Structural damage identification using transfer matrix with lumped crack properties
23 Mar 2016-Inverse Problems in Science and Engineering (Taylor & Francis)-Vol. 24, Iss: 3, pp 422-447
TL;DR: In this paper, a beam element with multiple cracks is modeled as an element of zero length and mass, but with elastic properties, and a transfer matrix (TM) approach is used to detect the cracks.
Abstract: A novel damage detection scheme is developed for detecting multiple cracks in beams, based on a transfer matrix (TM) approach. Lumped Crack TM of a beam element with multiple cracks is derived based on lumped crack properties. A cracked beam element is assumed as two intact beam elements connected with a hinge or torsional spring. The crack is modelled as an element of zero length and mass, but with elastic properties. Lumped crack approach is simpler for multiple cracks than the possible alternative methods. The state vector at a node includes displacements, forces and moments at that node; when it is multiplied with TM the state vector at the adjacent node can be obtained. The crack identification strategy used here, involves measuring the initial state vector at a node, in the zone of interest. The displacements at the adjacent nodes are measured and these are predicted using TM. Using an optimization algorithm the unknown crack parameters in the TM are solved by minimizing the deviation between measur...
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TL;DR: In this paper, the authors considered the high-order vibration characteristics of structures with multi-cracks and established finite element models for concrete steel beam and bridge with cracks under three different conditions and obtained vibration frequency and three order modes through simulation.
Abstract: Complex bridges will inevitably have cracks in operation. Dynamic characteristics with crack structures have been researched central issues. In the past, few researches were conducted from the whole structure of bridges with multi-cracks. In the meanwhile, related experimental research and systematic numerical simulation were lacking. In addition, researches on cracks seldom considered the high-order vibration characteristics of structures with multi-cracks. Aimed at this problem, this paper selected the whole bridge structure which was widely applied in engineering to study dynamic characteristics. For the concrete steel bridge with two cracks, this paper established finite element models for concrete steel beam and bridge with cracks under three different conditions and obtained vibration frequency and three order modes through simulation. Then, this paper analyzed and verified the correctness of numerical simulation result through experiment. Based on the verified model, this paper conducted a systematic analysis and summary, and obtained the following findings: The vibration frequency of concrete steel beams with cracks was obviously affected by cracks. The higher the order was, the greater the impact of cracks on frequency would be and the smaller the impact of cracks on the amplitude of modes would be. With the increased crack depth, the impact on the vibration frequency of concrete steel beams was more obvious. Additionally, crack distance also had some impacts on the dynamic characteristics of concrete steel beams. Numerical simulation model and method in this paper provided foundation and reference for continuing to analyze concrete steel beams with other crack forms or other structural forms. In the meanwhile, the three-dimensional analytical contour in this paper could help engineers to more intuitively understand and valuably apply the change rule of impact of crack depth and position on concrete steel beams.
35 citations
Cites background from "Structural damage identification us..."
...For example, the fatigue strength reached the limit to cause the structural cracks under the condition of operation [4-8]....
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TL;DR: In this paper, the capabilities of an enhanced sensitivity relation for the structural model updating are validated using a subset of the measured frequency response function (FRF) and natural freq...
Abstract: In this paper, the capabilities of an enhanced sensitivity relation for the structural model updating are validated using a subset of the measured frequency response function (FRF) and natural freq...
6 citations
Cites methods from "Structural damage identification us..."
...Nandakumar and Shankar [34] used experimental transfer function data for identification of multiple cracks of beam models....
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TL;DR: In this paper, the free vibration analysis of a double tapered beam having linearly varying both thickness and width, by using finite element and component mode synthesis methods, is presented.
Abstract: This study presents the free vibration analysis of a double tapered beam having linearly varying both thickness and width, by using finite element and component mode synthesis methods. To determine...
3 citations
TL;DR: In this paper, a novel spectral transfer matrix for a cracked beam element is developed and the same matrix is used to identify the crack parameters on the beam structures, where the same spectral transfer matrices are used to detect the cracks in the beam elements.
Abstract: A novel spectral transfer matrix for a cracked beam element is developed in this article and the same is used to identify the crack parameters on the beam structures. Spectral transfer matrix is de...
1 citations
References
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TL;DR: In this paper, a new simplified approach to modeling cracks in beams undergoing transverse vibration is presented, which uses Euler-Bernoulli beam elements with small modifications to the local flexibility in the vicinity of cracks.
364 citations
"Structural damage identification us..." refers background in this paper
...[3] formulated a new stiffness matrix for cracked beam element with equivalent varying flexural rigidity near the crack, which gives better results only at lower modes....
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TL;DR: In this article, a finite element for the cracked prismatic beam is developed to evaluate the dynamic response of a cracked cantilever beam to harmonic point force excitation, which can be used in any appropriate matrix analysis of structures program.
228 citations
"Structural damage identification us..." refers background in this paper
...Gounaris and Dimarogonas [1] developed a compliance matrix for cracked beam element by assuming the crack increases the flexibility due to strain energy ∗Corresponding author....
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...Gounaris and Dimarogonas [1] developed a compliance matrix for cracked beam element by assuming the crack increases the flexibility due to strain energy...
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TL;DR: In this paper, a simple and easy non-destructive evaluation procedure is presented for identifying a crack, the location and size of the crack, in a one-dimensional beam-type structure using the natural frequency data.
219 citations
"Structural damage identification us..." refers background or methods in this paper
...The geometric correction function is given by [33]...
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...of slender beams.[33] Two DOF per node is considered (k = 2)....
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TL;DR: In this paper, a substructure approach is used to estimate the stiffness and damping coefficients of structures from measurement of dynamic responses, and the structures are decomposed into smaller subsystems for which state and observation equations are formulated and solved by the method of extended Kalman filter with a weighted global iteration algorithm.
Abstract: A substructure approach is used to estimate the stiffness and damping coefficients of structures from measurement of dynamic responses. The structures are decomposed into smaller subsystems for which state and observation equations are formulated and solved by the method of extended Kalman filter with a weighted global iteration algorithm. Substructural identification methods with and without overlapping members are proposed. In both methods, the convergence of the structural parameters to the optimal values is improved significantly with less computation time as compared to a complete structural approach. Numerical simulation studies are performed for three types of structures, namely a shear building, a plane frame building and a plane truss bridge. The effects of measurement noise and response observations required for identification of system parameters are also investigated.
204 citations
"Structural damage identification us..." refers methods in this paper
...[19,20] were the first to formulate a substructural identification method, which significantly reduces the computational effort....
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Book•
01 Jan 1971
TL;DR: In this paper, the authors describe a deterministic deterministic model for periodic motion in distributed systems. But they do not consider the effects of random and nonlinear Vibration.
Abstract: Dynamics. Periodic Motion. Energy Methods. Forced Periodic Motion. Initial Conditions and Transient Vibration. Damping. Damped Forced Vibrations. Nonlinear Vibration. Two Degrees of Freedom. Torsional Vibration. Discrete Systems: Matrix Methods. Discrete Systems: Finite Elements. Distributed Systems. Random Vibration. References. Index.
194 citations
"Structural damage identification us..." refers background or methods in this paper
...Steidel [25] also presented the formulation for harmonic forced response using TM....
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...The TM for the torsional spring is formulated from the static equilibrium equations of the spring as given in [25]....
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...Steidel [25] derived the TM for a spring mass system and a beam element by assuming that the mass is concentrated only at two end nodes of the element....
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