• Title, Summary, Keyword: mode superposition method

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Dynamic analysis for complex structures using the improved component mode method (개선된 콤포넌트 모드법을 이용한 거대구조물의 동적해석)

  • 심재수;박명균
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • pp.37-44
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    • 1993
  • There are a lot of linear dynamic analysis methods for complex structures. Each method has advantages and shortcomings. Method of dynamic analysis for complex structure is selected considering characteristics of dynamic loading, computer facility available number of degree of freedem and accuracy of results. It is a main point of view to get economical results rather then accurate ones for analysis of general complex structures, Mode superposition method and direct integration method are generally used. However, the characteristics of load is not considered in mode superpositon method, the personal computer cannot be used in direct integration methods. To over-come these shortcomings, the component mode method incorporating Ritz algorithm updated is proposed to solve economically dynamic behavior of the structures. The purpose of study is a formulation of algorithm, and computer programing suitable for dynamic analysis of the complex structure in personal computer environment.

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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.

A Study on Equivalent Modal Damping Values of Soil-Structure Coupling Models (지반-구조물 연계모델의 등가감쇠값에 관한 연구)

  • Park, Hyung Ghee
    • Journal of The Korean Society of Civil Engineers
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    • v.7 no.3
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    • pp.241-248
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    • 1987
  • The theoretical backgrounds of the several methods were surveyed and reviewed to fin out the adequate one to determine equivalent modal damping values in solving the dynamic problem of soil-structure interaction by mode superposition method. Furthermore the rigorous damping matrix of equation of motion was obtained through component mode synthesis technique and used in direct integration of the equation. The analytical results by direct integration method were compared with those of mode superposition approach using the various sets of equivalent modal damping values calculated by the methods to be reviewed. Two types of superstructures and four kinds of subsurface conditions were considered and combined to make soil-structure coupled models. It was realized that dissipating energy method gives the equivalent modal damping values which lead the most similar results to direct integration ones. In case of fixed base, the responses of all methods except stiffness weighted approach are almost equal to those of direct integration method.

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A Numerical Analysis on Acoustic Radiation Efficiency of One Side-Wetted Rectangular Mindlin Plate with Simply Supported Boundaries (Mindlin 판 이론을 적용한 단순지지 단면 접수평판의 음향방사효율 수치해석)

  • Lee, Jong-Ho;Cho, Dae-Seung
    • Journal of the Society of Naval Architects of Korea
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    • v.55 no.4
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    • pp.281-288
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    • 2018
  • Acoustic radiation efficiency is a crucial factor to estimate Underwater Radiated Noise (URN) of ships accurately. This paper describes a numerical method to analyse acoustic radiation efficiency of one side-wetted rectangular Mindlin plate with simply supported boundaries excited by a harmonic point force. Transverse displacements of plate and acoustic radiation pressures are evaluated by the mode superposition method. The acoustic radiation efficiencies analyzed by both Mindlin and thin plate theories show little differences at monopole and corner modes of low frequency regions but relatively large differences at edge and critical modes of high frequency regions. Especially, the critical frequency with the highest acoustic radiation efficiency evaluated by the Mindlin plate theory is higher than that of thin plate theory. In addition, the acoustic loading effect of fluid also increases bending wave-number of plate and its critical frequency. Finally, the acoustic radiation characteristics of plates with different aspect ratios and thicknesses through numerical analyses are investigated and discussed.

Ritz Mode Superposition Method in Frequency Domain (주파수 영역에서의 Ritz 모드 중첩법)

  • 주관정
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • pp.33-37
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    • 1989
  • According to the Rayleigh-Ritz approximation method, a solution can be represented as a finite series consisting of space-dependent functions, which satisfy all the geometric boundary conditions of the problem and appropriate smoothness requirement in the interior of the domain. In this paper, an efficient formulation for solving structural dynamics systems in frequency domain is presented. A general procedure called Ritz modes (or vectors) generation algorithm is used to generate the admissible functions, i.e. Ritz modes, Then, the use of direct superposition of the Ritz modes is utilized to reduce the size of the problem in spatial dimension via geometric coordinates projection. For the reduced system, the frequency domain approach is applied. Finally, a numerical example is presented to illustrate the effectiveness of the proposed method.

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Extension of a semi-analytical approach to determine natural frequencies and mode shapes of a multi-span orthotropic bridge deck

  • Rezaiguia, A.;Fisli, Y.;Ellagoune, S.;Laefer, D.F.;Ouelaa, N.
    • Structural Engineering and Mechanics
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    • v.43 no.1
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    • pp.71-87
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    • 2012
  • This paper extends a single equation, semi-analytical approach for three-span bridges to multi-span ones for the rapid and precise determination of natural frequencies and natural mode shapes of an orthotropic, multi-span plate. This method can be used to study the dynamic interaction between bridges and vehicles. It is based on the modal superposition method taking into account intermodal coupling to determine natural frequencies and mode shapes of a bridge deck. In this paper, a four- and a five-span orthotropic roadway bridge deck are compared in the first 10 modes with a finite element method analysis using ANSYS software. This simplified implementation matches numerical modeling within 2% in all cases. This paper verifies that applicability of a single formula approach as a simpler alternative to finite element modeling.

A Study on Bayesian Approach of Software Stochastic Reliability Superposition Model using General Order Statistics (일반 순서 통계량을 이용한 소프트웨어 신뢰확률 중첩모형에 관한 베이지안 접근에 관한 연구)

  • Lee, Byeong-Su;Kim, Hui-Cheol;Baek, Su-Gi;Jeong, Gwan-Hui;Yun, Ju-Yong
    • The Transactions of the Korea Information Processing Society
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    • v.6 no.8
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    • pp.2060-2071
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    • 1999
  • The complicate software failure system is defined to the superposition of the points of failure from several component point process. Because the likelihood function is difficulty in computing, we consider Gibbs sampler using iteration sampling based method. For each observed failure epoch, we applied to latent variables that indicates with component of the superposition mode. For model selection, we explored the posterior Bayesian criterion and the sum of relative errors for the comparison simple pattern with superposition model. A numerical example with NHPP simulated data set applies the thinning method proposed by Lewis and Shedler[25] is given, we consider Goel-Okumoto model and Weibull model with GOS, inference of parameter is studied. Using the posterior Bayesian criterion and the sum of relative errors, as we would expect, the superposition model is best on model under diffuse priors.

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Resonant Wavelength Characteristics of Arc-Induced Long-Period Fiber Gratings (아크 유도 장주기 광섬유 격자의 공진 파장 특성)

  • Chung, Chul;Lee, Ho-Joon
    • Journal of the Institute of Electronics Engineers of Korea SD
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    • v.39 no.10
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    • pp.48-56
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    • 2002
  • A fabrication method of long--period fiber gratings (LPFGs) that can be easily controlled resonance wavelength and losses is introduced. We used the superposition method that core and cladding diameter are modulated by applying a number of small electric-arc to the normal fiber. We derived an equation of resonance wavelength change according to core diameter variation using the phase matching condition and showed the results are well matched with experiments. The measured resonant wavelengths of arc-induced superposition LPFGs according to grating period are well coincident with that of phase matching condition. The resonance wavelength is measured for the temperature changes and a slight mechanical strength degradation of arc-induced LPFGs is observed by increasing arc times.

Estimation of Equivalent Viscous Damping of Structure with Base Isolation Devices (면진장치를 가지는 구조물의 등가점성감쇠비 산정)

  • 김태호;이동근
    • Proceedings of the Earthquake Engineering Society of Korea Conference
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    • pp.359-366
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    • 2002
  • Direct Integration method(D.I) and Mode Superposition method(M.S) are used widely in dynamic analysis method for structure with isolation devices. D.I is used firstly because it is consider to nonlinearity of isolation device. M.S is applied in elastic region, but it is difficult to apply M.S because coincidence with othogonality condition in the case of adding the damping of isolation device. In this study, the method for calculation of damping ratio of isolated structure is proposed, and proposed method is verified with analysis for example structure.

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Structural Dynamic Analysis by Ritz Vector Method Modified with Lanczos Algorithm (Lanczos 알고리즘을 도입한 Ritz Vector법에 의한 구조물의 동적해석)

  • 심재수;황의승;박주경
    • Computational Structural Engineering
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    • v.8 no.4
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    • pp.181-187
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    • 1995
  • Recent researches in dynamics are focused on finding effective methods to analyze the dynamic behavior of structures by fewer mode shapes their number of dgrees of freedom. Ritz algorithm and mode acceleration method were developed to improved the mode superposition. Ritz algorithm can include distribution of external loads but be apt to lose the orthogonality condition, which is useful properties in the analysis. Also mode acceleration method should consider a large number of mode shapes to get a satisfactory results. Another method, combining previous two method, was developed but too much computational efforts and times were required. The purpose of this study is to develop and evaluate the Ritz algorithm modified with the lanczos algorithm to improve the efficiency and accuracy. As a result of !this study, dynamic analysis using modified Ritz algorithm was proved to be the rational analysis method.

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