• Title, Summary, Keyword: mode superposition method

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Efficient Mode Superposition Method for Non-Classically Damped Systems (비비례 감쇠시스템의 해석을 위한 효율적인 모드 중첩법)

  • Cho, Sang-Won;Cho, Ji-Seong;Park, Sun-Kyu;Lee, In-Won
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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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.

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Generalized complex mode superposition approach for non-classically damped systems

  • Chen, Huating;Liu, Yanhui;Tan, Ping
    • 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.

Vortex-Induced Vibration Analysis of Deep-Sea Riser (심해 라이저의 와류유기 진동해석)

  • Park, Seongjong;Kim, Bongjae
    • Journal of Ocean Engineering and Technology
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    • v.31 no.5
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    • pp.364-370
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    • 2017
  • A numerical model based on the mode superposition method is used to study the vortex-induced vibration response characteristics of a deep-sea riser such as steel catenary riser (SCR). A steel catenary riser can be modeled using a flexible cable with simple supports at both ends. The natural frequency, mode shape and mode curvature of the riser are calculated and the vortex-induced vibration response of the riser is obtained using the equilibrium of the input and output power. The mode superposition method is applied to the vibrational stresses for each mode to calculate the overall riser fatigue life.

Modified complex mode superposition design response spectrum method and parameters optimization for linear seismic base-isolation structures

  • Huang, Dong-Mei;Ren, Wei-Xin;Mao, Yun
    • Earthquakes and Structures
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    • v.4 no.4
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    • pp.341-363
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    • 2013
  • Earthquake response calculation, parametric analysis and seismic parameter optimization of base-isolated structures are some critical issues for seismic design of base-isolated structures. To calculate the earthquake responses for such non-symmetric and non-classical damping linear systems and to implement the earthquake resistant design codes, a modified complex mode superposition design response spectrum method is put forward. Furthermore, to do parameter optimization for base-isolation structures, a graphical approach is proposed by analyzing the relationship between the base shear ratio of a seismic base-isolation floor to non-seismic base-isolation one and frequency ratio-damping ratio, as well as the relationship between the seismic base-isolation floor displacement and frequency ratio-damping ratio. In addition, the influences of mode number and site classification on the seismic base-isolation structure and corresponding optimum parameters are investigated. It is demonstrated that the modified complex mode superposition design response spectrum method is more precise and more convenient to engineering applications for utilizing the damping reduction factors and the design response spectrum, and the proposed graphical approach for parameter optimization of seismic base-isolation structures is compendious and feasible.

Comparison of Mode Superposition Method and Mode Acceleration Method in Dynamic Analysis of Suspension Bridges under Wind Loads (풍하중을 받는 현수교의 진동 해석에 있어서 모우드 중첩법과 모우드 가속도법의 비교)

  • 김태남
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • pp.223-230
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    • 1997
  • A method of stochastic dynamic analysis of suspension bridge subjected to random wind loads has been developed in this paper. Example analyses are carried out by mode superposition method(MSM), mode acceleration method(MAM) and advanced mode acceleration method(AMAM) in frequency domain for the Nam-Hae Bridge. In this study the statistical characterics of random wind loads we assumed to be Gaussian stationary zero mean processes. The considered structural response quanties are displacements, shear forces and bending moments. The mean extreme responses are approximately calculated by three times of standard deviations. The followings are the conclusions from this study. 1. Numerical results which obtained by three methods of computer program developed in this paper agree reasonably well when the numbers of modes increase. 2. AMAM is simple, accurate, economic and reliable method compared with the MSM and the MAM.

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3-D Dynamic Response of Buried Pipelines (매설관의 3차원 동적응답거동)

  • Jeong, Jin-Ho;Kim, Chun-Jin
    • Journal of the Earthquake Engineering Society of Korea
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    • v.15 no.3
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    • pp.27-35
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    • 2011
  • Larbi (1995) and Jeong et al. (2005) analyzed the various boundary end conditions of buried pipelines using the mode superposition method as one of the dynamic analysis methods of buried pipelines. However, it is very complicated to derive calculation equations for the solutions to be obtained by this method, and even the derived calculation equations need separate computer programming for the numerical analysis in order to obtain the solutions. For this reason, this method is extremely difficult for engineers to apply in their field works. In consideration of the shortcoming of the mode superposition method, this study's purpose is to propose a 3D dynamic finite difference method, which is more easily applicable in the field. For this purpose, we tested the accuracy of the 3D dynamic analysis and compared the results with those of the mode superposition method and certified that the 3D dynamic analysis could be an alternative method to obtain the seismic responses of the pipelines.

Non-Liner Analysis of Shear Beam Model using Mode Superposition (모드중첩법을 이용한 전단보 모델의 비선형 해석)

  • 김원종;홍성목
    • Journal of the Earthquake Engineering Society of Korea
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    • v.3 no.2
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    • pp.87-96
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    • 1999
  • To analyze the dynamic behavior of structure, direct integration and mode superposition may be utilized in time domain analysis. As finite number of frequencies can give relatively exact solutions, mode superposition is preferable in analyzing structural behavior. In non-linear analysis, however, mode superposition is seldom used since time-varying element stiffness changes stiffness matrix, and the change of stiffness matrix leads to the change of essential constants - natural frequencies and mode shapes. In spite of these difficulties, there are some attempts to adopt mode superposition because of low cost compared to direct integration, but the result is not satisfactory. In this paper, a method using mode superposition in non-linear analysis is presented by separating local element stiffness from global stiffness matrix with the difference between linear and non-linear restoring forces to the external force vectors included. Moreover, the hysteresis model changing with the relative deformation in each floor makes it possible to analyze non-linear behavior of structure. The proposed algorithm is applied to shear beam model and the maximum displacement is compared with the result using direct integration method.

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Fast Simulation of Output Voltage for High-Shock Piezoresistive Microaccelerometer Using Mode Superposition Method and Least Square Method (모드중첩법 및 최소자승법을 통한 고충격 압저항 미소가속도계의 출력전압 해석)

  • Han, Jeong-Sam;Kwon, Ki-Beom
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.36 no.7
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    • pp.777-787
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    • 2012
  • The transient analysis for the output voltage of a piezoresistive microaccelerometer takes a relatively high computation time because at least two iterations are required to calculate the piezoresistive-structural coupled response at each time step. In this study, the high computational cost for calculating the transient output voltage is considerably reduced by an approach integrating the mode superposition method and the least square method. In the approach, data on static displacement and output voltage calculated by piezoresistive-structural coupled simulation for three acceleration inputs are used to develop a quadratic regression model, relating the output voltage to the displacement at a certain observation point. The transient output voltage is then approximated by a regression model using the displacement response cheaply calculated by the mode superposition method. A high-impact microaccelerometer subject to several types of acceleration inputs such as 100,000 G shock, sine, step, and square pulses are adopted as a numerical example to represent the efficiency and accuracy of the suggested approach.

Dynamic Analysis of Offshore Structures by the Advanced Mode Acceleration Method (개선된 Mode Acceleration Method에 의한 해양(海洋) 구조물(構造物)의 동적(動的) 해석(解析))

  • Kim, Tae Nam
    • Journal of The Korean Society of Civil Engineers
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    • v.14 no.1
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    • pp.13-20
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    • 1994
  • Determination of the number of modes to be included in the mode superposition method(MSM) is very important and difficult. Mode acceleration method(MAM) is recommended recently with the intention to overcome the problem. But the solution of the MAM is complex and complicate in frequency domain analysis. In this paper, advanced mode acceleration method(AMAM) is formulated and examined. The results from example analyses show that AMAM is a simple, accurate and reliable method compared with the MSM and the MAM.

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3D Bridge-Vehicle interaction Analysis of Cable-Supported Bridges Using Mode Superposition Method (모드중첩법을 이용한 케이블지지교량의 3차원 교량-차량 상호작용 해석)

  • Lee Jun-Seok;Im Myoung-Hoon;Kim Moon-Young
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • pp.265-272
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    • 2005
  • For bridge-vehicle interaction analysis of cable-supported brides, the superposition method is applied based on the results of 3-dimensional free vibration analysis using General-purpose FEM Software. This study firstly performs the eigenvalue analysis for the free vertical and the torsional vibration of bridges using FEM analysis. Next the equations of motion considering interaction between bridges and vehicles/train are derived from mode superposition method. And then dynamic analysis is performed using the Newmark numericial method. Finally through the numerical examples, the dynamic responses of cable-supported bridges by this study are presented and discussed.

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