• Structural Engineering and Mechanics
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• 제54권4호
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• pp.771-792
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• 2015

In the paper we study dynamic response of a finite, simply supported Timoshenko beam subject to a moving continuously distributed forces. Three problems have been considered. The dynamic response of the Timoshenko beam under a uniform distributed load moving with a constant velocity v has been considered as the first problem. Obtained solutions allow to find the response of the beam under the interval of the finite length a uniformly distributed moving load. Part of the solutions are presented in a closed form instead of an infinite series. As the second problem the steady-state vibrations of the beam under uniformly distributed mass $m_1$ moving with the constant velocity has been considered. The vibrations of the beam caused by the interval of the finite length randomly distributed load moving with constant velocity is considered as the last problem. It is assumed that load process is space-time stationary stochastic process.

• 한국안전학회지
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• 제11권2호
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• pp.116-121
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• 1996

On the stability of Timoshenko cantilever beam subjected to a follower force, the influence of the characteristics of elastic constraints at the free end Is studied. The equations of motion and boundary conditions of this nonconservative elastic system are estabilished by using the Hamilton's principle. Upon evaluation of the stability of this system, the effect of shear deformation and rotatory inertia is considered in calculation. Using cowper's formulae Timoshenko's shear coefficient K'are determined. From this imvestigation it is found that the constrain parameter have an appreciable stabilizing effect in this nonconservative system. Moreover, it is obvious that the small values of K'decrease the flutter load of this system.

• 한국정밀공학회지
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• 제25권6호
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• pp.99-107
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• 2008

In this paper, the stability of a cracked cantilever Timoshenko beam with a tip mass subjected to follower force is investigated. In addition, an analysis of the flutter instability(flutter critical follower force) and a critical natural frequency of a cracked cantilever Euler / Timoshenko beam with a tip mass subjected to a follower force is presented. The vibration analysis on such cracked beam is conducted to identify the critical follower force for flutter instability based on the variation of the first two resonant frequencies of the beam. Therefore, the effect of the crack's intensity, location and a tip mass on the flutter follower force is studied. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2000년도 추계학술대회논문집
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• pp.540-545
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• 2000

This paper presents the exact dynamic element for composite Timoshenko beam, which is inherently subject both to bending and torsional vibration. The coupling effect between bending and torsional vibrations is rigorouly considered in the derivation of the exact dynamic element. Two examples are provided to validate and illustrate the proposed exact dynamic element matrix for composite Timoshenko beam.

• 한국소음진동공학회논문집
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• 제18권12호
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• pp.1327-1334
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• 2008

In this paper, the purpose is to investigate the stability of cracked Timoshenko cantilever beams subjected to subtangential follower force. In addition, an analysis of the instability(critical follower force of flutter and divergence) of a cracked beam as slenderness ratio and subtangential coefficient is investigated. The governing differential equations of a Timoshenko beam subjected to an end tangential follower force is derived via Hamilton's principle. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations. The results of this study will contribute to the safety test and stability estimation of structures of a cracked beam subjected to subtangential follower force.

• 한국정밀공학회지
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• 제12권4호
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• pp.39-45
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• 1995

본 논문은 복수 집중질량을 갖고 제어 종동력을 받는 자유 Timoshenko보의 동적 안정성에 관한 것으로, 비행중의 미사일이나 로켓의 연료탱크, Payload등의 기계장치부를 복수의 집중질량으로 간주하여 이러한 항공우주 구조물들이 추진력인 종동력을 받을때에 대한 계의 동적 안정성을 판별한다. 수학적 모델에 대한 운동방정식은 확장된 해밀톤 원리를 이용한 유한요소법에 의해 유도되며, 복수 부가질량의 위치 및 크기변화, 센서의 위치 및 게인(gain)의 변화에 따른 계의 안정성 지도(stability maps)를 보여준다. 또한 보의 전단 변형이나 회전관성의 효과 뿐만아니라, 추질력의 방향이 제어되는 경우와 제어되지 않는 경우에 대한 최대 추진력 값이 수치 시뮬레이션을 통해 예측된다.

• 대한조선학회지
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• 제20권3호
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• pp.33-38
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• 1983

• 한국도로학회:학술대회논문집
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• 한국도로학회 2008년도 추계학술대회 논문집
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• pp.217-220
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• 2008

• 대한기계학회논문집
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• 제15권2호
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• pp.478-487
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• 1991

In this study, dynamic stability of discontinuous free Timoshenko beam, barring a concentrated mass, under constant follower force is considered. Governing differential equations are derived based on the extended Hamilton's principle and finite element method is applied for numerical analysis. Conclusions of the study are as follows : (1) Without force direction control, (i) the critical follower force at instability is increased with concentrated mass regardless of discontinuity. (ii) the minimum critical follower force is located in the vicinity of discontinuity position .xi.$_{d}$=0.75. (iii) at mass location .mu. .leq.0.5 the force at instability is decreased as magnitude of concentrated mass is increased but, at .mu. .geq. 0.5 the force is increased as the mass is increased. (2) With force direction control, (i) shear deformation parameter S contributes insignificantly to the force at instability when S>10$^{[-993]}$ (ii) maximum critical follower force can be obtained for the discontinuity location .xi.$_{d}$=0.25. (iii) the critical follower force is increased as magnitude of concentrated mass .alpha. is increased at mass location .mu. .geq.0.4, but is increased, .mu ..leq.0.4.4.

• Structural Engineering and Mechanics
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• 제44권1호
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• pp.109-125
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• 2012

Post-buckling behavior of Timoshenko beams subjected to uniform temperature rising with temperature dependent physical properties are studied in this paper by using the total Lagrangian Timoshenko beam element approximation. The beam is clamped at both ends. In the case of beams with immovable ends, temperature rise causes compressible forces end therefore buckling and post-buckling phenomena occurs. It is known that post-buckling problems are geometrically nonlinear problems. Also, the material properties (Young's modulus, coefficient of thermal expansion, yield stress) are temperature dependent: That is the coefficients of the governing equations are not constant in this study. This situation suggests the physical nonlinearity of the problem. Hence, the considered problem is both geometrically and physically nonlinear. The considered highly non-linear problem is solved considering full geometric non-linearity by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. The beams considered in numerical examples are made of Austenitic Stainless Steel (316). The convergence studies are made. In this study, the difference between temperature dependent and independent physical properties are investigated in detail in post-buckling case. The relationships between deflections, thermal post-buckling configuration, critical buckling temperature, maximum stresses of the beams and temperature rising are illustrated in detail in post-buckling case.