• Smart Structures and Systems
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• v.16 no.5
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• pp.919-935
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• 2015

The Hilbert-Huang transform (HHT) consists of empirical mode decomposition (EMD) and Hilbert spectral analysis. EMD has been successfully applied for identification of mode shapes of structures based on input-output approaches. This paper aims to extend application of EMD for output-only identification of mode shapes of linear structures. In this regard, a new simple and efficient method based on band-pass filtering and EMD is proposed. Having rather accurate estimates of modal frequencies from measured responses, the proposed method is capable to extract the corresponding mode shapes. In order to evaluate the accuracy and performance of the proposed identification method, two case studies are considered. In the first case, the performance of the method is validated through the analysis of simulated responses obtained from an analytical structural model with known dynamical properties. The low-amplitude responses recorded from the UCLA Factor Building during the 2004 Parkfield earthquake are used in the second case to identify the first three mode shapes of the building in three different directions. The results demonstrate the remarkable ability of the proposed method in correct estimation of mode shapes of the linear structures based on rather accurate modal frequencies.

• Smart Structures and Systems
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• v.32 no.1
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• pp.1-7
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• 2023

In modal analysis, the mode shape reflects the vibration characteristics of the structure, and thus it is widely performed for finite element model updating and structural health monitoring. Generally, the acceleration-based mode shape is suitable to express the characteristics of structures for the translational vibration; however, it is difficult to represent the rotational mode at boundary conditions. A tilt sensor and gyroscope capable of measuring rotational mode are used to analyze the overall behavior of the structure, but extracting its mode shape is the major challenge under the small vibration always. Herein, we conducted a feasibility study on a multi-mode shape estimating approach utilizing a single physical quantity signal. The basic concept of the proposed method is to receive multi-metric dynamic responses from two sensors and obtain mode shapes through bridge loading test with relatively large deformation. In addition, the linear transformation matrix for estimating two mode shapes is derived, and the mode shape based on the gyro sensor data is obtained by acceleration response using ambient vibration. Because the structure's behavior with respect to translational and rotational mode can be confirmed, the proposed method can obtain the total response of the structure considering boundary conditions. To verify the feasibility of the proposed method, we pre-measured dynamic data acquired from five accelerometers and five gyro sensors in a lab-scale test considering bridge structures, and obtained a linear transformation matrix for estimating the multi-mode shapes. In addition, the mode shapes for two physical quantities could be extracted by using only the acceleration data. Finally, the mode shapes estimated by the proposed method were compared with the mode shapes obtained from the two sensors. This study confirmed the applicability of the multi-mode shape estimation approach for accurate damage assessment using multi-dimensional mode shapes of bridge structures, and can be used to evaluate the behavior of structures under ambient vibration.

• 제어로봇시스템학회:학술대회논문집
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• 2002.10a
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• pp.52.3-52
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• 2002

Natural frequencies and mode shapes are two important modal data which specify the system. If the real system and FE model don't have the same local physical parameters, there will be a difference between modal data from real system and FE model. Because there is little difference in displacement mode shapes measured by an accelerometer, displacement modal update based on mode shapes including measurement errors may not be successful. In this research, strain mode shapes are used as modal data because the strain mode shapes measured by strain gauges are more sensitive than the displacement mode shapes with respect to the change of the parameters concerned in FE stiffness matrix...

• Structural Engineering and Mechanics
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• v.39 no.5
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• pp.733-750
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• 2011

Recently, identification of modal parameters using the response only data has attracted considerable attention particularly where the classic modal testing methods is difficult to conduct. One drawback of the response only data, also known as Operational Modal Analysis (OMA), is that only the unscaled mode shapes can be obtained which restricts the applications of OMA. The Mass change method is a usual way to scale the operational mode shapes. In this article a new method is proposed to optimize the additive mass for scaling of the unscaled mode shapes from OMA for which a priori knowledge of the Finite Element model of structure is required. It is shown that the total error of the scaled mode shapes is minimized using the proposed method. The method is validated using a numerical case study of a beam. Moreover, the experimental results of a clamped-clamped beam demonstrate the applicability of the method.

• Journal of the Korean Society of Safety
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• v.28 no.6
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• pp.36-41
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• 2013

Previous study showed that delamination region in concrete structures can be successfully visualized using mode shapes of delaminated concrete section. However, modal tests for this purpose to obtain mode shapes of the delaminated concrete section may not be applicable in practice since, to correctly obtain the mode shapes of the section, the location and the shape of the delamination region in a structure should be known in advance. Unfortunately those are normally unknown in a real structure. Therefore, a moving forward test method may be useful to obtain the mode shapes of the concrete section when the location and the shape of the delamination region are not known. In this study, impact-echo testing based mode shape estimation technique is proposed and experimentally validated for visualization of delamination region.

• Structural Engineering and Mechanics
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• v.49 no.2
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• pp.183-202
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• 2014

A new method of multiple damage detection in beam like structures is introduced. The mode shapes of both healthy and damaged structures are used in damage detection process (DDP). Multiple Damage Localization Index Based on Mode Shapes (MDLIBMS) is presented as a criterion in detecting damaged elements. A finite element modeling of structures is used to calculate the mode shapes parameters. The main advantages of the proposed method are its simplicity, flexibility on the number of elements and so the accuracy of the damage(s) position(s), sensitivity to small damage extend, capability in prediction of required number of mode shapes and low sensitivity to noisy data. In fact, because of differential and comparative form of MDLIBMS, using noise polluted data doesn't have major effect on the results. This makes the proposed method a powerful one in damage detection according to measured mode shape data. Because of its flexibility, damage detection process in multi span bridge girders with non-prismatic sections can be done by this method. Numerical simulations used to demonstrate these advantages.

• Structural Engineering and Mechanics
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• v.2 no.4
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• pp.345-357
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• 1994

The differential equations governing free, in-plane vibrations of linearly elastic circular arches with variable cross-sections are derived and solve numerically for quadratic arches with three types of rectangular cross sections. Frequencies, mode shapes, cross-sectional load distributions, and the effects of rotatory inertia on frequencies are reported. Experimental measurements of frequencies and their corresponding mode shapes agree closely with those predicted by theory. The numerical methods presented here for computing frequencies and mode shapes are efficient and reliable.

• International Journal of Naval Architecture and Ocean Engineering
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• v.7 no.6
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• pp.979-994
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• 2015

The mode shapes of a segmented hull model towed in a model basin were predicted using both the Proper Orthogonal Decomposition (POD) and cross random decrement technique. The proper orthogonal decomposition, which is also known as Karhunen-Loeve decomposition, is an emerging technology as a useful signal processing technique in structural dynamics. The technique is based on the fact that the eigenvectors of a spatial coherence matrix become the mode shapes of the system under free and randomly excited forced vibration conditions. Taking advantage of the simplicity of POD, efforts have been made to reveal the mode shapes of vibrating flexible hull under random wave excitation. First, the segmented hull model of a 400 K ore carrier with 3 flexible connections was towed in a model basin under different sea states and the time histories of the vertical bending moment at three different locations were measured. The measured response time histories were processed using the proper orthogonal decomposition, eventually to obtain both the first and second vertical vibration modes of the flexible hull. A comparison of the obtained mode shapes with those obtained using the cross random decrement technique showed excellent correspondence between the two results.

• Journal of the Korean Society of Safety
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• v.28 no.5
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• pp.21-26
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• 2013

Delamination of cover concrete due to re-bar corrosion is a critical damage reducing structural safety of reinforced concrete structures. Therefore, it should be detected and evaluated to provide appropriate maintenance to recover structural integrity. Impact-echo method, which utilizes thickness vibration characteristics of delaminated concrete section, is effective for detection and evaluation of small areal size delamination. However, it may not be applicable for large areal size delamination in which flexural vibration modes are dominated. In this study, applicability of vibration mode shapes of delaminated concrete section is investigated for visualization of delamination region in concrete structures. Numerical and experimental modal tests are performed to estimate mode shapes of delaminated concrete section and linear absolute summation technique is proposed for effective visualization of delamination region based on estimated mode shapes.

• Steel and Composite Structures
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• v.2 no.3
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• pp.223-236
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• 2002

An analytical procedure based on the transfer matrix method to estimate not only the natural frequencies but also vibration mode shapes of the thin-walled members composed of interconnected cylindrical shell panels is presented. The transfer matrix is derived from the differential equations for the cylindrical shell panels. The point matrix relating the state vectors between consecutive shell panels are used to allow the transfer procedures over the cross section of the members. As a result, the interactions between the shell panels of the cross sections of the members can be considered. Although the transfer matrix method is naturally a solution procedure for the one-dimensional problems, this method is well applied to thin-walled members by introducing the trigonometric series into the governing equations of the problem. The natural frequencies and vibration mode shapes of the thin-walled members composed of number of interconnected cylindrical shell panels are observed in this analysis. In addition, the effects of the number of shell panels on the natural frequencies and vibration mode shapes are also examined.