• Title/Summary/Keyword: 양단자유

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A Study of the Vibration Safety Criterion on the Dynamic Behavior of Buried Pipeline with the Free Ends (양단자유 경계조건을 가진 매설관의 동적거동에서 진동안전 기준에 관한 연구)

  • 이병길;정진호;장봉현;안명석
    • Explosives and Blasting
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    • v.22 no.3
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    • pp.13-26
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    • 2004
  • This work reports results of our study on the dynamic response of buried pipelines depending on their boundary conditions. We have studied behavior of the buried pipelines both along the axial and the transverse direction with a boundary condition of free ends. The buried pipelines are modeled as beams on elastic foundation while the seismic wave as a ground displacement in the form of a sinusoidal wave. The natural frequency, its mode, and the effect of parameters have been interpreted in terms of the free vibration. In order to investigate the response on the earthquake, the resulting frequency and the mode shape obtained from the free vibration have been utilized to derive the mathematical formula for the farced vibration. We have also completed the computer program to simulate the time-displacement graphs of the pipe lines with free ends for both cases of vibrations.

A Study on the Vibration and Acoustic Radiation from an Elastic Free- Free Beam due to a Steel Ball Impact (강구의 충돌에 의한 양단자유 보의 진동 및 음향 방사에 관한 연구)

  • 박홍철;이효근;박윤식
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.16 no.9
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    • pp.1615-1626
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    • 1992
  • In this study, vibrations and resulting acoustic radiations from an elastic beam impacted by a steel ball were studied theoretically and experimentally. First the transverse vibrations of free-free elastic beams are analysed with modal analysis technique. The impact forces are modeled with the Hertz's theory and the contanct duration is compared with the measured values. Also the calculated beam vibrations are verified with the experimental results. Then the acoustic radiations due to the beam vibration are studied numberically and experimentally. The acousticpressure is calculated assuming the beam has an elliptical cross-section. The predicted acoustic pressure is compared with the measured value. It was found that both the predicted beamvibrations using the Hertz's theory and the estimated acoustic pressure under the assumption of an elliptical cross- section are in very good agreements with the measured values.

Characteristics of Dynamic Properties of Granite Specimen from Chungnam Yeongi Area (충남 연기군 지역 화강암 시험편의 동적물성 특성에 관한 연구)

  • Min, June-Hyun;Lee, Seung-Joong;Choi, Sung-O.
    • Tunnel and Underground Space
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    • v.21 no.6
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    • pp.480-493
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    • 2011
  • Dynamic rock property is one of most important parameters in design of earthquake-resistant structures. In this study, free-free resonant column test has been conducted to obtain dynamic Young's modulus, dynamic shear modulus, and damping ratio among dynamic properties with granite specimen of Chungnam Yeongi area. The dynamic properties obtained from this test were compared with the physical properties from static rock tests, and their relationship has been analyzed. From our study, it has been concluded that the dynamic Young's modulus and the dynamic shear modulus are linearly proportional to the elastic wave velocity. And also the damping ratio has been identified to be in non-linear inverse proportion to the elastic wave velocity.

Free Vibrations of Horizontally Curved Beams with Variable Cross Section (변다면 수평 곡선보의 자유진동에 관한 연구)

  • 이병구;박광규;모정만;이재만
    • Computational Structural Engineering
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    • v.11 no.3
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    • pp.155-164
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    • 1998
  • 이 논문은 변단면을 고려한 수평 곡선보의 자유진동에 관한 연구이다. 진동시 곡선보 요소에 작용하는 합응력과 관성력의 동적평형방정식을 이용하여 변단면 원호형 수평 곡선보의 자유진동을 지배하는 상미분방정식을 유도하였다. 이 미분방정식을 원형 단면을 갖는 선형변변단면에 적용하여 고유진동수, 진동형 및 합응력을 산출하였다. 수치 해석예에서는 양단고정 및 양단회전 곡선보를 채택하였으며, 수치해석 결과로서 고유진동수와 단면비, 세장비 및 중심각 사이의 관계를 그림에 나타내었다. 또한 실험실 규모의 실험을 통하여 본 연구결과의 타당성을 보였다.

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Nonlinear Analysis of Stepped Beam Immovable Ends for Free and Forced Vibrations (양단지지된 변단면보의 자유 및 강제진동의 비선형해석)

  • 심재수;함원식
    • Computational Structural Engineering
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    • v.3 no.2
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    • pp.67-75
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    • 1990
  • A stepped beam with immovable ends under the free and forced vibrations with large amplitude is investigated by using the finite element method to show the effects of longitudinal displacement, shear deformation and rotary inertia. A modified harmonic force matrix is introduced for analysis of finite amplitude vibration of the stepped beam under uniform harmonic loading and a beam under nonuniform harmonic loading. Numerical examples are analysed for deflections and natural frequencies of stepped beam under various support conditions. Results show that the proposed method is valid and efficient.

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Free Vibrations of Timoshenko Beam with Elastomeric Bearings at Two Far Ends (양단이 탄성받침으로 지지된 Timoshenko 보의 자유진동)

  • Lee, Byoung Koo;Lee, Tae Eun;Park, Chang Eun
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.31 no.3A
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    • pp.181-187
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    • 2011
  • This paper deals with free vibrations of the Timoshenko beam supported by two elastomeric bearings at two far ends. The ordinary differential equation governing free vibrations of such beam is derived, in which both effects of rotatory inertia and shear deformation are included as the Timoshenko beam theory. Also, boundary conditions of the free end are derived based on the Timoshenko beam theory. The ordinary differential equation is solved by the numerical methods for calculating natural frequencies and mode shapes. Both effects of the rotatory inertia and shear deformation on natural frequencies are extensively discussed. Also, relationships between natural frequencies and slenderness ratio, foundation modulus and bearing length are presented. Typical mode shapes of bending moment and shear force as well as deflection are given in figures which show the positions of maximum amplitudes and nodal points.

Numerical Analysis of Free Vibration of Parabolic Arches with Hinged Ends (양단(兩端)힌지 포물선(抛物線)아치의 자유진동(自由振動)에 관한 연구(研究))

  • Hwang, Hak Joo;Lee, Byoung Koo
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.4 no.1
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    • pp.69-77
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    • 1984
  • In this paper, the governing differential equations for the free vibration of uniform parabolic arches are derived on the basis of equilibrium equations of a small element of arch rib and the D'Alembert principle. A trial eigen value method is used for determining the natural frequencies and mode shapes. And the Runge-Kutta fourth order integration technique is also used in this method to perform the integration of the differential equations. A detailed study is made of the first mode for the symmetrical and anti-symmetrical vibrations of hinged arches with the Span length equal to 10 m. The effects of the rise of arch, the radius of gyration and the rotary inertia on free vibrations are presented in detail in curves and table.

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Lowest Symmetrical and Antisymmetrical Natural Frequencies of Shallow Arches on Two-Parameter Elastic Foundations (두 개의 매개변수로 표현되는 탄성지반 위에 놓인 낮은 아치의 최저차 대칭 및 역대칭 고유진동수)

  • 오상진;서종원;이병구
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.15 no.2
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    • pp.367-377
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    • 2002
  • This paper deals with the free vibrations of shallow arches resting on elastic foundations. Foundations we assumed to follow the hypothesis proposed by Pasternak. The governing differential equation is derived for the in-plane free vibration of linearly elastic arches of uniform stiffness and constant mass per unit length. Two arch shapes with hinged-hinged and clamped-clamped end constraints we considered in analysis. The frequency equations (lowest symmetrical and antisymmetrical frequency equations) we obtained by Galerkin's method. The effects of arch rise, Winkler foundation parameter and shear foundation parameter on the lowest two natural frequencies are investigated. The effect of initial arch shapes on frequencies is also studied.

Planar Free Vibrations of Catenary Arcs (현수 곡선부재의 면내 자유진동 해석)

  • Lee, Byoung Koo;Oh, Sang Jin;Suh, Ju Suhk
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.10 no.3
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    • pp.19-28
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    • 1990
  • The main purpose of this paper is to present both fundamental and some higher natural frequencies of catenary arcs. The differential equations governing planar free vibrations for these arcs are derived, in which the rotatory inertia is included, as non-dimensional forms and solved numerically to obtain frequencies and mode shapes. The hinged-hinged and clamped-clamped end constraints are applied in numerical examples. The lowest four natural frequencies are reported as the functions of non -dimensional system parameters; the slenderness ratio and the rise to span length ratio. The effects of rotatory inertia on natural frequencies are reported and some typical mode shapes are also presented.

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Evaluating Shear Wave Velocity of Rock Specimen Through Compressional Wave Velocities Obtained from FFRC and Ultrasonic Velocity Methods (양단자유공진주 및 초음파속도법으로 획득한 압축파 속도를 이용한 암석시편의 전단파 속도 도출)

  • Bang, Eun Seok;Park, Sam Gyu;Kim, Dong Soo
    • Geophysics and Geophysical Exploration
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    • v.16 no.4
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    • pp.250-256
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    • 2013
  • Using shear wave velocity is more reasonable to estimate strength and integrity of rock compared with using compressional wave. It is often ambiguous to pick the dominant frequency caused by torsional wave when evaluating $V_S$ of rock specimen from FFRC method. It is also sometimes ambiguous to pick the first arrival point of S wave compared with P wave in the signals acquired from ultrasonic velocity method. Otherwise, the procedure of evaluating $V_P$ using ultrasonic velocity method and $V_L$ using FFRC method is relatively stable. Through the relationship between elastic modulus, poisson's ratio and $V_S$ can be obtained from $V_P$, $V_L$. Applicability was checked using model specimens having different material property and length and rock specimens sampled in mine area, and usefulness of proposed procedure was verified.