• Title/Summary/Keyword: Mode shapes

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A Study on Failure Modes of Type4 Composite Pressure Cylinders according to Shapes of Domes (Type4 복합재 용기의 돔 형상에 따른 파열형태에 관한 연구)

  • Cho, Sungmin;Kim, Kwang Seok;Cho, Min-sik;Lee, Sun-kyu;Lee, Seung-kuk;Lyu, Sung-Ki
    • Journal of the Korean Society of Manufacturing Process Engineers
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    • v.16 no.5
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    • pp.13-18
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    • 2017
  • In this work the augmented safety of Type 4 composite vessel in accordance with uniform-stress design has been demonstrated through a series of burst tests and structural analyses. For this end, three sample vessels were used: (1) designed as guided by the isotensoid dome theory (called iso-dome cylinder); (2) with dome longer compared to uniform-stress design (called prolate cylinder); and (3) with dome wider than uniform-stress design (called oblate cylinder). Structural analyses have been performed using ABAQUS finite element code based on the periodic symmetry to circumferential direction. As a result, the maximum stresses are induced around the bodies of all three cylinders. However, the analyses, with the assumption of possible defect demonstrate that the maximum stresses are induced around the dome knuckles for the prolate and the oblate cylinders. The results of the burst tests for the three cylinders show that the burst initiates from the cylinder body of the iso-dome cylinder and from the dome knuckles of the prolate and the oblate cylinders. Finally, it is recommended that, to comply with DOT CFFC 2007, the dome shape should be designed and fabricated as guided by the isotensoid dome theory.

Vibration Analysis of Symmetrically Laminated Composite Rectangular Plates (대칭 복합적층 직사각형 판의 진동해석)

  • T.Y. Chung;J.H. Chung
    • Journal of the Society of Naval Architects of Korea
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    • v.29 no.3
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    • pp.140-148
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    • 1992
  • The free vibration problem of symmetrically laminated composite rectangular plates is formulated based on anisotropic thick plate theory including the effects of shear deformation and rotary inertia. Considering the difficulty of obtaining closed-form solutions, Rayleigh-Ritz analysis using polynomials having the property of Timoshenko beam functions as trial functions is adopted. The boundary conditions elastically restrained against rotation are accomodated as well as classical boundary conditions. From the results of numerical studies, the validity of the present method is verified. And it is also found that the adoption of thick plate theory for the vibration analysis of laminated composite plates is essential because of the relatively large shear deformation effect, and that the convergence of the Rayleigh quotient to the stationary value is less rapid in anisotropic composite plates than that in the orthotropic ones due to more complicated mode shapes of the former.

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Vibrations of Complete Paraboloidal Shells with Variable Thickness form a Three-Dimensional Theory

  • Chang, Kyong-Ho;Shim, Hyun-Ju;Kang, Jae-Hoon
    • Journal of Korean Association for Spatial Structures
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    • v.4 no.4 s.14
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    • pp.113-128
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    • 2004
  • A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies and mode shapes of solid paraboloidal and complete (that is, without a top opening) paraboloidal shells of revolution with variable wall thickness. Unlike conventional shell theories, which are mathematically two-dimensional (2-D), the present method is based upon the 3-D dynamic equations of elasticity. The ends of the shell may be free or may be subjected to any degree of constraint. Displacement components $u_r,\;u_{\theta},\;and\;u_z$ in the radial, circumferential, and axial directions, respectively, are taken to be sinusoidal in time, periodic in ${\theta}$, and algebraic polynomials in the r and z directions. Potential (strain) and kinetic energies of the paraboloidal shells of revolution are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four digit exactitude is demonstrated for the first five frequencies of the complete, shallow and deep paraboloidal shells of revolution with variable thickness. Numerical results are presented for a variety of paraboloidal shells having uniform or variable thickness, and being either shallow or deep. Frequencies for five solid paraboloids of different depth are also given. Comparisons are made between the frequencies from the present 3-D Ritz method and a 2-D thin shell theory.

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Operational modal analysis of a long-span suspension bridge under different earthquake events

  • Ni, Yi-Qing;Zhang, Feng-Liang;Xia, Yun-Xia;Au, Siu-Kui
    • Earthquakes and Structures
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    • v.8 no.4
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    • pp.859-887
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    • 2015
  • Structural health monitoring (SHM) has gained in popularity in recent years since it can assess the performance and condition of instrumented structures in real time and provide valuable information to the asset's manager and owner. Operational modal analysis plays an important role in SHM and it involves the determination of natural frequencies, damping ratios and mode shapes of a constructed structure based on measured dynamic data. This paper presents the operational modal analysis and seismic response characterization of the Tsing Ma Suspension Bridge of 2,160 m long subjected to different earthquake events. Three kinds of events, i.e., short-distance, middle-distance and long-distance earthquakes are taken into account. A fast Bayesian modal identification method is used to carry out the operational modal analysis. The modal properties of the bridge are identified and compared by use of the field monitoring data acquired before and after the earthquake for each type of the events. Research emphasis is given on identifying the predominant modes of the seismic responses in the deck during short-distance, middle-distance and long-distance earthquakes, respectively, and characterizing the response pattern of various structural portions (deck, towers, main cables, etc.) under different types of earthquakes. Since the bridge is over 2,000 m long, the seismic wave would arrive at the tower/anchorage basements of the two side spans at different time instants. The behaviors of structural dynamic responses on the Tsing Yi side span and on the Ma Wan side span under each type of the earthquake events are compared. The results obtained from this study would be beneficial to the seismic design of future long-span bridges to be built around Hong Kong (e.g., the Hong Kong-Zhuhai-Macau Bridge).

Free vibration of axially loaded Reddy-Bickford beam on elastic soil using the differential transform method

  • Yesilce, Yusuf;Catal, Seval
    • Structural Engineering and Mechanics
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    • v.31 no.4
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    • pp.453-475
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    • 2009
  • The literature regarding the free vibration analysis of Bernoulli-Euler and Timoshenko beams on elastic soil is plenty, but the free vibration analysis of Reddy-Bickford beams on elastic soil with/without axial force effect using the Differential Transform Method (DTM) has not been investigated by any of the studies in open literature so far. In this study, the free vibration analysis of axially loaded Reddy-Bickford beam on elastic soil is carried out by using DTM. The model has six degrees of freedom at the two ends, one transverse displacement and two rotations, and the end forces are a shear force and two end moments in this study. The governing differential equations of motion of the rectangular beam in free vibration are derived using Hamilton's principle and considering rotatory inertia. Parameters for the relative stiffness, stiffness ratio and nondimensionalized multiplication factor for the axial compressive force are incorporated into the equations of motion in order to investigate their effects on the natural frequencies. At first, the terms are found directly from the analytical solutions of the differential equations that describe the deformations of the cross-section according to the high-order theory. After the analytical solution, an efficient and easy mathematical technique called DTM is used to solve the governing differential equations of the motion. The calculated natural frequencies of one end fixed and the other end simply supported Reddy-Bickford beam on elastic soil using DTM are tabulated in several tables and figures and are compared with the results of the analytical solution where a very good agreement is observed and the mode shapes are presented in graphs.

Damage detection for beam structures using an angle-between-string-and-horizon flexibility matrix

  • Yan, Guirong;Duan, Zhongdong;Ou, Jinping
    • Structural Engineering and Mechanics
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    • v.36 no.5
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    • pp.643-667
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    • 2010
  • The classical flexibility difference method detects damage by observing the difference of conventional deflection flexibility matrices between pre- and post-damaged states of a structure. This method is not able to identify multiple damage scenarios, and its criteria to identify damage depend upon the boundary conditions of structures. The key point behind the inability and dependence is revealed in this study. A more feasible flexibility for damage detection, the Angle-between-String-and-Horizon (ASH) flexibility, is proposed. The physical meaning of the new flexibility is given, and synthesis of the new flexibility matrix by modal frequencies and translational mode shapes is formulated. The damage indicators are extracted from the difference of ASH flexibility matrices between the pre- and post-damaged structures. One feature of the ASH flexibility is that the components in the ASH flexibility matrix are associated with elements instead of Nodes or DOFs. Therefore, the damage indicators based on the ASH flexibility are mapped to structural elements directly, and thus they can pinpoint the damaged elements, which is appealing to damage detection for complex structures. In addition, the change in the ASH flexibility caused by damage is not affected by boundary conditions, which simplifies the criteria to identify damage. Moreover, the proposed method can determine relatively the damage severity. Because the proposed damage indicator of an element mainly reflects the deflection change within the element itself, which significantly reduces the influence of the damage in one element on the damage indicators of other damaged elements, the proposed method can identify multiple damage locations. The viability of the proposed approach has been demonstrated by numerical examples and experimental tests on a cantilever beam and a simply supported beam.

Evaluation of Axial Buckling Effect in On-Line Axial Power Shape Synthesis (실시간 노심출력분포 합성에서의 축방향 경계조건 영향평가)

  • In, Wang-Kee;Kim, Joon-Sung;Yoon, Tae-Young;Auh, Geun-Sun;Kim, Hee-Cheol
    • Nuclear Engineering and Technology
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    • v.25 no.1
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    • pp.148-153
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    • 1993
  • A fifth-order Fourier series technique is applied in Core Operating Limit Supervisory System (COLSS) to construct the on-line core average axial power shape from in-core detector signals because of its simplicity and fast computation. Such a synthesizing accuracy depends on number of Fourier series modes and axial boundary conditions. COLSS currently uses the five-mode Fourier series technique which utilizes the five axially located fixed in-core detector signals and a constant axial boundary condition. Therefore, the constant axial boundary condition should be appropriately chosen based on the evaluation of its effect on the accuracy of the on-line calculations. The four cases of axial buckling (0.75, 0.8, 0.9 and 1.0) were examined for Yonggwang Nuclear Units 3&4 as the axial boundary conditions in this paper. The core average axial power shapes and the operating margins were compared for each case to determine the optimal constant axial buckling. The axial buckling of 0.9 was found to be the optimal value.

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Fabrication Technology of the Focusing Grating Coupler using Single-step Electron Beam Lithography

  • Kim, Tae-Youb;Kim, Yark-Yeon;Han, Gee-Pyeong;Paek, Mun-Cheol;Kim, Hae-Sung;Lim, Byeong-Ok;Kim, Sung-Chan;Shin, Dong-Hoon;Rhee, Jin-Koo
    • Transactions on Electrical and Electronic Materials
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    • v.3 no.1
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    • pp.30-37
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    • 2002
  • A focusing grating coupler (FGC) was not fabricated by the 'Continuous Path Control'writing strategy but by an electron-beam lithography system of more general exposure mode, which matches not only the address grid with the grating period but also an integer multiple of the address grid resolution (5 nm). To more simplify the fabrication, we are able to reduce a process step without large decrease of pattern quality by excluding a conducting material or layer such as metal (Al, Cr, Au), which are deposited on top or bottom of an e-beam resist to prevent charge build-up during e-beam exposure. A grating pitch period and an aperture feature size of the FGC designed and fabricated by e-beam lithography and reactive ion etching were ranged over 384.3 nm to 448.2 nm, and 0.5 $\times$ 0.5 mm$^2$area, respectively. This fabrication method presented will reduce processing time and improve the grating quality by means of a consideration of the address grid resolution, grating direction, pitch size and shapes when exposing. Here our investigations concentrate on the design and efficient fabrication results of the FGC for coupling from slab waveguide to a spot in free space.

Design of Singly Fed Microstrip Antennas Having Circular Polarization (단일 급전 원형 편파 마이크로스트립 안테나 설계)

  • 오세창;전중창;박위상
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.10 no.7
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    • pp.998-1009
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    • 1999
  • In this paper, a microstrip aperture-patch antenna and a microstrip ring antenna, which have single microstrip line feeding systems for the circular polarization, are designed, and experimental results are presented at X-band. The microstrip aperture-patch antenna is characterized by its wide operating frequency range, and the microstrip ring antenna is suitable for a basic radiator in the large array antenna due to its small size. Several design parameters for these antennas are considered and analyzed to improve antenna characteristics such as VSWR bandwidth and axial ratio. Initially, the sizes of the aperture and ring radiator are determined on a basis of the cavity model, then shapes of the patch within the aperture and the inner stub of the ring are optimized using Ensemble software. Measurement results show that the aperture-patch antenna has 25% of VSWR bandwidth and 1.2dB of axial ratio at the boresight, and the ring antenna has 6.7% of VSWR bandwidth and 1.6dB of axial ratio at the boresight.

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Analysis of Ride Comfort for an Automobile with flexible Vehicle Body (차체의 유연성을 고려한 차량 승차감 해석)

  • Kim Junghoon;Choi Kwangsung;Park Sungyong;Lee Jangmoo;Kang Sangwook;Kang Juseok
    • Transactions of the Korean Society of Automotive Engineers
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    • v.13 no.4
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    • pp.121-128
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    • 2005
  • In most researches on the ride comfort analysis of passenger vehicles, the flexibility of the vehicle body has been not considered as an important factor, because the resonance frequencies of the vehicle body related to pitching, yawing and rolling motions are below 10Hz while the resonance frequencies of the vehicle body related to the flexibility are above 20Hz approximately. Nevertheless, the paper shows that the consideration of the local flexibility (or local stiffness) of the 4 corners on which shock absorbers are mounted influences the ride comfort. A simple beam model is devised to qualitatively examine the effect of the change of the local stiffness of the vehicle body on the ride comfort. Based on the results obtained from the analysis of the one-dimensional model, multi-body dynamic analysis considering the flexibility of the vehicle body is performed using ADAMS and MSC/NASTRAN. Natural frequencies and mode shapes computed by MSC/NASTRAN are used as input data for multi-body dynamic analysis in ADAMS. Through simulations using ADAMS, it has been found that the ride comfort can be improved by changing the local stiffness of the vehicle body and that the simulation results agree with experiment results.