• Journal of the Society of Naval Architects of Korea
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• v.30 no.1
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• pp.125-133
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• 1993

Most studies on the vibration analysis of a beam-column with ends elastically restrained and various intermediate constraints have been based on the Euler beam theory, which is inadequate for beam-columns of low slenderness ratios. In this paper, analytical methods for vibration and dynamic sensitivity of a Timoshenko beam-column with ends elastically restrained and various intermediate constraints are presented. Firstly, an exact solution method is shown. Since the exact method requires considerable computational effort, a Rayleigh-Ritz analysis is also investigated. In the latter two kinds of trial functions are examined for comparisions : eigenfunctions of the base system(the system without intermediate constraints) and polynomials having properties corresponding to the eigenfunctions of the base system. The results of some numerical Investigations show that the Rayleigh-Ritz analysis using the characteristic polynomials is competitive with the exact solutions in accuracy, and that it is much more efficient in computations than using the eigenfunctions of the base system, especially in the dynamic sensitivity analysis. In addition, the prediction of the changes of natural frequencies due to the changes of design variables based on the first order sensitivity is in good agreements with that by the ordinary reanalysis as long as the changes of design variables are moderate.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.3 no.4
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• pp.109-122
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• 1983

An accurate thick beam element (TB4) which includes the effects of the shear deformation and rotatory inertia has been degenerated from the three dimensional continuum by employing the Timoshenko beam assumptions. The proposed TB4 element has four nodes and two degrees of freedom at each node, totally eight degrees of freedom. The transverse deflection W and plane rotation ${\theta}$ with the cubic interpolation functions are selected as nodal variables. The element characteristics are formulated by discretizing the beam equations of motion, using the Galerkin weighted residual method, and are numerically integrated by the reduced shear integration technique, using the three-point Gauss quadrature with the various shear coefficients. Several numerical examples are analyzed to demonstrate the accuracy and the monotonic convergence behavior of the proposed TB4 beam element. The result indicates that the TB4 element shows the more excellent performance and the monotonic convergence behavior than the other existing Timoshenko beam type elements for the whole range of the beam aspect ratios, in both static and free vibration analyses.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.16 no.2
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• pp.183-195
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• 2003

In this study, the method of the finite element modeling for free vibration control of beam-type smart structures with bonded plate-type piezoelectric sensors and actuators is proposed. Constitutive equations for the direct piezoelectric effect and converse piezoelectric effect of piezoelectric materials are considered. By using the variational principle, the equations of motion for the smart beam finite element are derived. The proposed 2-node beam finite element is an isoparametric element based on Timoshenko beam theory. Therefore, by analyzing beam-type smart structures with smart beam finite elements, it is possible to simulate the control of the structural behavior by applying voltages to piezoelectric actuators and monitoring of the structural behavior by sensing voltages of piezoelectric sensors. By using the smart beam finite element and constant-gain feed back control scheme, the formulation of the free nitration control for the beam structures with bonded plate-tyPe Piezoelectric sensors and actuators is proposed.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2011.04a
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• pp.631-634
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• 2011

본 연구에서는 규칙 파랑 중에 있는 부유식 구조물의 유탄성 거동을 해석 하고, 수치모델의 수렴성을 살펴본다. 부유식 구조물은 보로 모델링 하며, 유체는 이상유체로 가정하여 문제를 해결한다. 보 모델의 경우 Euler-Bernoulli 보 모델과 Timoshenko 보 모델로 나누어 그 특성을 비교 해 본다. 문제의 해석법에 있어서 부유식 구조물의 경우는 유한요소법을, 유체의 경우는 경계요소법을 이용하여, 상호 연성된 방정식을 이끌어 낸다. 상호 연성된 방정식을 토대로 Euler-Bernoulli 보 모델과 Timoshenko 보 모델의 거동 특성을 살펴보고 제시된 수치 모델을 기준으로 수렴성을 분석해 본다.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.23 no.11 s.170
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• pp.2058-2066
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• 1999

The present paper proposes a new dynamic analysis method for multi-span Timoshenko beam structures supported by joints with damping subject to moving loads. An exact dynamic element matrix method is adopted to model Timoshenko beam structures. A generalized modal analysis method is applied to derive response formulae for beam structures subject to moving loads. The proposed method offers an exact and closed form solution. Two numerical examples are provided for validating and illustrating the proposed method. In the first numerical example, a single span beam with multiple moving loads is considered. A dynamic analysis on a multi-span beam under a moving load is considered as the second example, in which the flexibility and damping of supporting joints are taken into account. The numerical study proves that the proposed method is useful for the vibration analysis of multi-span beam-hype structures by moving loads.

• Journal of the Korean Society for Precision Engineering
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• v.26 no.9
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• pp.112-120
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• 2009

In this paper the purpose is to investigate the stability and variation of natural frequency of a cracked Timoshenko cantilever beams subjected to subtangential follower force. In addition, an analysis of the stability of a cantilever beam as the crack effect and slenderness ratio is investigated. The governing differential equations of a Timoshenko beam subjected to an end tangential follower force are derived via Hamilton's principle. The two coupled governing differential equations are reduced to one fourth order ordinary differential equation in terms of the flexural displacement. By using the results of this paper, we can obtain the judgment base that the choice of beam models for the effect of slenderness ratio and crack.

• Computational Structural Engineering
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• v.9 no.1
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• pp.133-139
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• 1996

In this paper, an approximate method is developed to obtain the natural frequencies of the out of plane vibration of circular curved beams. The governing differential equations are derived using the dynamic equilibrium equations with the Timoshenko theory, and solved numerically. The Runge-Kutta method and Regula-Falsi method are used to integrate the differential equations and to determine the natural frequencies, respectively. In numerical examples, the hinged-hinged and clamped-clamped end constraints are considered. For each case, the four lowest natural frequencies are reported as functions of four non-dimensional system parameters.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.23 no.12
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• pp.1103-1110
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• 2013

Based on the string, Euler beam, and Timoshenko beam theories, the transfer functions of axially translating web system to predict the lateral tracking are introduced in this paper. In addition, total transfer function of a multi-span web handling system is developed by the combination of the transfer functions of each single span. Experiments and computations are carried out and the results obtained for the Timoshenko beam model are compared with those of other models. The comparison indicates that the predictions from the Timoshenko and Euler beam models are quite different from that of the classical string model in both the gain and phase response. The results are expected to help in the development of high fidelity models of web tracking systems within a general computational framework.

• Journal of KSNVE
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• v.9 no.5
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• pp.1012-1018
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• 1999

This paper deals with the coupled flexural-torsional vibrations of Timoshenko beams with monosymmetric cross-section. The governing differtial equations for free vibration of such beams are derived and solved numerically to obtain frequencies and mode shapes. Numerical results are calculated for three specific examples of beams with free-free, clamped-free, hinged-hinged, clamped-hinged and clamped-clamped end constraints. The effect of warping stiffess on the natural frequencies and mode shapes is discussed and it is concluded that substantial error can be incurred if the effect is ignored.

• Journal of the Korea Society for Simulation
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• v.8 no.2
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• pp.111-122
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• 1999

The paper presents a stability analysis of uniform Timoshenko beams resting on two-parameter elastic foundations. The two-parameter elastic foundations were considered as a shearing layer and Winkler springs in soil models. Governing equations of motion were derived using the Hamilton's principle and finite element analysis was performed and the eigenvalues were obtained for the stability analysis. The numerical results for the buckling stability of beams under axial forces are demonstrated and compared with the exact or available confirmed solutions. Finally, several examples were given for Euler-Bernoulli and Timoshenko beams with various boundary conditions.