Higher Mode Shapes Research Articles

A comparison of high frequency force balance mode shape correction approaches for predicting wind effects on a high-rise building

A comparison of high frequency force balance mode shape correction approaches for predicting wind effects on a high-rise building

Full‐field out‐of‐plane vibration displacement acquisition based on speckle‐projection digital image correlation and its application in damage localization

AbstractStereo‐digital image correlation (Stereo‐DIC) has been widely explored for modal analysis in plate‐type structures due to its noncontact and full‐field advantages. However, when the traditional stereo‐DIC is adopted to capture the out‐of‐plane displacements, several challenging issues exist such as the development of surface speckles, asynchronous camera recording, and efficiency and accuracy degradation due to high computation costs. Moreover, with the captured out‐of‐plane displacements, effective and efficient evaluation of the high spatial resolution mode shapes and their application to damage localization are also critical problems. To tackle these issues, a speckle‐projection DIC technique using a single high‐speed camera is proposed to obtain the out‐of‐plane vibration displacements. Moreover, an enhanced peak‐picking modal analysis method is adopted to enhance the estimation accuracy and efficiency of mode shapes. In addition, the low‐rank property of mode shapes in an intact state and the spatial sparse property of damage locations are harnessed for the detection of damage positions without requiring reference data on the healthy state. Finally, the modal analysis and damage localization results based on the proposed speckle‐projection DIC are compared with those of the traditional two‐camera stereo‐DIC technique to verify its feasibility and effectiveness. It is found that the differences in the identified resonant frequencies between these two methods are smaller than 1% for higher modes. Moreover, the proposed speckle‐projection DIC has the same accuracy as the traditional two‐camera stereo‐DIC in terms of measurement accuracy, mode shape estimation, and damage localization.

3D structural vibration identification from dynamic point clouds

Video-based measurement has received increased attention for modal analysis and nondestructive evaluation, playing an important role in the development of the next-generation structural sensing technologies. As these techniques have evolved, more quantitative approaches based on computer vision techniques have emerged on full-field unsupervised structural identification, exploiting the benefits provided by the use of video cameras such as high spatial sensor density and low installation costs. More recent work has started to explore the use of laser point cloud data for 3D mapping of scenes and structures. Sensors such as LIDAR provide huge amounts of measurements at high spatial resolution from which it is possible to estimate accurate structural geometry for applications such as the generation of CAD models. Unfortunately to-date, the frame rate and depth resolution of LIDAR and other sensors capable of 3D geometry measurements has not been sufficient for measuring structural dynamics. In this paper, we introduce an approach for efficient and extremely high resolution 3D structural dynamic identification/modal analysis from point cloud data acquired using a commercial, low-cost, time-of-flight imager. Vibration mode shapes and modal coordinates are extracted from this data by creating virtual Lagrangian sensors based on the point clouds parameters. First, time-varying point cloud data are collected from a vibrating structure. Then, a mesh of virtual sensors is created based on the dynamic point cloud data for tracking the structure’s displacement over time. Next solutions to the blind source separation problem are employed to estimate high resolution 3D mode shapes, modal coordinates, and resonant frequencies. We demonstrate the potential of our proposed approach on laboratory tests and compare the results to the data collected from conventional laser displacement sensors. This technique represents an advance towards efficiently exploring the full advantages of using dynamic point cloud data for practical monitoring applications and has the potential to be extended for a wide range of 3D motion decomposition problems.

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.

An Innovative Tuned Liquid Damper for Vibration Mitigation of Structures

Tuned liquid dampers (TLDs) have been widely used for the vibration mitigation of structures. Conventional TLDs (CTLD) can only be tuned to one sloshing frequency. TLDs’ sloshing frequency is tuned to the fundamental period of structures because the dynamic response of the first mode shape is often dominant. In tall buildings and irregular structures, higher mode shapes’ response should also be controlled. Multiple tuned TLDs have been employed to control the dynamic response of higher mode shapes. However, in addition to a higher maintenance cost, multiple TLDs require a larger installation space. In this study, a modified TLD (MTLD) is introduced to mitigate multiple-mode shapes’ vibration simultaneously. The efficiency of the MTLD is demonstrated through several shake table tests conducted on a scaled 3-story structure. Free vibration tests show that the MTLD reduces the root mean square (RMS) of third floor’s displacement responses 1.9 times more than the CTLD. Besides, at the first resonance frequency (RF), the MTLD decreases the peak displacement response (PDR) and the peak acceleration response (PAR) of the third floor, respectively, 44% and 42% more than the CTLD. Results also indicate that while the CTLD cannot decrease the PAR of the third floor at the second RF, the MTLD decreases it by 44%. Moreover, at the second RF, MTLD reduces the PDR of the second floor 42% more than the CTLD.

Study on the dynamic characteristics of the horizontally encrypted column network spring vibration isolated turbine-generator foundation

To investigate the dynamic characteristics of the horizontally encrypted column network spring vibration isolated turbine-generator foundation, according to similarity theory, a 10:1 scale model of the horizontally encrypted column network spring vibration isolated turbine-generator foundation, including two condensers, was tested on site, and the dynamic characteristics of the model are analyzed by excitation method, and the natural frequencies, mode shapes and damping ratio of the integral structure are acquired. This study shows that the first two mode shapes of the turbine-generator foundation are translation and torsion, the high mode shape is accompanied by column-end swing and local distortion; the condenser is more stable in the integral structure; the natural frequency of this foundation is higher than the dual-row column spring vibration isolated turbine-generator foundation, and it is significantly lower than rigid foundation, and the mode shape distribution is different from them.

Identification of multiple cracks in noisy conditions using scale-correlation-based multiscale product of SWPT with laser vibration measurement

Simultaneous identification of multiple cracks is an unresolved issue in the structural health monitoring field. To address this issue, a new method is proposed for identifying multiple structural cracks using the scale-correlation-based multiscale product of the stationary wavelet packet transform (SWPT) of high-order (greater than 6) mode shapes, with particular emphasis on the ability of the method to distinguish damage in noisy conditions. With the method, the SWPT is firstly utilized to decompose a noisy high order mode shape into a set of uniform-frequency sub-bands. In each sub-band the SWPT coefficients have the property of shift invariance. Secondly, a scale correlation is introduced to screen out valid SWPT sub-bands containing an informative crack feature. On these sub-bands, manipulation of scale-correlation-based multiscale products is implemented to yield a multiscale product curve by multiplying sub-band coefficients across scales at every temporal step. In the curve, abrupt peaks form damage indicators that can pinpoint the locations of multiple cracks. In the damage indicator, the function of scale correlation in distinguishing effective sub-bands endows the scale-correlation-based multiscale product with strong ability to reveal damage while suppressing noise. The method is numerically verified using high-order mode shapes of beam-type structures with multiple cracks and experimentally validated on high-order mode shapes acquired using a scanning laser vibrometer, both demonstrating high accuracy and strong robustness against noise in the identification of multiple cracks. The proposed scale-correlation-based multiscale product forms a sophisticated mechanism for identifying multiple damage in noisy conditions, with promise for developing damage identification methods for a wide spectrum of structures.

High Frequency Modal Testing of the Multiblade Packets Using a Noncontact Measurement and Excitation System

High cycle failure of blades and vanes caused by the vibration is one of the major causes reducing the lifetime of turbomachines. For multiblade packets, the failure may occur at vibrations with high frequencies that can reach up to tens of kHz. The experimental modal testing of blades is crucial for the validation of numerical models and for the optimization of turbomachine design. In this paper, the test rig and procedure for measurements of dynamic characteristics of lightweight multiblade packets in wide and high frequency ranges are developed. The measurements are based on a noncontact excitation and noncontact measurement method, which allows the determination of the modal characteristics of the packets with high accuracy in wide frequency ranges. The responses of the multiblade packets are measured using a Scanning Laser Doppler Vibrometry (SLDV), while vibrations are excited by the acoustic excitation technique. Modal tests of the blade packet comprising 18 vane blades connected by shrouds are performed. The measurements are performed within the high frequency range of 0–30 kHz, and the natural frequencies and mode shapes are obtained for first 97 modes. To capture the complex high frequency blade mode shapes, each blade in the packet is scanned over 25 reference points uniformly distributed over the blade concave surface. In order to obtain the high frequency resolution, the frequency range used for the measurements is split into several frequency intervals accordingly to the number of spectral lines available in the used data acquisition system, and for each such interval, the test is performed separately. The finite model of the packet is created, and the numerical modal analysis is performed to compare the calculated natural frequencies and mode shapes with the experimental measurements. The comparison shows the satisfactory with those from finite element analysis. It illustrates the measurement method described in this work is effective and reliable.

Damage Detection Using Modal Rotational Mode Shapes Obtained with a Uniform Rate CSLDV Measurement

With the rapid development of a continuously scanning laser Doppler vibrometer (CSLDV) technique, the full-field mode shapes of structures with high accuracy can be obtained. In this paper, a novel damage detection method using modal rotational mode shapes obtained with a uniform rate CSLDV measurement is proposed. The modal rotational damage indicators considering the changes of modal rotational mode shapes between the damaged and the undamaged states are established. Because the modal rotational mode shapes are obtained through the derivative of the detailed displacement mode shapes of transitional degree-of-freedoms (DOFs) with respect to the orthogonal directions, they are more sensitive than the normal displacement mode shapes. The uniform rate CSLDV measurement is essentially a uniform straight-line scanning technique and the measured mode shapes can be directly obtained through the demodulation of vibration signals. Besides, taking it for granted that a priori knowledge of the undamaged structure is not known, the undamaged mode shapes can be reconstructed from the measured damaged data using the fitted polynomial functions in which the minimum number of polynomial function coefficients are determined by a fit value threshold. The proposed method is firstly demonstrated by numerical simulation of the crack plate and then a plate structure with three damaged cases is taken as an example for further experimental study. The experimental results indicate the following: (1) The uniform rate CSLDV measurement can obtain the high accuracy modal rotational mode shapes with the advantage of eliminating the contaminated noise in the measurement; (2) the modal rotational damage indicators of the torsional modes are the most sensitive to the crack damage and they can clearly identify single, multiple damages and locations of the plate, and even slight crack damage, respectively. The effectiveness of the method paves the way for practical applications, such as ultra-light or composite structures.

BAYESIAN FINITE ELEMENT MODEL UPDATING METHOD BASED ON MULTI-CHAIN DIFFERENTIAL EVOLUTION

To cope with the shortages of low sampling efficiency and difficult convergence of traditional Bayesian method under high-dimension parameters, a Bayesian based finite element model is proposed by the base of a multi-chain differential evolution algorithm. Based on the standard Markov chain Monte Carlo (MCMC) method, a differential evolution algorithm is introduced, and a random difference operation among multiple Markov chains is derived from the size and direction of an adaptive selection condition distribution to quickly approximate the target distribution. A subspace sampling algorithm which uses adaptive selection to select good parameter dimensions for sampling is introduced to improve sampling efficiency. Also, an anomaly Markov chain detection algorithm which detects and eliminates abnormities in Markov chains in the non-stationary period is introduced to improve the sampling efficiency in the stationary phase. The correction results of a simply-supported-beam model and a four-floor-frame-structure model show that the proposed method has a higher correction accuracy, better noise resistance, and better correction effects than that of DRAM algorithm under high order frequency and mode shapes, which provides a new way to improve the computational accuracy in uncertainty model correction.

STRESS AND VIBRATION ANALYSES OF THE WIND TURBINE BLADE (A NREL 5MW)

Owing to the fast development in the energy filed, the demand is increasing to improve energy efficiency and lifetime of wind turbine. Therefore, it's important to understand deeply the behavior of wind turbine under different load conditions. This research paper provides an approach to study and analyze the stresses and deformations under the steady-state condition. Also, it was investigated the vibration characteristics of the NREL offshore 5-MW blade (HAWT) with a long of (61.5 m) and with rotor diameter (126 m). The 3D model of wind turbine blade was created by using SOLIDWORKS and then exported to ANSYS/Workbench19 in order to achieve the numerical simulation based on Finite element method. The steady-state analysis of the selected wind turbine blade was performed at maximum rated power (maximum rotation velocity =12.1 rpm). In this work, three different materials (E-glass fiber, Kevlar, and Carbon fiber reinforced plastic) were selected to build the body of the wind blade parts. The results presented the von-Mises stresses, total deformations, first ten natural frequencies and mode shapes of NREL 5-MW wind turbine blade. In steady-state analysis, it was found that the optimum material was (CFRP) where the minimum level of stresses occurred. In vibration analysis, it was found the material that has a higher structural stiffness is CFRP material which avoids high frequencies and mode shapes.

Bayesian operational modal analysis and assessment of a full-scale coupled structural system using the Bayes-Mode-ID method

This paper presents a structural assessment project for a construction training center in Hong Kong. The training center consists of coupled main and complementary buildings. Due to the vigorous activities in the training center, the objectives of the project include conducting operational modal analysis (OMA) of the buildings to assess their structural performance and the coupling of vibrations between the two buildings. OMA is conducted using Bayes-Mode-ID recently developed by the authors, which is an efficient Bayesian modal-component-sampling system identification method for field testing of civil engineering structures under ambient vibrations. Implementation issues for Bayes-Mode-ID are discussed in detail for the full-scale coupled structural system. Due to the large number of measurement points (high resolution mode shapes are desired for understanding the coupling behavior of the system) and limited number of sensors, the measurements were divided into 21 setups in order to properly characterize the dynamics of the building. Each setup covered one portion of the training center and the partial mode shapes from different setups were assembled to provide the global mode shapes. By following a Bayesian approach, not only the most probable values (MPVs) of the modal parameters (modal frequencies, modal damping ratios and mode shapes) but also their associated uncertainties can be obtained. The identified modal parameters reveal interesting dynamic behaviors of the coupled-building and they will be helpful for structural assessment and structural health monitoring (SHM) of the training center in the future.

Effect of inclusion lagrange interpolation method in mode shape curvature based damage detection

Mode shape curvature based damage detection capable to detect damage in structure with high sensitivity. Sparse and high density mode shape displacement data obtained experimentally pose difficulties for mode shape curvature algorithm to quantify damage size accurately. The objective of this study is to compare damage detection sensitivity of different mode shape curvature algorithm with the inclusion of Lagrange interpolation to enhance the algorithm damage detection sensitivity for sparse and high density curvature mode shape displacement data. Finite element analysis (FEA) model with free-free boundary condition of an aluminum beam has been carried out to investigate the feasibility of the proposed method. Undamaged curvature mode shape data from the damaged structure was estimated using Gapped Smoothing Method (GSM) and Savitzky-Golay (SG) filters with two different grid points of 149 and 74. Structural Irregularity Index (SII) and Damage Estimate Reliability (DER) were used to evaluate the effectiveness of the proposed algorithm. Numerical results show inclusion of Lagrange interpolation in mode shape curvature algorithm with Savitzky-Golay filter has better performance on estimate damage size by 2.81% of DER value for less dense (74 grid points) compared to GSM. The present method shows the inclusion of Lagrange interpolation has increased the sensitivity of mode shape curvature algorithm to identify damage size in beam-type structures compared to the previous method.

An extension of a high order approach for free vibration analysis of the nano-scale sandwich beam with steel skins for two types of soft and stiff cores

The study investigates the free vibration of a nano-scale sandwich beam by an extended high order approach, which has not been reported in the existing literature. First-order shear deformation theory for steel skins and so-called high-order sandwich panel theory for the core are applied. Next, the modified couple stress theory is used for both skins and cores. The Hamilton principle is utilized for deriving equations and corresponding boundary conditions. First, in the study the three-mode shapes natural frequencies for various material parameters are investigated. Also, obtained results are evaluated for two types of stiff and soft cores and isotropic, homogenous steel skins. In the research since the governing equations and also the boundary conditions are nonhomogeneous, therefore some closed-form solutions are not applicable. So, to obtain natural frequencies, the boundary conditions are converted to initial conditions called the shooting method as the numerical one. This method is one of the most robust approaches to solve complex equations and boundary conditions. Moreover, three types of simply supported on both sides of the beam (S-S), simply on one side and clamp supported on the other one (S-C) and clamped supported on both sides (C-C) are scrutinized. The parametric study is followed to evaluate the effect of nano-size scale, geometrical configurations for skins, core and material property change for cores as well. Results show that natural frequencies increase by an increase in skins thickness and core Young modulus and a decrease in beam length, core thickness as well. Furthermore, differences between obtained frequencies for soft and stiff cores increase in higher mode shapes; while, the more differences are evaluated for the stiff one.

Efficient experimental identification of three-dimensional tyre structural properties

Modal testing is routinely applied to tyres for the identification of structural parameters and prediction of their vibration response to excitations. The present work focuses on the more demanding case of modal testing with the aim of constructing a full mathematical model of a tyre, appropriate for use in a generic time-based simulation. For this purpose, the less common free–free boundary condition is employed for the wheel, while the tyre belt is excited in all three directions, namely radial tangential and lateral. To improve efficiency, a novel partial identification method is developed for the mode shapes, whereby measured and predicted frequency responses are matched around distinct resonance peaks, while eliminating the effect of out-of-band modes. Axial symmetry of the tyre requires high purity mode shapes to avoid angular dependency of the tyre’s response. For this reason, experimental mode shapes are digitally filtered and combined with their orthogonal counterparts. Processed data reveal apparent repetition of selected mode shapes, and this is attributed to rim deflection.

Mass-normalized mode shape identification method for bridge structures using parking vehicle-induced frequency change

Mode shape identification is a crucial task in the field of bridge health monitoring. This paper proposes a mass-normalized mode shape identification method for bridge structures on the basis of its essential property of bearing vehicle load. First, the relationship between the bridge frequencies changes due to a parking vehicle, and the amplitudes of the mass-normalized mode shapes at the parking point is established through theoretical derivation. Subsequently, the algorithm and procedures to extract the mode shapes by using the frequencies measured on a two-axle vehicle that parks at different locations of the bridge progressively are proposed. Then the determination of the two-axle parking vehicle parameters and the distinctive features of the proposed method are discussed. Numerical and experimental examples of different bridge types are conducted to investigate the feasibility and effectiveness of the proposed identification method. The results indicate that the proposed method can obtain high spatial resolution mass-normalized mode shapes accurately with only one sensor on the parking vehicle.

Damage localization of beam structures using mode shape extracted from moving vehicle response

Mode shape curvature change has been regarded as a promising damage localization index (DLI). However, its application is limited by the requirement for high spatial resolution and reference mode shapes, and the central difference method induced low anti-noise ability. This paper aims to develop a new damage localization method by using the mode shapes extracted from moving vehicle response for beam structures without reference data. The first order mode shape with high spatial resolution in damaged state is extracted from the response measured on a moving vehicle via Hilbert transform (HT). Then regional mode shape curvature (RMSC) in damaged state which takes advantage of the high spatial resolution of mode shapes provided by moving vehicle test is defined to enhance the anti-noise ability. Subsequently the RMSC in undamaged state is estimated by the RMSC in damaged state and polynomial approximation under the assumption that RMSC in undamaged state has smooth surface. Finally an index is formulated based on RMSC before and after damage to localized damage. Numerical studies are conduced to investigate the effect of noise, moving velocity, uneven distribution of beam flexural rigidity, and road roughness on the accuracy of the proposed DLI.

High frequency mode shapes characterisation using Digital Image Correlation and phase-based motion magnification

Abstract High speed video cameras provide valuable information in dynamic events. Mechanical characterisation has been improved by the interpretation of the behaviour in slow-motion visualisations. In modal analysis, videos contribute to the evaluation of mode shapes but, generally, the motion is too subtle to be interpreted. In latest years, image treatment algorithms have been developed to generate a magnified version of the motion that could be interpreted by naked eye. Nevertheless, optical techniques such as Digital Image Correlation (DIC) are able to provide quantitative information of the motion with higher sensitivity than naked eye. For vibration analysis, mode shapes characterisation is one of the most interesting DIC performances. Full-field measurements provide higher spatial density than classical instrumentations or Scanning Laser Doppler Vibrometry. However, the accurateness of DIC is reduced at high frequencies as a consequence of the low displacements and hence it is habitually employed in low frequency spectra. In the current work, the combination of DIC and motion magnification is explored in order to provide numerical information in magnified videos and perform DIC mode shapes characterisation at unprecedented high frequencies through increasing the amplitude of displacements.

Finite element model updating of liquid rocket engine nozzle based on modal test results obtained from 3-D SLDV technique

In order to update the finite element model, the modal test results must be highly accurate since they are used as the basis. The major problems with traditional modal test method are limited measurement points and poor mode shape precision. In this paper, modal test based on 3-D Scanning Laser Doppler Vibrometry (SLDV) technique was carried out. High spatial resolution and accurate mode shapes were obtained, which is beneficial to subsequent correlation analysis and updating process. High order modal parameters were identified and more information can be added in the objective function. Due to the consistent coordinate system in modal test and finite element model, the measurement points and corresponding finite element nodes were easily matched in order to compare mode shapes. By means of a real liquid rocket engine nozzle, an integrated model updating process is presented from proper initial model, accurate modal test results, test/analysis correlation to automatic model updating. The single steps of detailed updating process are highlighted. The discrepancy between the finite element model predicted and the experiment measured modal parameters are minimized and satisfactory results were obtained.

Identificación de formas modales bajo excitación armónica usando sensores móviles

This paper presents a methodology for the identification of high spatial density mode shapes of a dynamical system under harmonic excitation that use information from a mobile sensor. The methodology is verified numerically and experimentally with uniform simply supported beams under sinusoidal excitation. High correlation is found between the theoretical and the numerically identified mode shapes in the simulations. High correlation is also obtained between the operational mode shape identified using a traditional modal identification approach and the one using the proposed methodology during the experimental validation. The methodology minimizes errors in the identification process due to the influence of the non-resonant modes and it is robust to uncertainties in the initial identification of the natural frequencies.