• Title/Summary/Keyword: eigenvalue analysis

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Free Vibration of a Rectangular Plate Partially in Contact with a Liquid at Both Sides (양면에서 부분적으로 유체와 접하는 사각평판의 고유진동)

  • Jeong, Kyeong-Hoon;Lee, Gyu-Mahn;Kim, Tae-Wan;Park, Keun-Bae
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.18 no.1
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    • pp.123-130
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    • 2008
  • An analytical method for the free vibration of a flexible rectangular plate in contact with water is developed by the Rayleigh-Ritz method. The plate clamped along the edges is partially contacted with water at both sides. It is assumed that the contained water is incompressible and inviscid. The wet mode shape of the plate is assumed as a combination of the dry mode shapes of a clamped beam. The liquid motion is described by using the liquid displacement potential and determined by using the compatibility conditions along the liquid interface with the plate. Minimizing the Rayleigh quotient based on the energy conservation gives an eigenvalue problem. It is found that the theoretical results can predict excellently the fluid-coupled natural frequencies comparing with the finite element analysis result.

A Study on the Dynamic Response Analysis of Shell Structure with Impulsive Load by Reanalysis Technique (재해석 기법에 의한 충격 하중을 받는 쉘 구조물의 동적 응답 해석에 관한 연구)

  • 배동명
    • Journal of the Korean Society of Fisheries and Ocean Technology
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    • v.29 no.2
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    • pp.132-151
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    • 1993
  • The proposed method in this paper. termed the substructural reanalysis technique, utilizes the computational merits of the component mode synthesis technique and of reanalysis technique for the design sensitivities of the dynamic characteristics of substructurally combined structure. It is shown that the dynamic characteristics of the entire structure can be obtained by synthesizing the substructural eigensolution and the characteristics of the eigensolution for the design variables of the modifiable substructure. In this paper , the characteristics of the eigenvalue problems obtained by this proposed method are compared to exact eigensolution in terms of accuracy and computational efficiency. and the advantage of this proposed method as compared to the direct application of the whole structure and experimental results is demonstrated through examples of numerical calculation for the dynamic characteristics (natural frequencies and mode shapes) of a flexible vibration of thin cylinderical shell with branch shell under 2-end fixed positions, boundary condition. Thin cylinderical shell of overall length 1280mm, external diameter 360mm, thickness 3mm with branch shell is made of mild steel. The load condition for dynamic response in this paper is impulsive load of which magnitude is 10kgf, which have short duration of 0.1 sec. and time interval applied to calculate. $\Delta$T is 1.0$\times$10 super(-4) seconds.

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Sensor placement selection of SHM using tolerance domain and second order eigenvalue sensitivity

  • He, L.;Zhang, C.W.;Ou, J.P.
    • Smart Structures and Systems
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    • v.2 no.2
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    • pp.189-208
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    • 2006
  • Monitoring large-scale civil engineering structures such as offshore platforms and high-large buildings requires a large number of sensors of different types. Innovative sensor data information technologies are very extremely important for data transmission, storage and retrieval of large volume sensor data generated from large sensor networks. How to obtain the optimal sensor set and placement is more and more concerned by researchers in vibration-based SHM. In this paper, a method of determining the sensor location which aims to extract the dynamic parameter effectively is presented. The method selects the number and place of sensor being installed on or in structure by through the tolerance domain statistical inference algorithm combined with second order sensitivity technology. The method proposal first finds and determines the sub-set sensors from the theoretic measure point derived from analytical model by the statistical tolerance domain procedure under the principle of modal effective independence. The second step is to judge whether the sorted out measured point set has sensitive to the dynamic change of structure by utilizing second order characteristic value sensitivity analysis. A 76-high-building benchmark mode and an offshore platform structure sensor optimal selection are demonstrated and result shows that the method is available and feasible.

A model experiment of damage detection for offshore jacket platforms based on partial measurement

  • Shi, Xiang;Li, Hua-Jun;Yang, Yong-Chun;Gong, Chen
    • Structural Engineering and Mechanics
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    • v.29 no.3
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    • pp.311-325
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    • 2008
  • Noting that damage occurrence of offshore jacket platforms is concentrated in two structural regions that are in the vicinity of still water surface and close to the seabed, a damage detection method by using only partial measurement of vibration in a suspect region was presented in this paper, which can not only locate damaged members but also evaluate damage severities. Then employing an experiment platform model under white-noise ground excitation by shaking table and using modal parameters of the first three modes identified by a scalar-type ARMA method on undamaged and damaged structures, the feasibility of the damage detection method was discussed. Modal parameters from eigenvalue analysis on the structural FEM model were also used to help the discussions. It is demonstrated that the damage detection algorithm is feasible on damage location and severity evaluation for broken slanted braces and it is robust against the errors of baseline FEM model to real structure when the principal errors is formed by difference of modal frequencies. It is also found that Z-value changes of modal shapes also play a role in the precise detection of damage.

Development of High-Definition 3D-PTV and its Application to High-Precision Measurements of a Sphere Wake (고해상 3차원 입자영상유속계 개발과 구 유동장 정밀해석 적용연구)

  • Hwang Tae-Gyu;Doh Deog-Hee
    • Korean Journal of Air-Conditioning and Refrigeration Engineering
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    • v.17 no.12
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    • pp.1161-1168
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    • 2005
  • A Multi-Sectional 3D-PTV algorithm was developed to reduce the calculation time of the conventional GA-3D-PTV. The hardware system of the constructed 3D-PTV system consists of two high-speed cameras ($1,024\times1,018$ pixels, 60 fps), a metal halogen lamp (400W) and a host computer. The sphere(D=30mm) is suspended in a circulating water channel $(300mm\times300mm\times1,200m)$ and Reynolds number is 1,130. About 5,000 instantaneous three-dimensional velocity vectors have been obtained by the constructed 3D-PTV system. Turbulent properties such as turbulent intensity, Reynolds stress and turbulent kinetic energy were obtained. An eigenvalue analysis was carried out using the obtained instantaneous 3D velocity vectors to get the topological relations of the asymptotically stable critical point. Two structured shells, inner shell and outer shell, were found in the sphere wake and their motions were clarified by the measured data.

Time delay estimation by iterative Wiener filter based recursive total least squares algorithm (반복형 위너 필터 방법에 기반한 재귀적 완전 최소 제곱 방법을 사용한 시간 지연 추정 알고리즘)

  • Lim, Jun-Seok
    • The Journal of the Acoustical Society of Korea
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    • v.40 no.5
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    • pp.452-459
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    • 2021
  • Estimating the mutual time delay between two acoustic sensors is used in various fields such as tracking and estimating the location of a target in room acoustics and sonar. In the time delay estimation methods, there are a non-parametric method, such as Generalized Cross Correlation (GCC), and a parametric method based on system identification. In this paper, we propose a time delay estimation method based on the parametric method. In particular, we propose a method that considers the noise in each receiving acoustic sensor. Simulation confirms that the proposed algorithm is superior to the existing generalized cross-correlation and adaptive eigenvalue analysis methods in white noise and reverberation environments.

Energy equivalent model in analysis of postbuckling of imperfect carbon nanotubes resting on nonlinear elastic foundation

  • Mohamed, Nazira;Eltaher, Mohamed A.;Mohamed, Salwa A.;Seddek, Laila F.
    • Structural Engineering and Mechanics
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    • v.70 no.6
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    • pp.737-750
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    • 2019
  • This paper investigates the static and dynamic behaviors of imperfect single walled carbon nanotube (SWCNT) modeled as a beam structure by using energy-equivalent model (EEM), for the first time. Based on EEM Young's modulus and Poisson's ratio for zigzag (n, 0), and armchair (n, n) carbon nanotubes (CNTs) are presented as functions of orientation and force constants. Nonlinear Euler-Bernoulli assumptions are proposed considering mid-plane stretching to exhibit a large deformation and a small strain. To simulate the interaction of CNTs with the surrounding elastic medium, nonlinear elastic foundation with cubic nonlinearity and shearing layer are employed. The equation governed the motion of curved CNTs is a nonlinear integropartial-differential equation. It is derived in terms of only the lateral displacement. The nonlinear integro-differential equation that governs the buckling of CNT is numerically solved using the differential integral quadrature method (DIQM) and Newton's method. The linear vibration problem around the static configurations is discretized using DIQM and then is solved as a linear eigenvalue problem. Numerical results are depicted to illustrate the influence of chirality angle and imperfection amplitude on static response, buckling load and dynamic behaviors of armchair and zigzag CNTs. Both, clamped-clamped (C-C) and simply supported (SS-SS) boundary conditions are examined. This model is helpful especially in mechanical design of NEMS manufactured from CNTs.

Improved nodal equivalence with leakage-corrected cross sections and discontinuity factors for PWR depletion analysis

  • Lee, Kyunghoon;Kim, Woosong;Kim, Yonghee
    • Nuclear Engineering and Technology
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    • v.51 no.5
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    • pp.1195-1208
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    • 2019
  • This paper introduces a new two-step procedure for PWR depletion analyses. This procedure adopts the albedo-corrected parameterized equivalence constants (APEC) method to correct the lattice-based raw cross sections (XSs) and discontinuity factors (DFs) by accounting for neutron leakage. The intrinsic limitations of the conventional two-step methods are discussed by analyzing a 2-dimensional SMR with the commercial DeCART2D/MASTER code system. For a full-scope development of the APEC correction, the MASTER nodal code was modified so that the group constants can be corrected in the middle of a microscopic core depletion. The basic APEC methodology is described and color-set problems are defined to determine the APEC functions for burnup-dependent XS and DF corrections. Then the new two-step method was applied to depletion analyses of the SMR without thermal feedback, and its validity was evaluated in terms of being able to predict accurately the reactor eigenvalue and nodal power profile. In addition, four variants of the original SMR core were also analyzed for a further evaluation of the APEC-assisted depletion. In this work, several combinations of the burnup-dependent and -independent XS and DF corrections were also considered. The results show that the APEC method could enhance the nodal equivalence significantly with inexpensive additional costs.

Why Are Cool Structures in the Universe Usually Filamentary?

  • Song, Inhyeok;Choe, Gwang Son;Yi, Sibaek;Jun, Hongdal
    • The Bulletin of The Korean Astronomical Society
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    • v.44 no.1
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    • pp.48.4-48.4
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    • 2019
  • Small-scale shear flows are ubiquitous in the universe, and astrophysical plasmas are often magnetized. We study the thermal condensation instability in magnetized plasmas with shear flows in relation to filamentary structure formation in cool structures in the universe, representatively solar prominences and supernova remnants. A linear stability analysis is extensively performed in the framework of magnetohydrodynamics (MHD) with radiative cooling, plasma heating and anisotropic thermal conduction to find the eigenfrequencies and eigenfunctions for the unstable modes. For a shear velocity less than the Alfven velocity of the background plasma, the eigenvalue with the maximum growth rate is found to correspond to a thermal condensation mode, for which the density and temperature variations are anti-phased (of opposite signs). Only when the shear velocity in the k-direction is near zero, the eigenfunctions for the condensation mode are of smooth sinusoidal forms. Otherwise each eigenfunction for density and temperature is singular and of a discrete form like delta functions. Our results indicate that any non-uniform velocity field with a magnitude larger than a millionth of the Alfven velocity can generate discrete eigenfunctions of the condensation mode. We therefore suggest that condensation at discrete layers or threads should be quite a natural and universal process whenever a thermal instability arises in magnetized plasmas.

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Analysis of Free Vibration Characteristics of Tapered Friction Piles in Non-homogeneous Soil Layers (불균질 지반에 설치된 테이퍼 마찰말뚝의 자유진동 특성 분석)

  • Lee, Joon Kyu;Ko, Junyoung;Lee, Kwangwoo;Kim, Dongwook
    • Journal of the Korean Geosynthetics Society
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    • v.18 no.3
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    • pp.69-77
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    • 2019
  • This paper presents a new analytical model for estimating the free vibration of tapered friction piles. The governing differential equation for the free vibration of statically axially-loaded piles embedded in non-homogeneous soil is derived. The equation is numerically integrated by the Runge-Kutta method, and then the eigenvalue of natural frequency is determined by the Regula-Falsi scheme. For a cylindrical non-tapered pile, the computed natural frequencies compare well with the available data from literature. Numerical examples are presented to investigate the effects of the tapering, the skin friction resistance, the end condition of the pile, the vertical compressive loading, and the soil non-homogeneity on the natural frequency and mode shape of tapered friction piles.