• Title/Summary/Keyword: Modal Superposition Method

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Dynamics of a HDD spindle system due to the change of FDBs (유체베어링의 설계변화에 따른 HDD 스핀들 시스템의 동특성 해석)

  • Park, Ki-Yong;Jang, Gun-Hee
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2008.11a
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    • pp.407-413
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    • 2008
  • This paper investigates the dynamics of a HDD spindle system due to the change of FDBs. Flying height of the HDD spindle system is determined through the static analysis of the FDBs, and the stiffness and damping coefficients are calculated through the dynamic analysis of the FDBs. Free vibration characteristics and shock response of the HDD spindle system are analyzed by using the finite element method and the mode superposition method. Experimental modal test is also performed to verify the accuracy of the proposed method. This research shows that the stiffness coefficients of journal heating mostly affect the rocking frequencies because their magnitude are within the range of the stiffness of supporting structure. It also shows that the damping coefficients of thrust bearing mostly affect the axial frequency because the stiffness of thrust bearing is much smaller that that of supporting structure.

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An Investigation into the Mode Superposition Method for the Foreced Transverse Vibration Analysis of Structures subject to the Timoshenko Beam Analogy (기준진동형중첩법(基準振動型重疊法)에 의한 Timoshenko보 유추(類推) 구조체(構造體)의 강제횡진동해석(强制橫振動解析))

  • K.C.,Kim;Y.I.,Park;H.M.,Kim;Y.J.,Kim
    • Bulletin of the Society of Naval Architects of Korea
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    • v.20 no.1
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    • pp.21-27
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    • 1983
  • The mode superposition method(MSM) for the forced transverse vibration analysis of structures subject to Timoshenko beam analogy, which had originally been developed by Ormondroyd and McGoldrick, is reviewed to formulate it in more general form taking account of rotary inertia, dampings in separate terms of internal and external ones, and simultaneous action of exciting forces and moments. To investigate some general features of the method in practical utilizations, resonant maximum amplitudes of 4 high speed ships under concentrated sinusoidal excitation at the stern are calculated by both MSM and the finite difference method(FDM). For the FDM the hulls are discretized into 40 equal segments, and in utilization of MSM contributions of the first six modes are summed up to obtain responses up to the six-nodes resonant mode. The numerical results show that MSM gives slightly higher values, $4{\sim}10%$, than those by FDM. Since there is always uncertainty in the damping estimation of actual systems, influences of the damping magnitude on resonant amplitudes and a practical method to estimate modal damping coefficients are discussed.

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Reverberation time evaluation considering the acoustical characteristics of a cabin (선실의 음향학적 특성을 고려한 잔향시간 평가)

  • Choi, Jae-Woong
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2000.06a
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    • pp.837-842
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    • 2000
  • Reverberation time is the well known theory and widely used in commercial apparatus to get reverberation time. However large fluctuation in low frequency region occurs in a small cabin due to superposition of a few modes. This paper investigates this phenomena in terms of modal density in frequency domain and suggests a method to get lower limit of reverberation time using the integration of the time-SPL diagram. The suggestion is confirmed by simulation and shows reasonable results to get lower limit of reverberation time and maximum absorbing power in the cabin.

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Finite Element Forced Response of a Spinning Flexible HDD Disk-spindle System Considering the Asymmetry Originating from Gyroscopic Effect and Fluid Dynamic Bearings (자이로스코픽 효과와 유체 동압 베어링에 의한 비대칭성을 고려한 회전 유연 디스크-스핀들 시스템의 유한요소 강제 진동 해석)

  • Park, Ki-Yong;Jang, Gun-Hee;Seo, Chan-Hee
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.20 no.10
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    • pp.915-922
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    • 2010
  • This paper presents an efficient method for determining the forced response of a spinning flexible disk-spindle system supported by fluid dynamic bearings(FDBs) in a computer hard disk drive(HDD). The spinning flexible disk-spindle system is represented by the asymmetric finite element equations of motion originating from the asymmetric dynamic coefficients of the FDBs and the gyroscopic moment of a spinning disk-spindle system. The proposed method utilizes only the right eigenvectors of the eigenvalue problem to transform the large asymmetric finite element equations of motion into a small number of coupled equations, guaranteeing the accuracy of their numerical integration. The results are then back-substituted into the equations of motion to determine the forced response. The effectiveness of the proposed method was verified by comparing it with the responses from the classical methods of mode superposition with the general eigenvalue problems, and mode superposition with modal approximation. The proposed method was shown to be effective in determining the forced response represented by the asymmetric finite element equations of motion of a spinning flexible disk-spindle system supported by FDBs.

Seismic Analysis of an Axial Blower Using a Commercial FEM Code (상용 유한요소해석 프로그램을 이용한 축류송풍기의 내진해석)

  • 정진태;임형빈;김강성;허진욱
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.12 no.3
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    • pp.181-186
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    • 2002
  • A seismic analysis is one of crucial design procedures of an axial blower used in nuclear power Plants. The blower should be operated even in ar emergency such as an earthquake. The blower should be designed in order to stand against an earthquake. For the seismic analysis, Ive perform the modal analysis and then evaluate the required response spectrum (PRS) from the given floor response spectrum (FRS). A finite element model of the blower is established by using a commercial FEM code of ANSYS. After the finite element modeling. the natural frequencies. the mode shapes and the participation factors are obtained from the modal analysis. The PRS is acquired by a numerical approach on the basis of the principle of mode superposition. We verify the structura safety of the axial blower and confirm the validity of the present seismic analysis results.

Indirect displacement monitoring of high-speed railway box girders consider bending and torsion coupling effects

  • Wang, Xin;Li, Zhonglong;Zhuo, Yi;Di, Hao;Wei, Jianfeng;Li, Yuchen;Li, Shunlong
    • Smart Structures and Systems
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    • v.28 no.6
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    • pp.827-838
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    • 2021
  • The dynamic displacement is considered to be an important indicator of structural safety, and becomes an indispensable part of Structural Health Monitoring (SHM) system for high-speed railway bridges. This paper proposes an indirect strain based dynamic displacement reconstruction methodology for high-speed railway box girders. For the typical box girders under eccentric train load, the plane section assumption and elementary beam theory is no longer applicable due to the bend-torsion coupling effects. The monitored strain was decoupled into bend and torsion induced strain, pre-trained multi-output support vector regression (M-SVR) model was employed for such decoupling process considering the sensor layout cost and reconstruction accuracy. The decoupled strained based displacement could be reconstructed respectively using box girder plate element analysis and mode superposition principle. For the transformation modal matrix has a significant impact on the reconstructed displacement accuracy, the modal order would be optimized using particle swarm algorithm (PSO), aiming to minimize the ill conditioned degree of transformation modal matrix and the displacement reconstruction error. Numerical simulation and dynamic load testing results show that the reconstructed displacement was in good agreement with the simulated or measured results, which verifies the validity and accuracy of the algorithm proposed in this paper.

Estimation of floor response spectra induced by artificial and real earthquake ground motions

  • Pu, Wuchuan;Xu, Xi
    • Structural Engineering and Mechanics
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    • v.71 no.4
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    • pp.377-390
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    • 2019
  • A method for estimating the floor response spectra (FRS) of elastic structures under earthquake excitations is proposed. The method is established based on a previously proposed direct estimation method for single degree of freedom systems, which generally overestimates the FRS of a structure, particularly in the resonance period range. A modification factor is introduced to modify the original method; the modification factor is expressed as a function of the period ratio and is determined through regression analysis on time history analysis results. Both real and artificial ground motions are considered in the analysis, and it is found that the modification factors obtained from the real and artificial ground motions are significantly different. This suggests that the effect of ground motion should be considered in the estimation of FRS. The modified FRS estimation method is further applied to a 10-story building structure, and it is verified that the proposed method can lead to a good estimation of FRS of multi-story buildings.

Parametric Study on Earthquake Responses of Soil-structure Interaction System by Substructure Method. (부분구조법에 의한 지반-구조물 상호작용 시스템의 지진응답 매재변수 해석)

  • 조양희
    • Proceedings of the Earthquake Engineering Society of Korea Conference
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    • 1997.10a
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    • pp.117-125
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    • 1997
  • ABSTRACT This paper presents results of parametric studies of the seismic responses of a reactor containment structure on layered base soil. Among the numerous parameters, this study concentrates on the effects of embedment of structure to the base soil, thickness of the soil layers, stiffness of the base soil, and the definition point of the input motion. For the analysis, a substructure method using frequency independent impedances is adopted. The method is based on the mode superposition method in time domain using the composite modal damping values of the SSI system computed from the ratio of dissipated energy to the strain energy for each mode. From the study results, the sensitives of each parameter on the earthquake responses have been suggested for the practical application of the substructure method of SSI analysis.

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Seismic Response Analysis of Steam Turbine-Generator Rotor System(1st Report, In case of rotor-bearing system only) (증기터빈$\cdot$발전기축계의 지진응답해석(제 1 보, 로터$\cdot$베어링시스템만을 고려한 경우))

  • 양보석;김용한
    • Journal of KSNVE
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    • v.9 no.3
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    • pp.554-564
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    • 1999
  • This paper presents the analytical method to evaluate the seismic responses on steam turbine-generator rotor system. Deterministic analytical methods, such as response spectrum approach, modal superposition method and direct integration method, are used to calculate the seismic response. The computer software is also developed based on the methods then can be applied to estimate the seismic safety of turbine-generator rotor system for power plants. Numerical example of a steam turbine-generator rotor system of 1007MW nuclear power plant is presented. The aseismatic performance are checked by comparing maximum seismic deflection at bearing positions with bearing clearance.

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

  • 조상원;조지성;이인원
    • Journal of the Earthquake Engineering Society of Korea
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    • v.4 no.1
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    • pp.89-98
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    • 2000
  • 본 연구에서는 비비례 감쇠시스템을 효율적으로 해석할 수 있도록 모드 가속도법(mode acceleration method)과 모드 절삭 보강법(modal truncation augmentation method)을 확장하고 그 사용성을 검증하였다,. 비례 감쇠시스템의 동응답해서에 널리 사용되는 모드 가속도법과 모드 절삭보강법은 누락된 고차모드의 영향을 보정하여 모드 중첩법의 결과를 개선하는 방법이다. 기존의 방법들로 비비례 감쇠시스템을 해석하는 경우 비비례 감쇠특성을 무시하지 않으며 정확하고 효율적으로 해석할 수 있도록 모드 가속도법과 모드 절삭보강법을 확장하였다. 비례 감쇠시스템에서는 모드 가속도법보다 모드 절삭보강법이 더 효율적인 반면에 비비례 감쇠시스템에서는 대부분의 경우에 있어서 확장된 두 방법의 효율성이 동일하다. 그러나 수치적 안정성은 확장된 모드 가속도법이 모드절삭 보강법보다 우수하다. 이와 같은 확장된 모드 가속도법과 모드 절삭보강법의 사용성 검?을 위해서 이론적 방법과 수치예제를 수행하였다.

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