• Title/Summary/Keyword: first mode shape

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Dynamic behaviour of multi-stiffened plates

  • Bedair, Osama
    • Structural Engineering and Mechanics
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    • v.31 no.3
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    • pp.277-296
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    • 2009
  • The paper investigates the dynamic behaviour of stiffened panels. The coupled differential equations for eccentric stiffening configuration are first derived. Then a semi-analytical procedure for dynamic analysis of stiffened panels is presented. Unlike finite element or finite strip methods, where the plate is discretized into a set of elements or strips, the plate in this procedure is treated as a single element. The potential energy of the structure is first expressed in terms generalized functions that describe the longitudinal and transverse displacement profiles. The resulting non-linear strain energy functions are then transformed into unconstrained optimization problem in which mathematical programming techniques are employed to determine the magnitude of the lowest natural frequency and the associated mode shape for pre-selected plate/stiffener geometric parameters. The described procedure is verified with other numerical methods for several stiffened panels. Results are then presented showing the variation of the natural frequency with plate/stiffener geometric parameters for various stiffening configurations.

Computational Study on Aeroacoustics of an Elastic Cantilevered Trailing-Edge (탄성 날개 끝단의 공력 소음에 관한 전산해석 연구)

  • Hwang Bon Chang;Moon Young June
    • 한국전산유체공학회:학술대회논문집
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    • 2005.04a
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    • pp.159-168
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    • 2005
  • Noise generated by the blunt trailing edge of lifting surfaces is investigated in this study using fluid structure interaction theory. First, through the eddy modeling, noise generation doe to the flow instability on the rigid trailing edge is surveyed. Then the behavior of elastic cantileverd beam is investigated. Parametric study based on various material properties is employed to analyze the motion of the beam. Moreover, each eigenmode approach of cantilevered beam is used to find when flow induced vibration is resonant. To analyze elastic behavior of cantilever beam efficiently, moving grid generation technique based on non-conservative form of Navier-Stokes equation is used. Equation of the motion associated with the cantilever beam is discretized by the Galerkin procedure with forced vibration. As a consequence, behavior of the elastic cantilevered beam is stable when the first mode natural frequency of the material is relatively higher than that of flow induced pressure fluctuation.

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Estimation of Interstory Drift for Moment Resisting Reinforced Concrete Frames Using Equivalent SDOF System (등가 1자유도계를 이용한 철근콘크리트 골조건물의 층간변위 응답 산정)

  • Kang, Ho-Geun;Jun, Dae-Han
    • Journal of the Earthquake Engineering Society of Korea
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    • v.8 no.5 s.39
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    • pp.25-33
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    • 2004
  • To evaluate the seismic capacity of a multistorey building structures in performance based seismic design, it is needed to convert MDOF model into equivalent SDOF model. This paper presents predictions for interstory drift of multistorey structures using method of converting a MDOF system into an equivalent SDOF model. The principal objective of this investigation is to evaluate appropriateness of converting method through performing nonlinear time history analysis of a multistory building structures and an equivalent SDOF model. Comparing the interstory drift of multistorey structures calculated by time history analysis and those evaluated by an equivalent SDOF model, the adequacy and the validity of converting method is verified. The conclusion of this study is following; A method of converting a MDOF system into an equivalent SDOF model through the nonlinear time history response analysis is valid. Inelastic first mode shapes are expected to be more accurate than elastic first mode shapes in obtaining interstory drift of multistorey structures from equivalent SDOF model.

Estimation of earthquake induced story hysteretic energy of multi-Story buildings

  • Wang, Feng;Zhang, Ning;Huang, Zhiyu
    • Earthquakes and Structures
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    • v.11 no.1
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    • pp.165-178
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    • 2016
  • The goal of energy-based seismic design is to obtain a structural design with a higher energy dissipation capacity than the energy dissipation demands incurred under earthquake motions. Accurate estimation of the story hysteretic energy demand of a multi-story structure is the key to meeting this goal. Based on the assumption of a mode-equivalent single-degree-of-freedom system, the energy equilibrium relationship of a multi-story structure under seismic action is transformed into that of a multi-mode analysis of several single degree-of-freedom systems. A simplified equation for the estimation of the story seismic hysteretic energy demand was then derived according to the story shear force and deformation of multi-story buildings, and the deformation and energy relationships between the mode-equivalent single-degree-of-freedom system and the original structure. Sites were categorized into three types based on soil hardness, namely, hard soil, intermediate hard (soft) soil, and soft soil. For each site type, a 5-story and 10-story reinforced concrete frame structure were designed and employed as calculation examples. Fifty-six earthquake acceleration records were used as horizontal excitations to validate the accuracy of the proposed method. The results verify the following. (1) The distribution of seismic hysteretic energy along the stories demonstrate a degree of regularity. (2) For the low rise buildings, use of only the first mode shape provides reasonably accurate results, whereas, for the medium or high rise buildings, several mode shapes should be included and superposed to achieve high precision. (3) The estimated hysteretic energy distribution of bottom stories tends to be underestimated, which should be modified in actual applications.

Fault Detection Method for Beam Structure Using Modified Laplacian and Natural Frequencies (수정 라플라시안 및 고유주파수를 이용한 보 구조물의 결함탐지기법)

  • Lee, Jong-Won
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.19 no.5
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    • pp.611-617
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    • 2018
  • The application of health monitoring, including a fault detection technique, is needed to secure the structural safety of large structures. A 2-step crack identification method for detecting the crack location and size of the beam structure is presented. First, a crack occurrence region was estimated using the modified Laplacian operator for the strain mode shape obtained from the distributed local strain data. The crack location and size were then identified based on the natural frequencies obtained from the acceleration data and the neural network technique for the pre-estimated crack occurrence region. The natural frequencies of a cracked beam were calculated based on an equivalent bending stiffness induced by the energy method, and used to generate the training patterns of the neural network. An experimental study was carried out on an aluminum cantilever beam to verify the present method for crack identification. Cracks were produced on the beam, and free vibration tests were performed. A crack occurrence region was estimated using the modified Laplacian operator for the strain mode shape, and the crack location and size were assessed using the natural frequencies and neural network technique. The identified crack occurrence region agrees well with the exact one, and the accuracy of the estimation results for the crack location and size could be enhanced considerably for 3 damage cases. The presented method could be applied effectively to the structural health monitoring of large structures.

Modal Analysis and Experiment of a Simply-supported Beam with Non-uniform Cross Sections (불균일 단면을 갖는 단순지지 보의 모달해석 및 실험)

  • Kim, In-Woo;Ryu, Bong-Jo;Kim, Youngshik
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.16 no.12
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    • pp.8654-8664
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    • 2015
  • Beam-type structures with non-uniform cross sections are widely used in mechanical, architectural, and civil engineering fields. This paper deals with dynamic characteristics and vibration problems. Governing equations are first derived by using local coordinates. Their solutions are then assumed by using Galerkin's mode summation method. Bisection method is also applied in solving the determinant of the matrix which can provide natural frequencies. Whereas finite element methods adopt admissible functions satisfying only geometric boundary condition, in this study we apply Galerkin's mode summation method which uses eigen-functions satisfying both governing equations and boundary conditions. Modal analysis and experimental tests are finally performed using simply-supported beams with four different non-uniform cross-sections. Our analytical results then show good agreement with experimental ones.

Free vibration analysis of a piezoelectric nanobeam using nonlocal elasticity theory

  • Kaghazian, Abbas;Hajnayeb, Ali;Foruzande, Hamidreza
    • Structural Engineering and Mechanics
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    • v.61 no.5
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    • pp.617-624
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    • 2017
  • Piezoelectric nanobeams are used in several nano electromechanical systems. The first step in designing these systems is conducting a vibration analysis. In this research, the free vibration of a piezoelectric nanobeam is analyzed by using the nonlocal elasticity theory. The nanobeam is modeled based on Euler-Bernoulli beam theory. Hamilton's principle is used to derive the equations of motion and also the boundary conditions of the system. The obtained equations of motion are solved by using both Galerkin and the Differential Quadrature (DQ) methods. The clamped-clamped and cantilever boundary conditions are analyzed and the effects of the applied voltage and nonlocal parameter on the natural frequencies and mode shapes are studied. The results show the success of Galerkin method in determining the natural frequencies. The results also show the influence of the nonlocal parameter on the natural frequencies. Increasing a positive voltage decreases the natural frequencies, while increasing a negative voltage increases them. It is also concluded that for the clamped parts of the beam and also other parts that encounter higher values of stress during free vibrations of the beam, anti-nodes in voltage mode shapes are observed. On the contrary, in the parts of the beam that the values of the induced stress are low, the values of the amplitude of the voltage mode shape are not significant. The obtained results and especially the mode shapes can be used in future studies on the forced vibrations of piezoelectric nanobeams based on Galerkin method.

Finite Element Analysis of Sloshing Eigen Behavior in Horizontal Baffled Fuel Tank (수평으로 놓인 배플형 연료탱크의 슬로싱 고유거동에 관한 유한요소 해석)

  • 조진래;하세윤;이홍우;박태학;이우용
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.15 no.4
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    • pp.619-628
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    • 2002
  • This paper deals with the FE analysis for the free vibration of sloshing in horizontal cylindrical tank with baffles. We use Laplace equation based on potential theory as governing equation. This problem is solved by FEM using lineal isoparametric elements. We assume that the tank as well as baffles is rigid body and by separating nodes into two at the baffle location, baffle effect is obtained by separating nodes into two at the baffle location. For the calculation of natural frequencies and mode shapes, we introduce Lanczos transformation and Jacobi iteration methods. Numerical results of the first longitudinal and transverse modes, while comparing with literature cited, are very good. In order for the baffle effects on the free vibration of sloshing, various combinations of baffle parameters, which are location, inner diameter and number, are examined.

Design of Multi-Layer Dual-Band Bandpass Filter Using Aperture-Coupling (개구 결합을 이용한 적층형 이중 대역 대역 통과 여파기 설계)

  • Shin, Bong-Geol;Lee, Ja-Hyeon;Lim, Yeong-Seog
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.23 no.5
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    • pp.598-605
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    • 2012
  • In this paper, a multi-layer dual-band bandpass filter using aperture-coupling is proposed. Two coupling paths are formed with the two apertures which exist between two dual-mode resonators. The coupling coefficients can be adjusted without changing the shape of resonators. The bandwidth of the second passband can be adjusted without affecting the bandwidth of the first passband using the size of an aperture between stubs of the dual-mode resonator. The aperture coupling mechanism is theoretically analysed. The dual-mode bandpass filter for the 2.4 GHz WLAN, 3.5 GHz WiMax was designed and fabricated. The fabricated filter shows centered 2.45 GHz and 3.5 GHz with 9 % and 8 % of the bandwidth.

Analysis of Acoustic Emission Signals during Long-Term Strength Tests of Brittle Materials (취성재료의 장기 강도시험 중 미소파괴음 신호 분석)

  • Cheon, Dae-Sung;Jung, Yong-Bok
    • Tunnel and Underground Space
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    • v.27 no.3
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    • pp.121-131
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    • 2017
  • We studied the time-dependent behaviors of rock and concrete materials by conducting the static and dynamic long-term strength tests. In particular, acoustic emission(AE) signals generated while the tests were analyzed and used for the long-term stability evaluation. In the static subcritical crack growth test, the long-term behavior and AE characteristics of Mode I and Mode II were investigated. In the dynamic long-term strength test, the fatigue limit and characteristics of generation of AE were analyzed through cyclic four points bending test. The graph of the cumulative AE hits versus time showed a shape similar to that of the creep curve with the first, second and third stages. The possibility for evaluating the static and dynamic long-term stability of rock and concrete is presented from the log - log relationship between the slope of the secondary stage of cumulative AE hits curve and the delayed failure time.