Strain Frequency Response Function Research Articles

Optical Fiber Serpentine Arrangements for Vibration Analysis Using Distributed Acoustic Sensing

Distributed acoustic sensors (DASs) are able to monitor in real-time acoustic excitation and mechanical vibration of the external environment for many kilometers along the length of the optical fiber. In the oil industry, the technology allows the monitoring of well structural health, identifying flow profile, acquiring seismic data, updating reservoir information, and feeding geological models. The spatial resolution of DAS is a limiting factor on the quality of information gathered. In this article, we propose and analyze a novel method of measuring local dynamic strain of structures using DAS. The method uses serpentine configurations to measure the frequency spectrum of the in-phase strain signals at discrete regions of the structure, enabling DAS to determine, among other vibration parameters, the strain frequency response function (SFRF). An experimental study of the sensor application with different arrangements in a small structure has been performed. The structure in the experiment consists of a free–free aluminum beam of approximately 2.7 m. Experiment results show agreement with numerical results developed by the finite element method (FEM) and using reference sensors, demonstrating a significant improvement of the DAS SFRF accuracy using the serpentine configuration and up to 12.9 dB increase in peak-to-noise ratio (PNR) for low excitation forces. The recovered response enabled the reconstruction of mode shapes.

Damage identification in beam-like structure using strain FRF-based damage index and artificial neural network

A novel approach for structural damage identification of beam-like structures based on strain frequency response functions (SFRFs) using artificial neural networks (ANNs) is proposed. The dominated singular values of the phase space matrix derived from SFRFs are reserved as the features to denote the characteristics of the original SFRFs. And the reserved singular values mean change ratio (RSVMCR) is described as a new damage index for damage detection. The RSVMCRs and the elemental residual stiffness vector are utilized to establish the ANN model. Two numerical examples are investigated to verify the feasibility and effectiveness of the proposed approach.

Material model robust identification procedure from dynamical measurements made on a flexible specimen-frame system

A procedure for the identification of the material model of beam specimens by means of harmonic force and displacement measurements in flexural condition is presented. Input-output frequency response function (FRF) evaluations are used in standard DMA instruments to estimate the material stress–strain frequency response function. Nevertheless, the contribution of the instrument frame model coupling and of the inertial contribution of the excitation moving substructure to the input–output FRFs can make such estimates meaningless in most practical applications, especially if a wide excitation frequency range is taken into account. In this work the instrument frame model contribution is estimated by means of doing calibration measurements on some reference beams and processing them by a procedure based on optimization algorithms. A signal processing-based procedure is also proposed to identify the optimal frame model rational function fit by eliminating computational and noise related contribution. The identified rational frame model is used to obtain the material model in the frequency domain being filtered from the contribution of the experimental system. The proposed technique robustness is tested on some numerical model cases. The same technique is then applied to some dynamical measurements made on specimens of different materials. The results are shown and critically discussed.

Finite element model updating of jointed structure based on modal and strain frequency response function

To acquire a reasonable model for structural dynamic strength analysis, a bottom-up finite element modeling and updating methodology based on multi responses is proposed. The fundamental principles of structural dynamics analysis and model updating were introduced, and the proposed strategy was applied to the case study of an L-shaped jointed structure. Components of the jointed structure were modeled sequentially, and inaccurate model parameters were updated based on the corresponding experimental modal results in the first stage. In the second stage, components were connected together by bolts. The joint interfaces were represented by thin-layer elements, and local joint parameters were updated based on strain frequency response function (FRF). Finally, the precision of finite element model (FEM) was validated by acceleration frequency response function. The results indicated that the proposed methodology is able to reduce model simulation errors in both components and the overall jointed structure. Not only can the updated model of a jointed structure reproduce the experimental results used in updating, but also predict responses that are not used in the process of model updating.

Frequency Response-Based Indirect Load Identification Using Optimum Placement of Strain Gages and Accelerometers

This paper presents an approach for indirect identification of dynamic loads acting on a structure through measurement of structural response at a finite number of optimally selected locations. Using the concept of frequency response function (FRF), the structure itself is considered as a load transducer. Two different types of sensors are investigated to measure the structural response. These include a use of accelerometers that leads to the identification of the displacement mode shapes. The second measurement approach involves a use of strain gages since strain measurements are directly related to imposed loads. A use of mixed strain-acceleration measurements is also considered in this work. Optimum sensor locations are determined herein using the D-optimal design algorithm that provides most precise load estimates. The concepts of indirect load identification, strain frequency response function (SFRF), displacement frequency response function (DFRF), along with the optimal locations for sensors are used in this paper. The fundamental theory for strain-based modal analysis is applied to help estimate imposed harmonic loads. The similarities and differences between acceleration-based load identification and strain-based load identification are discussed through numerical examples.

Structural Damage Identification Based on Strain Frequency Response Functions

Damage identification using the sensitivity of the dynamic characteristics of the structure of concern has been studied considerably. Among the dynamic characteristics used to locate and quantify structural damages, the frequency response function (FRF) data has the advantage of avoiding modal analysis errors. Additionally, previous studies demonstrated that strains are more sensitive to localized damages compared to displacements. So, in this study, the strain frequency response function (SFRF) data is utilized to identify structural damages using a sensitivity-based model updating approach. A pseudo-linear sensitivity equation which removes the adverse effects of incomplete measurement data is proposed. The approximation used for the sensitivity equation utilizes measured natural frequencies to reconstruct the unmeasured SFRFs. Moreover, new approaches are proposed for selecting the excitation and measurement locations for effective model updating. The efficiency of the proposed method is validated numerically through 2D truss and frame examples using incomplete and noise polluted SFRF data. Results indicate that the method can be used to accurately locate and quantify the severity of damage.

A updating method using strain frequency response function with emphasis on local structure

Abstract A dynamic finite element model updating method for the concerned local structure is presented using strain frequency response function test data. Firstly, a dynamic condensation technique is developed to establish the dynamic finite element model of the concerned local structure for improving the analytical efficiency of the dynamic strains and their transfer relations in model updating. Then, the sensitivity of strain frequency response function of the local structure is conducted to construct the canonical equation for model updating. Furthermore, a model updating strategy of ‘grouping-iteration’ is proposed to stabilize the ill-posed problem in the model updating process. Finally, numerical simulation and experimental investigation for updating the dynamic finite element model of the cantilever plate structure with elastic support are performed to validate the feasibility and efficiency of the present method. The obtained results show that the present method can be successfully used to update the dynamic finite element model of the local structure in terms of achieving a good agreement between the strain frequency response functions of the updated finite element model and the actual structure.

Model updating using correlation analysis of strain frequency response function

A method is proposed to modify the structural parameters of a dynamic finite element (FE) model by using the correlation analysis for strain frequency response function (SFRF). Sensitivity analysis of correlation coefficients is used to establish the linear algebraic equations for model updating. In order to improve the accuracy of updated model, the regularization technique is used to solve the ill-posed problem in model updating procedure. Finally, a numerical study and a model updating experiment are performed to verify the feasibility and robustness of the proposed method. The results show that the updated SFRFs and experimental SFRFs agree well, especially in resonance regions. Meanwhile, the proposed method has good robustness to noise ability and remains good feasibility even the number of measurement locations reduced significantly.

Change Localization of a Steel-Stringer Bridge through Long-Gauge Strain Measurements

AbstractDevelopment of the long-gauge fiber-optic sensor provides an excellent opportunity for structural-change localization, because it measures averaged strains over a long gauge length. A practical structural-change localization, procedure using long-gauge dynamic strains in the modal space is proposed to process the ambient vibration data of a steel-stringer bridge. The proposed procedure is easy to execute by general bridge engineers; meanwhile, it has a solid theoretical basis, thus guaranteeing its effectiveness. By theoretically deriving the magnitude ratios between the analytical strain frequency response functions (FRFs) and the estimated strain FRFs from ambient vibration data, it is proved that the proposed procedure is the same as using long-gauge strain mode shapes for change location; therefore, it is effective and much simpler for general bridge engineers to use. An ambient vibration test of a steel-stringer bridge using long-gauge fiber-optic sensors has been performed. The results of ap...

The use of strain gauges in vibration-based damage detection

Strain gauges and strain measurements have been widely used in structural health monitoring (SHM) systems as a means of detecting and localizing damage, due to their higher sensitivity to local damage. These damage identification techniques normally use strain related measurements such as the mode curvature, strain frequency response function or strain energy as the main parameter to detect damage. However, damage detection techniques based on acceleration measurements have also been investigated in the past, using modal parameter comparison and other methodologies. In this paper, the use of vibration-based strain measurements for use in SHM systems will be evaluated, with the purpose of characterizing their higher sensitivity in damage detection, when compared to other vibration measurements, such as acceleration-based measurements. Since the choice and use of the most damage sensitive parameter can lead to a more sensitive and robust system, the assessment of the more suitable sensor and processing of information is very important. For this purpose, numerical and experimental examples will be discussed to evaluate the higher performance of the strain gauges.

Structural identification and damage detection through long-gauge strain measurements

Strain measurements from traditional point-type gauges only reveal structural local information. This feature significantly limits the development and application of strain modal theory in civil engineering. The long-gauge fiber optic strain sensor emerging recently has the unique merit of reflecting both local and global information of a structure by measuring the averaged strain within a long gauge length (e.g., 1–2m). Based on this advantage, strain modal identification by processing the dynamic macro strain measurement is investigated. First, the macro strain frequency response function is derived based on the mapping relationship between the long gauge strain and displacement. Then, two methods are proposed for structural strain modal identification and their results are compared. Moreover, damage indexes based on identified macro strain modal shapes are investigated for structural damage detection. The example of a steel stringer bridge model successfully illustrates that the proposed methods accurately identify structural macro strain modal shapes, and the results also reveals that macro strain based indexes are much more robust than traditional modal parameter based indexes for structural damage detection.

Strain flexibility identification of bridges from long-gauge strain measurements

Strain flexibility, defined as the strain response of a structure׳s element to a unit input force, is import for structural safety evaluation, but its identification is seldom investigated. A novel long-gauge fiber optic sensor has been developed to measure the averaged strain within a long gauge length. Its advantage of measuring both local and global information of the structure offers an excellent opportunity of developing the strain flexibility identification theory. In this article, the method to identify structural strain flexibility from long-gauge dynamic strain measurements is proposed. It includes the following main steps: (a) macro strain frequency response function (FRF) estimation from macro strain measurements and its feature characterization; (b) general strain modal parameter identification; (c) scaling factor calculation, and (d) strain flexibility identification. Numerical and experimental examples successfully verify the effectiveness of the proposed method.

動ひずみ測定を用いた振動入力の同定精度向上に関する研究

Transfer Path Analysis (TPA) has been conducted in order to improve the noise and vibration quality of mechanical structures. However, the force identification in the TPA is still challenging problem and its accuracy has to be improved. The Matrix Inversion Method and the Apparent-Mass Matrix Method are approaches for force identification. The Matrix Inversion Method estimates the excitation force by the product of an inverse matrix of accelerance and a vector of actual operational acceleration. It is known that the Matrix Inversion Method is very sensitive to measurement noise especially at the resonance. Apparent-Mass Matrix Method has been recently proposed, which provides more accurate results than the Matrix Inversion Method. However, these methods are still insufficient in accuracy, and improvement of identification accuracy is required. This paper proposes a new force identification method by using strain measurement. The method estimates the force using the Strain Frequency Response Function (SFRF) instead of acceleration or Apparent-Mass Matrix. The SFRFs are more strongly affected by higher-order modes than accelerance FRF. Therefore, we considered that more accurate force identification can be obtained by using SFRF than the conventional method. A numerical simulation and a vibration experiment are conducted to compare the results by the proposed method with the conventional method.

Structural Identification by Processing Dynamic Macro Strain Measurements

In contrast to traditional modal identification methods processing structural accelerations for modal parameter identification, a multiple reference impact testing method using long-gauge fiber optical sensors and the related data processing approach are proposed. First, macro strains of key structural elements during the impact testing are measured through long-gauge fiber optic sensors, which subsequently are used to estimate the strain frequency response functions (FRFs) of the structure. Second, an approach is proposed to estimate strain mode shapes from the strain FRFs, and corresponding displacement mode shapes are calculated by applying an improved conjugate beam method. Finally, the strain flexibility character of the structure is identified by using the identified strain and displacement mode shapes with normalization. The advantage of long-gauge fiber optic sensors measuring averaged strains in a long length (e.g., 1 meter) provides the opportunity for strain modal analysis. The output of the proposed method, strain flexibility, is meaningful for static strain prediction and structural capacity evaluation. Examples investigated successfully verified the effectiveness of the proposed method for structural strain flexibility identification.

Observed deviations from isotropic linear viscoelastic behavior of asphalt concrete through modal testing

The complex Young’s moduli, complex shear moduli and complex Poisson’s ratio of a beam shaped asphalt concrete specimen have been characterized through low strain (∼10−7) frequency response function measurements. The assumption of isotropic linear viscoelastic behavior has been applied and investigated. The results indicate that the asphalt concrete specimen agree with the isotropic linear viscoelastic assumption at low temperatures and high frequencies (>10kHz at 0°C), but at higher temperatures and lower frequencies, discrepancies from isotropic linear behavior are shown. The dynamic shear moduli calculated from the estimated Young’s moduli and Poisson’s ratio of the asphalt concrete specimen are overestimated for frequencies and temperatures often applied to pavements.

Research on Crack Damage Identification Based on SFRF and Fiber Bragg Grating Sensors

This paper applies strain frequency response function (SFRF), presenting crack damage identification index based on change amplitude of SFRF. Crack propagation identification of four corners fixed thin plate experiment system based on fiber bragg grating sensors is established, experiments and analysis are carried out. Results show that: this crack damage identification system can identify crack damage occurs and propagation effectively.

유한요소해석을 이용한 TPMS용 압전 발전소자의 동특성 해석

Energy harvesting is a clean technology to obtain energy from the surrounding environment such as wind, sun, vibration and so on. In particular, the current TPMS (Tire Pressure Monitoring Device) is very small and attached to the outside of a vehicle and power supply of the TPMS is limited. Therefore, energy harvesting using vibration energy of piezoelectric materials is important to the TPMS. In this paper, we analyzed several models using ANSYS which is one of the FEA (Finite Element Analysis) package and compared corresponding strain frequency response functions of the TPMS. In addition, we confirmed that dynamic characteristics variations according to geometry changes have effects on the performance of the TPMS.

Damage detection by mixed measurements using accelerometers and strain gages

This work investigates the relationship between the FRFs (frequency response functions) measured by accelerometers and strain gages utilized widely for investigating structural performance. Modifying the GDM (global-deviation method), this study examines the possibility of damage detection in utilizing both sensors together. The experimental results on the mixed utilization of two sensors show that the SFRF (strain frequency response function) data measured by strain gages in the neighborhood of end supports are more practical in establishing the baseline curve than the DFRF (displacement frequency response function) data measured by accelerometers. It is shown that the modified GDM can be effectively utilized in detecting damage based on the mixed measurements of accelerometers and strain gages.

FIBER BRAGG GRATING SENSORS - BASED MECHANICAL STRUCTURE DAMAGE IDENTIFICATION

This paper describes a method for identifying the damage location for two dimensional plate - like structures. This method uses measured strain frequency response functions from intact and damage state to define a damage identification index. The strain frequency response functions are measured by distributed fiber Bragg grating (FBG) sensors. Numerical simulation and experimental tests are carried out. Both results show that this method combining strain frequency response function - based index with FBG distributed sensing can successfully identify the damage location.DOI: http://dx.doi.org/10.5755/j01.mech.18.1.1291

Hypersensitivity of strain-based indicators for structural damage identification: A review

Because of the sensitive characteristic to local defects, strain has been widely utilized to identify the presence, location, and severity of damage in structures, and this paper reviews recent publications regarding strain-related techniques on structural damage identification. A brief description on the strain–displacement relationship at defective areas is first presented. Then, damage identification using various strain-related parameters, such as strain (curvature) mode shape, strain energy, strain frequency response function, etc., is explored and the hypersensitivity of corresponding damage indicators will be examined systematically. Finally, some generalized criteria on the selection of strain-based parameters for damage identification are concluded and suggestions for future work are discussed.