Damage Assessment of Seismically Excited Buildings Through Incomplete Measurements

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
Chi-Chang Lin ◽  
Ging-Long Lin ◽  
Kun-Shu Hsieh
Keyword(s):  
Mode Shape ◽  
Damage Assessment ◽  
Degrees Of Freedom ◽  
Information Matrix ◽  
Damage Index ◽  
Mode Shapes ◽  
Numerical Verification ◽  
Earthquake Excitation ◽  
Practical Applications ◽  
Identification Technique

Measuring responses at all degrees of freedom (DOF) of a real structure is impossible and impractical when few sensors are available. This study presents a damage-assessment technique for seismically excited buildings using only a few floor-response measurements. In the first step, the system realization using information matrix (SRIM) identification technique was applied to estimate such modal properties as frequencies and damping ratios of an instrumented building. However, the complete mode shapes cannot be acquired due to a lack of comprehensive measurements. A novel optimal mode-shape-recovery (OMSR) technique was applied to reconstruct the complete first mode shape of the building system. An optimization process was then applied to minimize a prescribed objective function that represents the difference between measured and estimated outputs at instrumented locations. A story damage index (SDI) computed using the first mode shape recovered was applied to determine the degree of story damage. Noisy floor measurements of a five-story shear building under earthquake excitation were utilized for numerical verification. Moreover, a three-story benchmark building was analyzed to assess the accuracy and applicability of the proposed OMSR technique via experimental data. The proposed method obtained results in fairly good agreement with those of full measurements and is of value in practical application. The damage-assessment results obtained with the proposed method agree well with the actual damage, demonstrating that the proposed method is suitable for practical applications.

Story Damage Identification of Irregular Buildings Based on Earthquake Records

2013 ◽  
Vol 29 (3) ◽  
pp. 963-985 ◽  
Author(s):  
Jer-Fu Wang ◽  
Chi-Chang Lin ◽  
Ging-Long Lin ◽  
Chun-Hao Yang
Keyword(s):  
Damage Assessment ◽  
Visual Inspection ◽  
Damage Identification ◽  
Damage Index ◽  
Analytical Formula ◽  
Mode Shapes ◽  
Severe Damage ◽  
Concrete Building ◽  
Damage Condition ◽  
Identification Techniques

In this paper, a story damage index was developed to evaluate the damage condition of a torsionally coupled building based on its dominant modal frequencies and mode shapes. This index has an analytical formula with a calculated value ranging from 0 (undamaged) to 1.0 (collapsed) to indicate the reduction of story lateral stiffness. The involved computation is simple once the modal parameters of any three modes are obtained through system identification techniques from few floor acceleration measurements. The damage region within a story can also be identified through tracking the change of eccentricity of center of rigidity. This index was verified by numerical simulations and a data analysis of the ASCE benchmark model. In addition, it was also applied to the damage assessment of a four-story reinforced concrete building in Taiwan, which experienced severe damage during the 2006 Taitung Beinan earthquake ( M = 6.2). The results agree fairly well with the visual inspection and show the applicability of the proposed damage assessment technique.

USE OF MODAL FLEXIBILITY AND NORMALIZED MODAL DIFFERENCE FOR VIBRATION MODE SHAPE EXPANSION

2009 ◽  
Vol 09 (04) ◽  
pp. 765-775 ◽  
Author(s):  
WEI-XIN REN ◽  
BIJAYA JAISHI
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Mode Shape ◽  
Degrees Of Freedom ◽  
Vibration Mode ◽  
Mode Shapes ◽  
Modal Expansion ◽  
Simply Supported ◽  
Modal Flexibility ◽  
Actual Test

Proposed herein are two possible ways for mode shape expansion for future use. The first method minimizes the modal flexibility error between the experimental and analytical mode shapes corresponding to the measured degrees of freedom (DOFs) to determine the multiplication matrix. In the second method, Normalized Modal Difference (NMD) is used to calculate the multiplication matrix using the analytical DOFs corresponding to the measured DOFs. This matrix is then used to expand the measured mode shape to unmeasured DOFs. A simulated simply supported beam is used to demonstrate the performance of the methods. These methods are then compared with two most promising existing methods, namely the Kidder dynamic expansion and the modal expansion methods. It is observed that the performance of the modal flexibility method is comparable with existing methods. NMD also have the potential to expand the mode shapes though it is seen to be more sensitive to the distribution of error between finite element method and actual test data.

Numerical and Experimental Study on the Application of Mode Shape Curvature for Damage Detection in Plate-Like Structures

2015 ◽  
Vol 220-221 ◽  
pp. 264-270 ◽  
Author(s):  
Sandris Rucevskis ◽  
Pavel Akishin ◽  
Andris Chate
Keyword(s):  
Experimental Study ◽  
Damage Detection ◽  
Mode Shape ◽  
Research Effort ◽  
Random Noise ◽  
Damage Index ◽  
Simulated Data ◽  
Detection Algorithm ◽  
Mode Shapes ◽  
Laser Vibrometer

The paper describes on-going research effort at detecting and localizing damage in plate-like structures using mode shape curvature based damage detection algorithm. The proposed damage index uses data on exclusively mode shape curvature from the damaged structure. This method was originally developed for beam-like structures. The article generalizes the method of plate-like structures characterized by two-dimensional mode shape curvature. To examine limitations of the method, several sets of simulated data are applied and the obtained results of the numerical detection of damage are validated by comparing them with the findings of the case of the experimental test. The simulated test cases include the damage of various levels of severity. In order to ascertain the sensitivity of the proposed method for noisy experimental data, numerical mode shapes are corrupted with different levels of random noise. Modal frequencies and corresponding mode shapes of an aluminium plate containing mill-cut damage are obtained via finite element models for numerical simulations and by using a scanning laser vibrometer (SLV) for the experimental study.

A pseudo-modal structural damage index based on orthogonal empirical mode decomposition

2019 ◽  
Vol 233 (23-24) ◽  
pp. 7545-7564 ◽  
Author(s):  
Egidio Lofrano ◽  
Francesco Romeo ◽  
Achille Paolone
Keyword(s):  
Empirical Mode Decomposition ◽  
Structural Damage ◽  
Degrees Of Freedom ◽  
Damage Identification ◽  
Damage Index ◽  
Experimental Tests ◽  
Intrinsic Mode Functions ◽  
Mode Decomposition ◽  
Identification Technique ◽  
Output Only

A structural damage identification technique hinged on the combination of orthogonal empirical mode decomposition and modal analysis is proposed. The output-only technique is based on the comparison between pre- and post-damage free structural vibrations signals. The latter are either kinematic (displacements, velocities or accelerations) or deformation measures (strains or curvatures). The response data are decomposed by means of the orthogonal empirical mode decomposition to derive a finite set of orthogonal intrinsic mode functions; the latter are used as a multi-frequency and data-driven basis to build pseudo-modal shapes. A new damage index, the so-called pseudo-mode index, is introduced to compare the response obtained for the two states of the structural system and detect potential damages. The performance of the devised index in detecting a localised damage is shown through numerical and experimental tests on two structural models, namely a 4-degrees-of-freedom system and a two-hinged parabolic arch.

Non-Model-Based Delamination Detection of Composite Plates Using Measured Mode Shapes

2017 ◽  
Author(s):  
Y. F. Xu ◽  
Da-Ming Chen ◽  
W. D. Zhu
Keyword(s):  
Mode Shape ◽  
Composite Plate ◽  
Damage Index ◽  
Laminated Composite ◽  
Composite Plates ◽  
Measurement Noise ◽  
Mode Shapes ◽  
Model Based ◽  
Damage Indices ◽  
Delamination Area

Delamination is one type of damage that frequently occurs in laminated composite structures, and identification of such damage has been a major research topic in the past few decades. This paper proposes an accurate non-model-based method for delamination identification of laminated composite plates. A weighted mode shape damage index is formulated using squared weighted difference between a measured mode shape of a composite plate with delamination and one from a polynomial that fits the measured mode shape of the composite plate with a proper order. Weighted mode shape damage indices associated with at least two measured mode shapes of the same mode are synthesized to formulate a synthetic mode shape damage index to exclude some false positive identification results due to measurement noise and error. An auxiliary mode shape damage index is proposed to further assist delamination identification, by which some false negative identification results can be excluded and edges of a delamination area can be accurately and completely identified. Numerical examples are presented to investigate effectiveness of the proposed method, and it is shown that edges of a delamination area in composite plates can be accurately and completely identified when measured mode shapes are contaminated by measurement noise and error.

scholarly journals Modal Mass and Length of Mode Shapes in Structural Dynamics

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
M. Aenlle ◽  
Martin Juul ◽  
R. Brincker
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Structural Dynamics ◽  
Mode Shape ◽  
Physical Meaning ◽  
Frequency Response Function ◽  
Degrees Of Freedom ◽  
Mode Shapes ◽  
Length Measure ◽  
Modal Mass

The literature about the mass associated with a certain mode, usually denoted as the modal mass, is sparse. Moreover, the units of the modal mass depend on the technique which is used to normalize the mode shapes, and its magnitude depends on the number of degrees of freedom (DOFs) which is used to discretize the model. This has led to a situation where the meaning of the modal mass and the length of the associated mode shape is not well understood. As a result, normally, both the modal mass and the length measure have no meaning as individual quantities but only when they are combined in the frequency response function. In this paper, the problems of defining the modal mass and mode shape length are discussed, and solutions are found to define the quantities in such a way that they have individual physical meaning and can be estimated in an objective way.

Analysis of Vibrating Micropolar Plate in Contact With a Fluid

2010 ◽  
Author(s):  
A. Najafi ◽  
F. Daneshmand ◽  
S. R. Mohebpour
Keyword(s):  
Classical Theory ◽  
Degrees Of Freedom ◽  
Ritz Method ◽  
Theory Of Elasticity ◽  
Material Point ◽  
Mode Shapes ◽  
Micropolar Theory ◽  
Fluid Structure ◽  
Practical Applications ◽  
Micropolar Plate

Micropolar theory constitutes extension of the classical field theories. It is based on the idea that every particles of the material can make both micro rotation and volumetric micro elongation in addition to the bulk deformation. Since this theory includes the effects of micro structure which could affect the overall behaviour of the medium, it reflects the physical realities much better than the classical theory for the engineering materials. In the micropolar theory, the material points are considered to possess orientations. A material point carrying three rigid directors introduces one extra degree of freedom over the classical theory. This is because in micropolar continuum, a point is endowed with three rigid directors only. A material point is then equipped with the degrees of freedom for rigid rotations, in addition to the classical translational degrees of freedom. In fact, the micropolar covers the results of the classical continuum mechanics. The micropolar theory recently takes attentions in fluid mechanics and mathematicians and engineers are implementing this theory in various theoretical and practical applications. In this paper the fluid-structure analysis of a vibrating micropolar plate in contact with a fluid is considered. The fluid is contained in a cube which all faces except for one of the lateral faces are rigid. The only non-rigid lateral face is made of a flexible micropolar plate and therefore, interacts with the fluid. An analytical approach is utilized to investigate the vibration characteristics of the aforementioned fluid-structure problem. The fluid is non-viscous and incompressible. Duplicate Chebyshev series, multiplied by boundary functions are used as admissible functions and the frequency equations of the micropolar plate are obtained by the use of Chebyshev-Ritz method. Also the vibration analysis of the plates modeled by micropolar theory has been done. This analysis shows that some additional frequencies due to the micropolarity of the plate appears among the values of the frequencies obtained in the classical theory of elasticity, as expected. These new frequencies are called micro-rotational waves. We also observed that when the micropolar material constants vanish, these additional frequencies disappear and only the classical frequencies remain. Specially, we observed that these additional frequencies are more sensitive to the change of the micro elastic constants than the classical frequencies. The frequencies and mode shapes of the coupled fluid structure interaction problem are obtained in the present study based on the micropolar and classical modeling. The numerical results for the problem are compared with those obtained by the analytical method for their differences and to confirm the proposed method. The microrotatinal wave frequencies and mode shapes are also developed. The results show that the natural frequencies and mode shapes for the transverse vibrations of the problem are in good agreement with the classical one and our knowledge from the physical nature of the problem.

Parameter Adaptation With Automatically Selected Co-Ordinates From Measured Eigenvectors As a Way to a Validated FE Model

1997 ◽  
Author(s):  
Manfred W. Zehn ◽  
Gerald Schmidt ◽  
Oliver Martin
Keyword(s):  
Mode Shape ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
High Sensitivity ◽  
Mode Shapes ◽  
Problem Solver ◽  
Fe Model ◽  
Parameter Adaptation ◽  
Fine Mesh ◽  
Reduction Techniques

Abstract This paper considers an algorithm on the basis of parameter adaptation for mass and stiffness embedded in the eigenvalue problem solver. The algorithm is intended for large finite element (FE) models. The errors, which can be reduced by the procedure described in this paper, occur due to detailed features, which would require an unduly fine mesh to be included in the model, or in uncertainties in the description of mechanical behaviour, material properties, etc. Another source for errors are model reduction techniques (superelement technique) necessary for the application of the model structure in an automatic control circuit (smart structures). It is a well-known fact that the natural frequencies can be measured much more accurately than mode shapes, for mode shapes can only be measured for accessible regions and normally for translational degrees of freedom (DOF). Therefore the algorithm uses only measured natural frequencies (frequency differences) and the calculated mode shape vectors to determine the parameter changes. In a new approach it is also possible to select automatically, or by experience, those co-ordinates from the measured mode shape vectors that correspond to points with high sensitivity or other very reliable points. An interface system designed to exchange data between the experimental modal analysis system (EMA) and the FE program ensures, that the measured and calculated mode shape vectors are orthonormalised in the same way and the points of the FE mesh correspond to the pick up points for the measurement. Examples of industrial parts at the end of the paper illustrate how the procedure works and what influence we can obtain by inclusion of some co-ordinates of measured mode shape vectors.

scholarly journals Corrigendum to “Modal Mass and Length of Mode Shapes in Structural Dynamics”

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
M. Aenlle ◽  
Martin Juul ◽  
R. Brincker
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Structural Dynamics ◽  
Mode Shape ◽  
Physical Meaning ◽  
Frequency Response Function ◽  
Degrees Of Freedom ◽  
Mode Shapes ◽  
Length Measure ◽  
Modal Mass

The literature about the mass associated with a certain mode, usually denoted as the modal mass, is sparse. Moreover, the units of the modal mass depend on the technique used to normalize the mode shapes, and its magnitude depends on the number of degrees of freedom (DOFs) used to discretize the model. This has led to a situation where the meaning of the modal mass and the length of the associated mode shape is not well understood. As a result, normally, both the modal mass and the length measure have no meaning as individual quantities, but only when they are combined in the frequency response function. In this paper, the problems of defining the modal mass and mode shape length are discussed, and solutions are found to define the quantities in such a way that they have individual physical meaning and can be estimated in an objective way.

scholarly journals Modal analysis and insights into damping phenomena of a special vibration chain

2021 ◽  
Author(s):  
Peter C. Müller ◽  
Wolfgang E. Weber
Keyword(s):  
Fluid Flow ◽  
Modal Analysis ◽  
Mode Shape ◽  
Mode Shapes ◽  
Hydraulic Systems ◽  
Practical Applications ◽  
Damping Matrix ◽  
Modal Damping ◽  
Future Work

AbstractVibration chains are of interest in many fields of practical applications. In this contribution, a modal analysis of the rather special Mikota’s vibration chain  is performed. Herein, focus is set on the mode shapes of this multibody oscillator, which was firstly introduced by Mikota as a solid body compensator in hydraulic systems for filtering out fluid flow pulsations. The mode shapes show interesting properties, e.g. an increase in the polynomial representing the coordinates of each mode shape with an increasing eigenfrequency associated with the respective mode shape. This and other properties are discussed exemplary. Some of these properties still have to be proven, which is the task of future work. Additionally, modal damping of Mikota’s vibration chain is discussed. Moreover, an approach for determining the damping matrix for given Lehr’s damping measures without knowing the mode shapes in advance is introduced. This approach involves the determination of a matrix root.

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