• Structural Engineering and Mechanics
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• v.73 no.3
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• pp.271-286
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• 2020

Passive control technologies are commonly used in several areas to suppress structural vibrations by the addition of supplementary damping, and some modal damping may be heavy beyond critical damping even for regular structures with energy dissipation devices. The design of passive control structures is typically based on (complex) mode superposition approaches. However, the conventional mode superposition approach is predominantly applied to cases of under-critical damping. Moreover, when any modal damping ratio is equal or close to 1.0, the system becomes defective, i.e., a complete set of eigenvectors cannot be obtained such that some well-known algorithms for the quadratic eigenvalue problem are invalid. In this paper, a generalized complex mode superposition method that is suitable for under-critical, critical and over-critical damping is proposed and expressed in a unified form for structural displacement, velocity and acceleration responses. In the new method, the conventional algorithm for the eigenvalue problem is still valid, even though the system becomes defective due to critical modal damping. Based on the modal truncation error analysis, modal corrected methods for displacement and acceleration responses are developed to approximately consider the contribution of the truncated higher modes. Finally, the implementation of the proposed methods is presented through two numerical examples, and the effectiveness is investigated. The results also show that over-critically damped modes have a significant impact on structural responses. This study is a development of the original complex mode superposition method and can be applied well to dynamic analyses of non-classically damped systems.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.2
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• pp.363-373
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• 1995

In this study, a FE model tuning method using experimental modal data was suggested after examining all the published conventional methods. The idea of this method is introducing scale factors to maintain both the structural connectivity and the consistency in the corrected stiffness matrix which makes it always possible to interpret the stiffness elements with the corresponding physical configuration of the targeting structure. The scale factors are determined to minimize the objective function of eigen-properties. The proposed method was tested to determine the joint stiffness of a T shaped beam. The test results were also compared with the tuned stiffness obtained from a probed commercial package (SYSTUNE) and found that this method is very accurate and compatible.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.29 no.1
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• pp.39-55
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• 1993

Modal Analysis is the process of characterizing the dynamic properties of an elastic structure by identifying its modes of vibration. A mode of vibration is a global property of an elastic structure. That is, a mode has a specific natural frequency and damping factor which can be identified from response data at practically any point on a structure, and it has a characteristic mode shape which identifies the mode spatially over the entire structure. Modal testing is able to be performed on structural and mechanical structure in an effort to learn more about their elastic behavior. Once the dynamic properties of a structure are known its behavior can be predicted and therefore controlled or corrected. Resonant frequencies, damping factors and mode shape data can be used directly by a mechanical designer to pin point weak spots in a structure design, or this data can also be used to confirm or synthesize equations of motion for the elastic structure. These differential equations can be used to simulate structural response to know input forces and to examine the effects of pertubations in the distributed mass, stiffness and damping properties of the structure in more detail. In this paper the measurement of transfer functions in digital form, and the application of digital parameter identification techniques to identify modal parameters from the measured transfer function data are discussed. It is first shown that the transfer matrix, which is a complete dynamic model of an elastic plate structure can be written in terms of the structural modes of vibration. This special mathematical form allows one to identify the complete dynamics of the structure from a much reduced set of test data, and is the essence of the modal approach to identifying the dynamics of a structure. Finally, the application of transfer function models and identification techniques for obtaining modal parameters from the transfer function data are discussed. Characteristics on vibration response of elastic plate structure obtained from the dynamic analysis by Finite Element Method are compared with results of modal analysis.

• Journal of Positioning, Navigation, and Timing
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• v.11 no.1
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• pp.35-44
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• 2022

In this paper, a dual foot (DF)-PDR system is proposed for the fusion of integration (IA)-based PDR systems independently applied on both shoes. The horizontal positions of the two shoes estimated from each PDR system are fused based on a particle filter. The proposed method bounds the position error even if the walking time increases without an additional sensor. The distribution of particles is a non-Gaussian distribution to express the lateral error due to systematic drift. Assuming that the shoe position is the pedestrian position, the multi-modal position distribution can be fused into one using the Gaussian sum. The fused pedestrian position is used as a measurement of each particle filter so that the position error is corrected. As a result, experimental results show that position of pedestrians can be effectively estimated by using only the inertial sensors attached to both shoes.

• Smart Structures and Systems
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• v.18 no.3
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• pp.541-568
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• 2016

The goal of this study is to investigate the effect of non-synchronous sensing when using wireless sensors on structural identification and to attempt correcting such errors in order to obtain a better identification result. The sources causing non-synchronous sensing are discussed first and the magnitudes of such synchronization errors are estimated based on time stamps of data samples collected from Imote2 sensors; next the impact of synchronization errors on power spectral densities (PSDs) and correlation functions of output responses are derived analytically; finally a new method is proposed to correct such errors. In this correction method, the corrected PSDs of output responses are estimated using non-synchronous samples based on a modified FFT. The effect of synchronization errors in the measured output responses on structural identification and the application of this correction method are demonstrated using simulation examples. The simulation results show that even small synchronization errors in the output responses can distort the identified modal and stiffness parameters remarkably while the parameters identified using the proposed correction method can achieve high accuracy.

• Journal of Ocean Engineering and Technology
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• v.23 no.1
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• pp.74-80
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• 2009

In this study, the static and modal analyses to find the characteristic of eigenvalues for a towed cable were with a free boundary condition at the bottom end carried out with numerical study. The resulting numerical code with finite element method was used to study sample problems for a cable with towing speeds. After tracing the equilibrium state with a towing speed through the static analysis, modal analysis on the basis of static results was performed. The static top tension for a critical towing speed is nearly 50 percent of what it was for a free hanging pipe. From static analyses, it is found that towing speed has a noticeable effect on top tension of a towed pipe. At a high towing speed, differences between the first and second periods become larger. Compared to the fundamental period for a free hanging pipe, that for a towed pipe with a critical towing speed is approximately 1.4 times larger. This result is very important point in that the lock in condition and tension of the towed cable system with top excitation can be predicted. The corrected close form solution to solve natural periods for a towed cable was presented in this study. The code is validated by comparison of the results of theoretical and numerical studies. Two results were in very good agreement. This study can contribute to predicting the lock-in condition and tension for a towed cable or pipe with top excitation.

• Smart Structures and Systems
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• v.25 no.6
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• pp.657-668
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• 2020

A novel multistage approach is developed for structural model updating based on sensitivity ranking of the selected updating parameters. Modal energy-based sensitivities are formulated, and maximum-normalized indices are designed for sensitivity ranking. Based on the ranking strategy, a multistage approach is proposed, where these parameters to be corrected with similar sensitivity levels are updated simultaneously at the same stage, and the complete procedure continues sequentially at several stages, from large to small, according to the predefined levels of the updating parameters. At every single stage, a previously developed cross model cross mode (CMCM) method is used for structural model updating. The effectiveness and robustness of the multistage approach are investigated by implementing it on an offshore structure, and the performances are compared with non-multistage approach using numerical and experimental vibration information. These results demonstrate that the multistage approach is more effective for structural model updating of offshore platform structures even with limited information and measured noise. These findings serve as a preliminary strategy for structural model updating of an offshore platform in service.