Strain Mode Shapes Research Articles

Study on the Method of Crack Detection of Steel Rods Based on Modal Analysis

Steel rods are widely used in the areas of petroleum, chemical, architecture and transportation, steel rods with cracks will cause terrible accident and great losses when working in production practice. In view of traditional Non-destructive Testing (NDT) method can only realize static detection, this paper provide the method based on modal calculate analysis, including the choice of damage index and the judgment of damage degree and damage location for cracks of steel rods. The damage location is judged by the strain mode shape difference curve and the function expression of damage degrees and mutation degrees of curvature mode shapes is acquired by the method of least square fitting, which can achieve quantitative analysis of single crack of steel rods, this provide theoretical support and technical reference for experimental modal analysis and dynamic NDT.

Damage Detection Analysis of Simple Beams Based on Strain Mode

The damage identification research based on strain mode was discussed in this paper, and based on MATLAB, the models on the severy conditions of preset damaged was compared also. The results show that this method is more rapid, and the parameters impact of the strain mode is more intuitive than other finite element analysis software. The damage location and the extent of injury of simply beam can accurately determined by strain mode shapes. The conclusion is theoretical academic significance value of assess in service bridge structure examination.

Dual use of PZT patches as sensors in global dynamic and local electromechanical impedance techniques for structural health monitoring

In this article, a new approach is proposed to effectively detect the initiation and progression of structural damage by combining the global dynamic and the local electromechanical impedance (EMI) techniques, using the same set of surface-bonded piezoelectric ceramic (PZT) patches as sensors. The PZT patches are used to determine the natural frequencies and the strain mode shapes of the structure (for use in the global dynamic technique) as well as to acquire the electromechanical admittance signature (for use in the EMI technique) to facilitate an improved damage assessment. Occurrence and location of the incipient damage are determined using the EMI technique, whereas for moderate to severe damages, the location and the severity are arrived at through the global dynamic technique. Finally, damage severity is determined in terms of the original stiffness of structure using the strain mode shapes directly determined using the PZT patches. The proposed technique is illustrated using two specimens—a 4-m long steel beam and a mild steel plate 1260 mm × 630 mm × 6.5 mm in size. The integrated approach provides greater information about damage, is simple to apply, does not involve any numerical/analytical modeling a priori, and is at the same time very cost effective.

INTEGRATED OPTIMAL PLACEMENT OF DISPLACEMENT TRANSDUCERS AND STRAIN GAUGES FOR BETTER ESTIMATION OF STRUCTURAL RESPONSE

Although a variety of sensors provide more comprehensive information and advanced features of structures, their distinct properties and limitations considerably complicate the design procedure of multi type sensor systems. This paper is focused on the optimal design of integrated sensor systems with both strain gauges and displacement transducers. Unlike traditional sensor placement approaches, in which these two types of sensors are often designed separately to monitor structural deformations and displacements respectively, the integrated design procedure presented in this study treats the sensor system as a whole. The number and locations of strain gauges and displacement transducers are optimized simultaneously, and their measurement data are fused together to better predict the unobserved structural response. The theoretical criterion for the optimization procedure is first formulated based on the strain and displacement mode shapes extracted from finite element models. Then, the initial candidate sensor locations are reduced to a smaller optimal set with minimized prediction error of structural response. A two-dimensional cantilever beam is then analyzed as a numerical example to investigate the effectiveness and accuracy of the presented optimal sensor placement approach. The results indicate that the integrated sensor system provides better estimation of structural response than single-type sensor system.

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.

Damage detection for truss or frame structures using an axial strain flexibility

Damage detection using structural classical deflection flexibility has received considerable attention due to the unique features of the flexibility in the last two decades. However, for relatively complex structures, most methods based on classical deflection flexibility fail to locate damage sites to the exact members. In this study, for structures whose members are dominated by axial forces, such as truss structures, a more feasible flexibility for damage detection is proposed, which is called the Axial Strain (AS) flexibility. It is synthesized from measured modal frequencies and axial strain mode shapes which are expressed in terms of translational mode shapes. A damage indicator based on AS flexibility is proposed. In addition, how to integrate the AS flexibility into the Damage Location Vector (DLV) approach (Bernal and Gunes 2004) to improve its performance of damage localization is presented. The methods based on AS flexbility localize multiple damages to the exact members and they are suitable for the cases where the baseline data of the intact structure is not available. The proposed methods are demonstrated by numerical simulations of a 14-bay planar truss and a five-story steel frame and experiments on a five-story steel frame.

Modal power flow analysis of a damaged plate

Variation of the modal reactive power distribution of a damaged plate is analyzed. Large variation of local reactive power flow in or around the damage region of a plate under resonant vibration is related to the change of strain and kinetic energies in the damage region. Feasibility of damage identification based on the detection of this local variation of modal reactive power flow in a structure is studied. Compared with the damage identification techniques based on the determination of the active power flow in a damaged plate, the proposed method only requires data of a vibration mode shape of the structure and it is easier to apply in practice. Two common types of damage have been tested for identification, the first with a region of reduced stiffness in the plate while the second with a small hole in the plate. Numerical tests show that the proposed method is effective for both types of damage and the modal power flow is more sensitive to the change of plate stiffness than the strain mode shape in the test case.

A probabilistic method for the detection of obstructed cracks of beam-type structures using spatial wavelet transform

This paper reports both the theoretical development and the numerical verification of a practical wavelet-based crack detection method, which identifies first the number of cracks and then the corresponding crack locations and extents. The value of the proposed method lies in its ability to detect obstructed cracks when measurement at or close to the cracked region is not possible. In such situations, most nonmodel-based methods, which rely on the abnormal change of certain indicators (e.g., curvature and strain mode shapes) at or close to the cracks, cannot be used. Most model-based methods follow the model updating approach. That is, they treat the crack location and extent as model parameters and identify them by minimizing the discrepancy between the modelled and measured dynamic responses. Most model-based methods in the literature can only be used in single- or multi-crack cases with a given number of cracks. One of the objectives of this paper is to develop a model-based crack detection method that is applicable in a general situation when the number of cracks is not known in advance. To explicitly handle the uncertainties associated with measurement noise and modelling error, the proposed method uses the Bayesian probabilistic approach. In particular, the method aims to calculate the posterior (updated) probability density function (PDF) of the crack locations and the corresponding extents. The proposed wavelet-based crack detection method is verified and demonstrated through a comprehensive series of numerical case studies, in which noisy data were generated by a Bernoulli–Euler beam with semi-rigid connections. The results show that the method can correctly identify the number of cracks even when the crack extent is small. The effects of the number of cracks and the crack extents on the results of crack detection are also studied and discussed in this paper.

Post-seismic Structural Health Monitoring of a Column Subjected to Near Source Ground Motions

This study reports on the results acquired from shaking table tests of a column subjected to progressively increasing amplitudes of seismic motions recorded during the Northridge earthquake. Scope of the investigation includes application and evaluation of deterministic structural health monitoring methods to assess the post-seismic conditions following application of the various amplitudes of earthquake motions. Results from this study demonstrate the applicability of specially designed surface-adhered fiber optic sensors for detecting the formation and the progression of cracks subjected to reverse dynamic loads, as well as application of various SHM techniques for evaluation of damage. The range of damage identification methods evaluated comprises of simple frequency and damping analysis of the column under free vibrations, and modal analysis techniques including curvature mode shapes. The concept of strain mode shape analysis, which was previously established for dynamic analysis of structures, is also introduced here for damage identification. Evaluation of the SHM techniques involves efficiency in terms of the number of sensors required to investigate the progression of damage, and resolution in terms of damage identification both in terms of location as well as the state of the damage.

Influence of inhomogeneity and geometry on lung response to low-frequency underwater sound

An effective medium, finite-element model has been developed for human lung response to low-frequency underwater sound [Wochner et al., J. Acoust. Soc. Am. 121, 3082 (2007)]. Macroscopic properties are determined by averaging over microscopic properties associated with lung tissue elasticity and alveolar geometry. The resulting elastic constants depend on lung volume, and thus vary with the phase of the breathing cycle. This presentation discusses effects due to spatial variations in lung and geometric features specific to the anatomy of lung. An important variation in elastic properties occurs where soft tissue of the parenchyma attaches to much stiffer bronchial tissue, resulting in stresses that may cause injury at high levels of acoustic excitation. A factor affecting inhomogeneity within the parenchyma is the orientation of the swimmer. When vertical, the suspension of the lung under its own weight may cause the stiffness to be higher at the top of the lung than at the bottom, resulting in a change in the lung resonance frequency. Finally, patient-specific geometries based on volumetric data of the human thorax are considered. Results will be presented showing stress and strain fields, lung resonance, and mode shapes. [Work supported by ONR and ARL:UT IR&D.]

Model Updating with Closed-Loop Strain Mode Shapes

M ODEL updating is a method of correcting analytical models, such as the finite element model, by improving the correlation between the measured data and the analytical model. The correlation can be determined by a penalty function that involves modal data such as natural frequencies and mode shapes [1,2]. However, a modal sensitivity matrix that is ill conditioned due to a lack of modal data can incur inaccurate model updating. For more efficient model updating, we need to increase the amount of modal data. Recently, some researchers have used closed-loop schemes to capture additional modal data [3,4]. Strain mode shapes have also been used instead of displacement mode shapes because of their perceived advantages [5,6]. For example, the difference in the strain mode shapes of an intact case and a damaged case is greater than the corresponding difference in the displacement mode shapes. This phenomenon explains why strain mode shapes are generally considered more sensitive than displacement mode shapes with respect to the local change of a structure. However, this property is valid when the local change of a structure can change the displacement mode shapes because strain mode shapes are spatial derivatives of displacement mode shapes. If we simultaneously use strain mode shapes and the closed-loop scheme, we can enhance the performance of model updating. We, therefore, propose a novel method of combining strain mode shapes and the closed-loop scheme for effective model updating. In addition, to demonstrate the feasibility of the proposed method, we provide a numerical simulation of model updating based on the closed-loop strain mode shapes.

Uncertainty analysis of strain modal parameters by Bayesian method using frequency response function

Structural strain modes are able to detect changes in local structural performance, but errors are inevitably intermixed in the measured data. In this paper, strain modal parameters are considered as random variables, and their uncertainty is analyzed by a Bayesian method based on the structural frequency response function (FRF). The estimates of strain modal parameters with maximal posterior probability are determined. Several independent measurements of the FRF of a four-story reinforced concrete frame structural model were performed in the laboratory. The ability to identify the stiffness change in a concrete column using the strain mode was verified. It is shown that the uncertainty of the natural frequency is very small. Compared with the displacement mode shape, the variations of strain mode shapes at each point are quite different. The damping ratios are more affected by the types of test systems. Except for the case where a high order strain mode does not identify local damage, the first order strain mode can provide an exact indication of the damage location.

Characteristics of Crack Detection on Plates Using Strain Mode Shapes; Sensor Grids and Geometry

The existence of a crack in a structure produces changes in modal parameters of it such as natural frequencies, damping, displacement and strain mode shapes. This paper is focused on characterization of crack detection methods using strain mode shapes. To characterize crack detection methods, we changed sensing grids from corner grid to cross grid and geometry of the specimens from rectangular to triangular plate. Rest of conditions was fixed. For crack detection criteria, COMAC, ECOMAC, ADSM and new method have been used and the results are compared with each other. The COMAC, ECOMAC and ADSM showed limited capacity of crack detection on plates but the new method gave good results in 90% of all cases.

Experimental modal analysis of an aircraft model wing by embedded fiber Bragg grating sensors

A critical issue in practical structural health monitoring is related to the capability of proper sensing systems integrated within the host structures to detect, identify, and localize damage generation. To this aim, many techniques have been proposed involving dynamic measurements such as modal analysis, acoustic emission, and ultrasonics. This paper relies on the use of embedded fiber Bragg grating sensors for performing an experimental modal analysis on a wing of an aircraft model. Time domain response of the embedded fiber-optic sensors induced by hammer impacts were acquired and transformed into the frequency domain. Using a classical technique based on the frequency transfer function, the first displacement and strain mode shapes of the wing have been retrieved in terms of natural frequencies and amplitudes. Experimental results confirm the excellent performances of this class of sensing devices to determine the modal behavior within complex structures compared with conventional accelerometer-based detection systems.

Vibration analysis of a piezoelectric composite plate with cracks

The vibration behavior of a piezoelectric composite plate with cracks is analyzed in this paper. Based on the principle of minimum energy, a dynamical model is established, and the effects of cracks and piezoelectric materials on mode shapes are analyzed. Numerical simulations for a rectangular aluminum plate with and without cracks are conducted to validate the model. The contours of the displacement and strain mode shapes are compared. It is shown that the strain mode is more sensitive to cracks rather than the displacement mode. The approach is expected to detect damages of piezoelectric composite plates.

Controllability assessment of plate-like structures with uncertainties under piezoelectric actuation

A controllability assessment of plate-like structures with uncertainties under piezoelectric actuation is performed in this paper. Different from the previous studies, a novel index is proposed to quantify the degree of controllability using the sensor/actuator transfer function. Influences of unmodelled high-frequency dynamics and structural parameter variations on controllability are discussed, and the relationship between the indices for the nominal and uncertain cases is derived. In order to validate the controllability assessment numerically, the modelling of a plate with piezoelectric actuation is developed with the consideration of the full coupling between the PZT actuators and the host plate, and verified by experiments. It is demonstrated that a proper design of the polyvinylidene flouride sensor would help eliminate effects of higher order modes on the basis of strain mode shapes. Since the latter is very sensitive to the mass and stiffness added by PZT actuators, the dynamics of PZT actuators must be taken into account during the design, as opposed to the case where a point transducer is used.

Quantification and localisation of damage in beam-like structures by using artificial neural networks with experimental validation

This paper presents a damage detection algorithm using a combination of global (changes in natural frequencies) and local (curvature mode shapes) vibration-based analysis data as input in artificial neural networks (ANNs) for location and severity prediction of damage in beam-like structures. A finite element analysis tool has been used to obtain the dynamic characteristics of intact and damaged cantilever steel beams for the first three natural modes. Different damage scenarios have been introduced by reducing the local thickness of the selected elements at different locations along finite element model (FEM) of the beam structure. The necessary features for damage detection have been selected by performing sensitivity analyses and different input–output sets have been introduced to various ANNs. In order to check the robustness of the input used in the analysis and to simulate the experimental uncertainties, artificial random noise has been generated numerically and added to noise-free data during the training of the ANNs. In the experimental analysis, two steel beams with eight distributed surface-bonded electrical strain gauges and an accelerometer mounted at the tip have been used to obtain modal parameters such as resonant frequencies and strain mode shapes. Finally, trained feed-forward backpropagation ANNs have been tested using the data obtained from the experimental damage case for quantification and localisation of the damage.

Identification of damage locations for plate-like structures using damage sensitive indices: strain modal approach

This paper addresses the problem of identification of damage locations for plate-like structures using strain mode technique. Based on the Rayleigh–Ritz approach, the strain modal analysis of a damaged plate is performed and strain mode shapes are consequently obtained. In light of the continuity condition and the residual strain mode shape technique, two novel damage sensitive parameters are proposed to determine the locations of damage, and corresponding damage indices are constructed. Compared with the conventional indices, they are simple and intuitive, and easy to be used in practice. Numerical simulations and experiments are carried out. Results show a good consistency and a strong identification capability of the proposed indices.

EXPERIMENTAL STUDY ON THE VORTEX-INDUCED VIBRATION OF TOWED PIPES

We experimentally attempted to understand the vibration characteristics of a flexible pipe excited by vortex shedding. This has been extensively studied in the previous decades (for example, see Sarpkaya 1979 Journal of Applied Mechanics46, 241–258; Price et al. 1989 Eighth International Conference on Offshore Mechanics and Arctic Engineering, The Hague-March 19 –23, 447–454; Yoerger et al. 1991 Journal of Offshore Mechanics and Arctic Engineering, Transaction of Engineers113, 117–127; Grosenbaugh et al. 1991Journal of Offshore Mechanics and Arctic Engineering, Transaction of Engineers113 , 199–204; Brika and Laneville 1992 Journal of Fluid Mechanics250, 481–508; Chakrabarti et al. 1993 Ocean Engineering20, 135–162; Jong 1983 Ph.D. Dissertation, Department of Ocean Engineering, M. I. T.; Kimet al. 1986 Journal of Energy Resources Technology, Transactions of American Society of Mechanical Engineers108, 77–83). However, there are still areas that need more study. One of them is the relation between spatial characteristics of a flow-induced vibrating pipe, such as its length, the distribution of wave number, and frequency responses. A non-linear mechanism between the responses of in-line and cross-flow directions is also an area of interest, if the pipe is relatively long so that structural modal density is reasonably high. In order to investigate such areas, two kinds of instrumented pipe were designed. The instrumented pipes, of which the lengths are equally 6 m, are wound with rubber and silicon tape in different ways, having different vortex-shedding conditions. One has uniform cross-section of diameter of 26·7 mm, and the other has equally spaced four sub-sections, which are composed of different diameters of 75·9, 61·1, 45·6 and 26·7 mm. Both pipes are towed in a water tank (200 m×16 m×7 m) so that they experienced different vortex-shedding excitations. Various measures were obtained from the towing experiment, including frequency responses, the time-domain tracing of in-line and cross-flow responses, and Wigner–Ville distributions. The experimental results analyzed by using these measures exhibit several valuable features. One of them is that the natural frequencies and their corresponding strain mode shapes dominate the strain response of the uniform pipe. However for those of non-uniform pipe, the responses are more likely local and many modes participate in it.

Structural Damage Monitoring and Localization with Longitudinal Wave Measuring Technique by PZT Patches.

This paper presents a practical and quantitative technique for assessment and localization of infancy damages in a structure by measuring the impedance change of piezoelectric patches which were glued on the structure. The consideration of longitudinal wave propagation in structures is introduced for quantitative assessment of damage characteristics because the corresponding frequency regions are easily determined with longitudinal wave propagation analysis. It is shown that the damage location can be simply estimated by measuring the PZT's electric impedance and comparing with the longitudinal strain mode shape functions in the healthy structure.