (SOC) and state of health (SOH) of lithium-ion battery. This paper presents the estimation method of SOC and SOH of lithium-ion battery based on ultrasonic guided wave technology. In the experiment, the guided wave signals are activated by a single fixed piezoelectric transducer and the propagating guided waves are rapidly captured using a scanning laser Doppler vibrometer system. The multi-parameter analysis of the direct wave signals including time-domain, frequency-domain and time-frequency distribution are performed, and thus three guided-wave parameters, namely signal amplitude, time of flight and power spectral density connected with the charge discharge cycle and aging of battery, are successively set to comprehensively evaluate SOC/SOH of lithium-ion battery. The results show that the guided wave parameters in time-domain, frequency-domain and time-frequency distribution have well consistent correspondence with SOC/SOH, and the differential curve analysis of signal amplitude can effectively reflect the phase transitions in the charge-discharge cycle and the aging process. In addition, the sensitivity of ultrasonic guided wave technology to estimation of SOC/SOH gradually decreases with the battery aging.

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.

Sparse Reconstruction and Damage Imaging Method Based on Uniform Sparse Sampling

The full wavefield detection method based on guided waves can efficiently detect and locate damages relying on the collection of large amounts of wavefield data. The acquisition process by scanning laser Doppler vibrometer (SLDV) is generally time-consuming, which is limited by Nyquist sampling theorem. To reduce the acquisition time, full wavefield data can be reconstructed from a small number of random sampling point signals combining with compressed sensing. However, the random sampling point signals need to be obtained by adding additional components to the SLDV system or offline processing. Because the random sparse sampling is difficult to achieve via the SLDV system, a new uniform sparse sampling strategy is proposed in this paper. By using the uniform sparse sampling coordinates instead of the random spatial sampling point coordinates, sparse sampling can be applied to SLDV without adding additional components or offline processing. The simulation and experimental results show that the proposed strategy can reduce the measurement locations required for accurate signal recovery to less than 90% of the Nyquist sampling grid, and the damage location error is within the minimum half wavelength. Compared with the conventional jittered sampling strategy, the proposed sampling strategy can directly reduce the sampling time of the SLDV system by more than 90% without adding additional components and achieve the same accuracy of guided wavefield reconstruction and damage location as the jittered sampling strategy. The research results can greatly improve the efficiency of damage detection technology based on wavefield analysis.

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.

Localization and characterization of delamination in laminates using the local wavenumber method

This paper proposes a method to effectively locate and characterize mode I delamination in carbon fiber/epoxy (CF/EP) composite laminates using the local wavenumber method of propagating guided waves in a fine grid of spatial sampling points. Mode I interlaminar fracture tests were conducted using a double cantilever beam (DCB) specimen to evaluate the developed method. Wave propagation in composite laminates with delamination at different center frequencies were investigated by two-dimensional finite element (FE) simulation. The results revealed some unique mechanisms of interaction between guided wave and delamination in detail. They demonstrated that the wave propagation velocity is transformed at the delamination, and the wave attenuation and dispersion are larger with the increase of the center frequency. The guided waves were rapidly excited at each grid point using a non-contact scanning laser Doppler vibrometer (SLDV) system and actuated by a single fixed piezoelectric (PZT) sensor in the experimental study. The spatially dependent wavenumber value of the center frequency was determined by the local Fourier domain analysis method for processing guided wave filed data. The results showed that the local wavenumber method for guided waves is capable of locating and characterizing the delamination in composite laminates.

Low reflection effect by 3D printed functionally graded acoustic black holes

The acoustic black hole (ABH) effect produces drastic wave compression and energy trapping in thin-walled structures. Recent research has shown that the reflected wave in laboratory ABH structures can be reduced by attaching a thin absorbing layer in specific wave concentration areas. In this paper, a novel design and implementation of one-dimensional (1D) functionally graded acoustic black hole (FG-ABH) is presented, as an alternative to achieve low reflection effects. Two configurations of the FG-ABHs are demonstrated, i.e., an axially graded ABH and a thickness graded ABH. The FG-ABH beams are manufactured by 3D printing technology using an Objet Connex 500 printer. Materials with varying levels of viscoelastic characteristics are produced using two base materials called TangoPlus and VeroWhitePlus. The FG-ABH beams have both diminishing thickness and elastic modulus in the tip of the ABH wedge. Numerical investigation of wave propagation, attenuation and reflection are conducted utilizing a viscoelastic code: University of Michigan’s Local Interaction Simulation Approach (UM/LISA). The damping effect of the materials is included based on Kelvin-Voigt viscoelastic theory. Finally, the process of wave propagation in FG-ABHs, traditional ABH and uniform beam are experimentally investigated using a Scanning Laser Doppler Vibrometer (SLDV) system. The reflection coefficients, i.e. the ratios between the amplitude of reflected wave and incident wave, are computed. Results indicate that the FG-ABHs enhance the ABH effect, and lower reflection is observed when compared to a traditional ABH structure.

Pulsed laser-scanning laser Doppler vibrometer (PL-SLDV) phased arrays for damage detection in aluminum plates

Lamb wave phased arrays employ sensors placed close to each other in compact distributions and can quickly inspect large plate-like structures through time (or phase) delays in the way analogous to radar. Traditional Lamb wave phased arrays usually adopt large-size ultrasonic transducers bonded on (or placed close to the surface of) a structure, and hence they limit the array configurability and cannot perform inspection from a far distance to the structure. This paper presents Lamb wave phased arrays implemented with a fully noncontact pulsed laser – scanning laser Doppler vibrometer (PL-SLDV) system, which employs a PL for exciting Lamb waves at a single PL spot through the thermoelastic effect and an SLDV for acquiring signals of Lamb waves at multiple scanning points based on the Doppler effect, respectively. The fully noncontact PL-SLDV phased arrays enable inspection from a far distance, as well as easily constructible receiver phased arrays in various configurations due to the use of high-resolution scanning laser. To generate inspection images with the acquired signals of Lamb waves, an improved delay-and-sum (DAS) imaging algorithm for receiver phased arrays is developed, where the exact Lamb wave frequency-wavenumber dispersion relation is considered for both the phase delay and back-propagation phase. This improved DAS imaging algorithm addresses the dispersion effect and results in higher radial imaging resolution, compared to the conventional DAS imaging algorithm. In addition, adaptive weighting factors are implemented to improve the angular imaging resolution. Proof-of-concept experiments demonstrate that multiple simulated defects of different sizes as well as broadside and offside simulated cracks can be successfully detected using a PL-SLDV phased array with a high-dispersion A0 mode. The experimental study also shows that the improved DAS imaging algorithm can achieve high radial and angular imaging resolution.

Identification of damage in plates using full-field measurement with a continuously scanning laser Doppler vibrometer system

An effective and reliable damage identification method for plates with a continuously scanning laser Doppler vibrometer (CSLDV) system is proposed. A new constant-speed scan algorithm is proposed to create a two-dimensional (2D) scan trajectory and automatically scan a whole plate surface. Full-field measurement of the plate can be achieved by applying the algorithm to the CSLDV system. Based on the new scan algorithm, the demodulation method is extended from one dimension for beams to two dimensions for plates to obtain a full-field operating deflection shape (ODS) of the plate from velocity response measured by the CSLDV system. The full-field ODS of an associated undamaged plate is obtained by using polynomials with proper orders to fit the corresponding full-field ODS from the demodulation method. A curvature damage index (CDI) using differences between curvatures of ODSs (CODSs) associated with ODSs that are obtained by the demodulation method and the polynomial fit is proposed to identify damage. An auxiliary CDI obtained by averaging CDIs at different excitation frequencies is defined to further assist damage identification. An experiment of an aluminum plate with damage in the form of 10.5% thickness reduction in a damage area of 0.86% of the whole scan area is conducted to investigate the proposed method. Six frequencies close to natural frequencies of the plate and one randomly selected frequency are used as sinusoidal excitation frequencies. Two 2D scan trajectories, i.e., a horizontally moving 2D scan trajectory and a vertically moving 2D scan trajectory, are used to obtain ODSs, CODSs, and CDIs of the plate. The damage is successfully identified near areas with consistently high values of CDIs at different excitation frequencies along the two 2D scan trajectories; the damage area is also identified by auxiliary CDIs.

Non-Model-Based Identification of Delamination in Laminated Composite Plates Using a Continuously Scanning Laser Doppler Vibrometer System

Delamination frequently occurs in a laminated composite structure and can cause prominent local anomalies in curvature vibration shapes associated with vibration shapes of the composite structure. Spatially dense vibration shapes of a structure can be rapidly obtained by use of a continuously scanning laser Doppler vibrometer (CSLDV) system, which sweeps its laser spot over a vibrating surface of the structure. This paper introduces a continuous scanning scheme for general quadrangular scan areas assigned on plates and extends two damage identification methods for beams to identify delamination in laminated composite plates using a CSLDV system. One method is based on the technique that a curvature vibration shape from a polynomial that fits a vibration shape of a damaged structure can well approximate an associated curvature vibration shape of an undamaged structure and local anomalies caused by structural damage can be identified by comparing the curvature vibration shape of the damaged structure with that from the polynomial fit, and the other is based on the technique that a continuous wavelet transform can directly identify local anomalies in a curvature vibration shape caused by structural damage. The two methods yield corresponding damage indices and local anomalies in curvature vibration shapes can be identified in neighborhoods with high damage index values. Both numerical and experimental investigations on effectiveness of the two methods are conducted on a laminated composite plate with a delamination area. In the experimental investigation, delamination identification results from the two methods were compared with that from a C-scan image of the composite plate.

Sound wave propagation on the human skull surface with bone conduction stimulation

BackgroundBone conduction (BC) is an alternative to air conduction to stimulate the inner ear. In general, the stimulation for BC occurs on a specific location directly on the skull bone or through the skin covering the skull bone. The stimulation propagates to the ipsilateral and contralateral cochlea, mainly via the skull bone and possibly via other skull contents. This study aims to investigate the wave propagation on the surface of the skull bone during BC stimulation at the forehead and at ipsilateral mastoid. MethodsMeasurements were performed in five human cadaveric whole heads. The electro-magnetic transducer from a BCHA (bone conducting hearing aid), a Baha® Cordelle II transducer in particular, was attached to a percutaneously implanted screw or positioned with a 5-Newton steel headband at the mastoid and forehead. The Baha transducer was driven directly with single tone signals in the frequency range of 0.25–8 kHz, while skull bone vibrations were measured at multiple points on the skull using a scanning laser Doppler vibrometer (SLDV) system and a 3D LDV system. The 3D velocity components, defined by the 3D LDV measurement coordinate system, have been transformed into tangent (in-plane) and normal (out-of-plane) components in a local intrinsic coordinate system at each measurement point, which is based on the cadaver head's shape, estimated by the spatial locations of all measurement points. ResultsRigid-body-like motion was dominant at low frequencies below 1 kHz, and clear transverse traveling waves were observed at high frequencies above 2 kHz for both measurement systems. The surface waves propagation speeds were approximately 450 m/s at 8 kHz, corresponding trans-cranial time interval of 0.4 ms. The 3D velocity measurements confirmed the complex space and frequency dependent response of the cadaver heads indicated by the 1D data from the SLDV system. Comparison between the tangent and normal motion components, extracted by transforming the 3D velocity components into a local coordinate system, indicates that the normal component, with spatially varying phase, is dominant above 2 kHz, consistent with local bending vibration modes and traveling surface waves. ConclusionBoth SLDV and 3D LDV data indicate that sound transmission in the skull bone causes rigid-body-like motion at low frequencies whereas transverse deformations and travelling waves were observed above 2 kHz, with propagation speeds of approximately of 450 m/s at 8 kHz.

Non-model-based multiple damage identification of beams by a continuously scanning laser Doppler vibrometer system

An effective non-model-based multiple damage identification method for beams by using a continuously scanning laser Doppler vibrometer (CSLDV) system is presented. Velocity response of a beam along a scan line under sinusoidal excitation is measured by the CSLDV system and a spatially dense operating deflection shape (ODS) of the beam along the scan line is obtained by the demodulation method from velocity response. An ODS of an associated undamaged beam is obtained by using a polynomial with a proper order to fit the ODS from the demodulation method. The curvature of an ODS (CODS) is used to identify abnormality induced by multiple damage. A curvature damage index (CDI) using differences between CODSs associated with ODSs that are obtained by the demodulation method and the polynomial fit is proposed to identify multiple damage. A normalized average CDI obtained by averaging CDIs at different excitation frequencies is defined to further assist multiple damage identification. Experiments on three beams with three damage on each beam in the form of three small cuts are conducted. Widths and depths of the three damage are varied from 3mm to 9mm with an increment of 3mm and from 5% thickness reduction to 15% with an increment of 5%, respectively, and their effects on ODSs, CODSs, and CDIs are investigated. Five frequencies obtained by rounding the first through fifth natural frequencies of the beams and one arbitrarily selected frequency that is not close to any natural frequency of the beams are used as sinusoidal excitation frequencies. Each damage is successfully identified near regions with consistently high values of CDIs at different excitation frequencies. The three damage on each beam is successfully identified with the normalized average CDI by obvious peaks at locations of the three damage.