• 한국전산구조공학회논문집
• /
• 제25권3호
• /
• pp.185-194
• /
• 2012

이 연구는 회전관성과 전단변형을 동시에 고려한 변단면 Timoshenko 보의 자유진동에 관한 연구이다. 변단면 보의 단면은 폭이 포물선 함수로 변화하는 변화폭 직사각형 단면으로 채택하였다. 이러한 보의 자유진동을 지배하는 수직변위에 대한 4계 상미분방정식을 유도하였다. 이 상미분방정식을 수치해석하여 고유진동수와 진동형을 산출하였다. 수치해석 예에서는 회전-회전, 회전-고정, 고정-고정 지점을 고려하였다. 진동형은 변위의 진동형뿐만 아니라 합응력의 진동형도 산출하여 그림에 나타내었다. 휨 회전각과 전단변형에 의한 수직변위 및 전단면 회전각의 구성비율을 산정하였다.

• 한국도로학회논문집
• /
• 제11권4호
• /
• pp.79-85
• /
• 2009

국내의 줄눈 콘크리트 포장설계에 주로 사용되는 다웰바 설계 기준은 국외 기준과 검증되지 않은 경험에 의해 사용되고 있다. 또한 다웰바의 설치는 길어깨나 하부층의 조건 등을 고려하지 못한 상태에서 슬래브 폭에 대하여 일률적으로 적용되고 있다. 이에 다웰바를 합리적으로 설계하기 위해서는 다웰바 거동에 대한 고찰이 요구되며, 이를 3차원 유한요소해석을 이용하여 수행하였다. 다웰바의 거동에 대한 3차원 유한요소해석 결과의 타당성을 검토하기 위하여 Timoshenko이론의 다웰바 거동을 비교하였다. 또한 실제 도로에서 교통하중이 여러 개의 다웰바에 분산 전달하는 다웰바의 그룹작용(Dowel Group Action)을 3차원 유한요소해석을 통하여 다웰바 그룹작용 적용범위를 산정하였다. 본 연구에서 제시된 다웰바 그룹작용 범위는 Friberg의 그룹작용 범위와는 상이한 결과가 나타났으며, 비교적 최근 연구 결과인 Tabatabaie의 그룹작용 범위의 연구결과와 유사한 결과가 도출되었다.

• Structural Engineering and Mechanics
• /
• 제26권1호
• /
• pp.1-14
• /
• 2007

Because of complexity, the literature regarding the free vibration analysis of a Timoshenko beam carrying "multiple" spring-mass systems is rare, particular that regarding the "exact" solutions. As to the "exact" solutions by further considering the joint terms of shear deformation and rotary inertia in the differential equation of motion of a Timoshenko beam carrying multiple concentrated attachments, the information concerned is not found yet. This is the reason why this paper aims at studying the natural frequencies and mode shapes of a uniform Timoshenko beam carrying multiple intermediate spring-mass systems using an exact as well as a numerical assembly method. Since the shear deformation and rotary inertia terms are dependent on the slenderness ratio of the beam, the shear coefficient of the cross-section, the total number of attachments and the support conditions of the beam, the individual and/or combined effects of these factors on the result are investigated in details. Numerical results reveal that the effect of the shear deformation and rotary inertia joint terms on the lowest five natural frequencies of the combined vibrating system is somehow complicated.

• 대한기계학회:학술대회논문집
• /
• 대한기계학회 2000년도 춘계학술대회논문집A
• /
• pp.596-601
• /
• 2000

The paper presents free vibration and stability analyses of a non-uniform Timoshenko beam resting on a two-parameter elastic soil. The soil parameters can vary along the spat and is assumed to be two-parameter model including the effects of both transverse shear deformation and elastic foundation Governing equations related to the vibration and the stability of the beam are derived from Hamilton's principle, and the resulting eigen-value problems can be solved to give natural frequencies and critical force by finite element method. Numerical results for both vibration and stability of beams under an axial force are presented and compared with other available solutions. Finally, vibration frequencies, mode shapes and critical forces are investigated for various thickness ratios, shear foundation parameter, Winkler foundation parameter and boundary conditions of tapered Timoshenko beams.

• Structural Engineering and Mechanics
• /
• 제80권6호
• /
• pp.657-668
• /
• 2021

In this study, a relationship between the resonance frequency ratio and Poisson's ratio was proposed that can be used to directly determine the elastic constants. Using this relationship, the frequency ratio between the 1st bending mode and 2nd bending mode for any rectangular Timoshenko beam can be directly estimated and used to determine the elastic constants efficiently. The exact solution of the Timoshenko beam vibration frequency equation under free-free boundary conditions was determined with an accurate shear shape factor. The highest percent difference for the frequency ratio between the theoretical values and the estimated values for all the beam dimensions studied was less than 0.02%. The proposed equations were used to obtain the elastic constants of beams with different material properties and dimensions using the first two measured transverse bending frequencies. Results show that using the equations proposed in this study, the Young's modulus and Poisson's ratio of rectangular Timoshenko beams can be determined more efficiently and accurately than those obtained from industry standards such as ASTM E1876-15 without the need to test the torsional vibration.

• 한국전산구조공학회:학술대회논문집
• /
• 한국전산구조공학회 2004년도 봄 학술발표회 논문집
• /
• pp.17-24
• /
• 2004

This paper established the dynamic model of a flexible Timoshenko beam with geometrical nonlinearities subject to large overall motions by using the finite element method. The equations of motion are derived by using Hamilton principle based on expressing the kinetic and potential energies of the flexible beam in terms of generalized coordinates. The nonlinear constraint equations are adjoined to the system equations of motion by using Lagrange multipliers.

• Structural Engineering and Mechanics
• /
• 제67권4호
• /
• pp.385-390
• /
• 2018

An incongruity is underlined about the analysis of Timoshenko beams subjected to concentrated loads modelled through the use of generalized functions. While for Euler-Bernoulli beams this modeling always leads to effective results, on the contrary, the contemporary assumptions of concentrated external moment, interpreted as a generalized function (doublet), and of shear deformation determine inconsistent discontinuities in the deflection laws. A physical/theoretical explanation of this not-neglecting incongruity is given in the text.

• Journal of Mechanical Science and Technology
• /
• 제19권9호
• /
• pp.1753-1760
• /
• 2005

The pseudo spectral method is applied to the free vibration analysis of double-span Timoshenko beams. The analysis is based on the Chebyshev polynomials. Each section of the double-span beam has its own basis functions, and the continuity conditions at the intermediate support as well as the boundary conditions are treated separately as the constraints of the basis functions. Natural frequencies are provided for different thickness-to-length ratios and for different span ratios, which agree with those of Euler-Bernoulli beams when the thickness-to-length ratio is small but deviate considerably as the thickness-to-length ratio grows larger.

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2002년도 추계학술대회논문초록집
• /
• pp.403-403
• /
• 2002

The use of frequency-dependent spectral element matrix (or exact dynamic stiffness matrix) in structural dynamics is known to provide very accurate solutions, while reducing the number of degrees-of-freedom to resolve the computational and cost problems. Thus, in the present paper, the spectral element model is formulated for the axially moving Timoshenko beam under a uniform axial tension. (omitted)

• International Journal of Precision Engineering and Manufacturing
• /
• 제5권2호
• /
• pp.53-59
• /
• 2004

The pseudospectral method is applied to the analysis of out-of$.$plane free vibration of circularly curved Timoshenko beams. The analysis is based on the Chebyshev polynomials and the basis functions are chosen to satisfy the boundary conditions. Natural frequencies are calculated for curved beams of circular cross sections under hinged-hinged, clamped-clamped and hinged-clamped end conditions. The present method gives good accuracy with only a limited number of collocation points.