• 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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.549-555
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• 2000

The improved mode superposition methods for non-classically damped systems are presented in this paper. Generally, the mode superposition method uses a relatively small subset of the normal modes of structures. The mode acceleration method and the modal truncation augmentation method improve the results of the mode superposition method by considering effects of truncated high modes. For using these methods to analyze non-classically damped systems, the systems are approximated to the classically damped systems and thereby the errors are induced. In this paper, the mode acceleration method and the modal truncation augmentation method are expanded to analyze the non-classically damped systems. The applicability of the expanded methods is verified by closed form solutions and numerical examples. The expanded modal truncation augmentation method is conditionally stable depending on the pattern of the external loading in the non-classically damped systems whereas the expanded mode acceleration method is stable for the all cases of loading. In the stable case, the results are the same with those of the expanded mode acceleration method.

• Structural Engineering and Mechanics
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• v.76 no.5
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• pp.643-651
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• 2020

Generally, it is necessary to perform transient structural analysis in order to verify and improve the seismic performance of high-rise buildings and bridges against earthquake loads. In this paper, we propose the model order reduction (MOR) method using the Krylov vectors to perform seismic analysis for linear and elastic systems in an efficient way. We then compared the proposed method with the mode superposition method (MSM) by using the limited numbers of modal vectors (or eigenvectors) calculated from the modal analysis. In the calculation, the data of the El Centro earthquake in 1940 were adopted for the seismic loading in the transient analysis. The numerical accuracy and efficiency of the two methods were compared in detail in the case of a simplified high-rise building.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.34 no.10
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• pp.1339-1344
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• 2010

MSM (Modal Superposition Method) is a technique for analyzing structural durability by taking the vibration characteristics into consideration. In this paper, MSR (Modal Stress Recovery) method, which is similar to MSM, was reviewed to check its validity as a durability analysis method. The MSR method directly calculates the modal displacement time history in multibody dynamics analysis; as a result, the total analysis time is shorter than that of MSM method. We conduct durability analysis using the MSR method and a durability test of a torsion beam axle that is affected by various road loads within the natural frequency of the beam axle. The analysis results for critical location and durability were in good agreement with the respective test results. Therefore, durability analysis using the MSR method is effective in predicting the durability of the structures of various dynamic systems.

• Transactions of the Korean Society of Automotive Engineers
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• v.16 no.4
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• pp.120-127
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• 2008

A military vehicle undergoes normal to extreme driving conditions, which consequently induce the fatigue and fracture of cabin and frame. So, it is important to estimate the fatigue life of two components at an initial design stage. In this paper, Modal Superposition Method(MSM) was applied to evaluate the durability performance of a small-sized military truck. For reliable durability analysis, a Virtual Test Lab(VTL) Model was established by correlation with experimental results. These data were extracted from actual driving test, modal test, and SPMD(Suspension Parameter Measuring Device) test. This process shows that Virtual Fatigue Analysis can be a useful approach in the development of military vehicles as well as commercial vehicles.

• Structural Engineering and Mechanics
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• v.42 no.4
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• pp.449-469
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• 2012

For generally damped linear systems with repeated eigenvalues and defective eigenvectors, this study provides a decomposition method based on residue matrix, which is suitable for engineering applications. Based on this method, a hybrid approach is presented, incorporating the merits of the modal superposition method and the residue matrix decomposition method, which does not need to consider the defective characteristics of the eigenvectors corresponding to repeated eigenvalues. The method derived in this study has clear physical concepts and is easily to be understood and mastered by engineering designers. Furthermore, this study analyzes the applicability of step-by-step methods, including the Newmark beta and Runge-Kutta methods for dynamic response calculation of defective systems. Finally, the implementation procedure of the proposed hybrid approach is illustrated by analyzing numerical examples, and the correctness and the effectiveness of the formula are judged by comparing the results obtained from the different methods.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11a
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• pp.361.1-361
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• 2002

Coupling adjacent steel frame using elastic dampers fer control of response to low and moderate dynamic event is investigated in this paper. The complex modal superposition method is first used to determine dynamic characteristic, mainly modal damping ratio and modal frequency, of damper linked linear adjacent steel frame for fractical use. Dynamic response of steel frame linked by hydraulic-excitation method. (omitted)

• Structural Engineering and Mechanics
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• v.81 no.4
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• pp.411-428
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• 2022

This paper presents the Campbell diagram analysis of the rotordynamic system using the full order model (FOM) and the reduced order model (ROM) techniques to determine the critical speeds, identify the stability and reduce the computational time. Due to the spin-speed-dependent matrices (e.g., centrifugal stiffening matrix), several model order reduction (MOR) techniques may be considered, such as the modal superposition (MS) method and the Krylov subspace-based MOR techniques (e.g., Ritz vector (RV), quasi-static Ritz vector (QSRV), multifrequency quasi-static Ritz vector (MQSRV), multifrequency/ multi-spin-speed quasi-static Ritz vector (MMQSRV) and the combined Ritz vector & modal superposition (RV+MS) methods). The proposed MMQSRV method in this study is extended from the MQSRV method by incorporating the rotational-speed-dependent stiffness matrices into the Krylov subspace during the MOR process. Thus, the objective of this note is to respond to the question of whether to use the MS method or the Krylov subspace-based MOR technique in establishing the Campbell diagram of the shaft-disc-blade assembly systems in three-dimensional (3D) finite element analysis (FEA). The Campbell diagrams produced by the FOM and various MOR methods are presented and discussed thoroughly by computing the norm of relative errors (ER). It is found that the RV and the MS methods are dominant at low and high rotating speeds, respectively. More precisely, as the spinning velocity becomes large, the calculated ER produced by the RV method is significantly increased; in contrast, the ER produced by the MS method is smaller and more consistent. From a computational point of view, the MORs have substantially reduced the time computing considerably compared to the FOM. Additionally, the verification of the 3D FE rotordynamic model is also provided and found to be in close agreement with the existing solutions.

• Journal of Ocean Engineering and Technology
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• v.34 no.2
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• pp.120-127
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• 2020

Evaluation of fatigue strength considering the springing effect of very large container ships is crucial in the design stage. In this study, we established a fatigue strength evaluation method considering a linear springing component in the frequency domain. Based on a three-dimensional global model, a fluid-structure interaction analysis was performed and the modal superposition method was applied to determine the hot spot stress at the hatch corner of very large container ships. Fatigue damage was directly estimated using the stress transfer function with a linear springing response. Furthermore, we proposed a new methodology to apply the springing effect to fatigue damage using hull girder loads. Subsequently, we estimated the fatigue damage contribution due to linear springing components along the ship length. Finally, we discussed the practical application of the proposed methods.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11b
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• pp.593-598
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• 2002

Coupling adjacent steel frame using elastic dampers for control of response to low and moderate dynamic event is investigated in this paper. The complex modal superposition method is first used to determine dynamic characteristic, mainly modal damping ratio and modal frequency, of damper linked linear adjacent steel frame for fractical use. Dynamic response of steel frame linked by hydraulic-excitation method. This combined method can efectively and accurately determine dynamic response of non-clasically damped systems in the frequency domain. Parametric studties are finally performed to identify optimal parameters of elastic dampers for achieving the maximum modal damping ratio or the maximum response reduction of steel frame. It is demonstrated that using discrete elasatic dampers of proper parameters to link steel frame can reduce dynamic response significantly.