• Structural Engineering and Mechanics
• /
• 제18권3호
• /
• pp.303-314
• /
• 2004

An artificial neural network (ANN) application is presented for flexural and axial vibration analysis of elastic beams with various support conditions. The first three natural frequencies of beams are obtained using multi layer neural network based back-propagation error learning algorithm. The natural frequencies of beams are calculated for six different boundary conditions via direct solution of governing differential equations of beams and Rayleigh's approximate method. The training of the network has been made using these data only flexural vibration case. The trained neural network, however, had been tested for cantilever beam (C-F), and both end free (F-F) in case the axial vibration, and clamped-clamped (C-C), and Guided-Pinned (G-P) support condition in case the flexural vibrations which were not included in the training set. The results found by using artificial neural network are sufficiently close to the theoretical results. It has been demonstrated that the artificial neural network approach applied in this study is highly successful for the purposes of free vibration analysis of elastic beams.

• Structural Engineering and Mechanics
• /
• 제8권3호
• /
• pp.243-256
• /
• 1999

Using appropriate transformations, the differential equation for flexural free vibration of a cantilever bar with variably distributed mass and stiffness is reduced to a Bessel's equation or an ordinary differential equation with constant coefficients by selecting suitable expressions, such as power functions and exponential functions, for the distributions of stiffness and mass. The general solutions for flexural free vibration of one-step bar with variable cross-section are derived and used to obtain the frequency equation of multi-step cantilever bars. The new exact approach is presented which combines the transfer matrix method and closed form solutions of one step bars. Two numerical examples demonstrate that the calculated natural frequencies and mode shapes of a 27-storey building and a television transmission tower are in good agreement with the corresponding experimental data. It is also shown through the numerical examples that the selected expressions are suitable for describing the distributions of stiffness and mass of typical tall buildings and high-rise structures.

• 소음진동
• /
• 제9권5호
• /
• pp.1012-1018
• /
• 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.

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2005년도 추계학술대회논문집
• /
• pp.764-767
• /
• 2005

This paper deals with the flexural-torsional free vibrations of circular strip foundations with a variable breadth. The breadth of strip foundation varies with the linear functional fashion, which is symmetric about the mid-arc. Differential equations governing free vibrations of such foundations are derived, in which Winkler foundation is considered as the model of elastic soils. Effects of the rotatory and torsional inertias and shear deformation are included in the governing equations. Differential equations are numerically solved to calculate the natural frequencies. In the numerical examples, the free-free end constraint is considered. Effects of the rotatory and torsional inertias and shear parameter on the natural frequencies are reported. Parametric studies between frequency parameters and various system parameters are investigated.

• Structural Engineering and Mechanics
• /
• 제82권6호
• /
• pp.725-734
• /
• 2022

This work presents a simple exponential shear deformation theory for the flexural and free vibration responses of thick bridge deck. Contrary to the existing higher order shear deformation theories (HSDT) and the first shear deformation theory (FSDT), the proposed model uses a new displacement field which incorporates undetermined integral terms and involves only two variables. Governing equations and boundary conditions of the theory are derived by the principle of virtual work. The simply supported thick isotropic square and rectangular plates are considered for the detailed numerical studies. Results of displacements, stresses and frequencies are compared with those of other refined theories and exact theory to show the efficiency of the proposed theory. Good agreement is achieved of the present results with those of higher order shear deformation theory (HSDT) and elasticity theory. Moreover, results demonstrate that the developed two variable refined plate theory is simple for solving the flexural and free vibration responses of thick bridge deck and can achieve the same accuracy of the existing HSDTs which have more number of variables.

• Journal of Advanced Marine Engineering and Technology
• /
• 제16권5호
• /
• pp.29-38
• /
• 1992

This paper describes the general formulation for the in-plane longitudinal and flexural coupled free vibration analysis of a branched structure. The branched structure, which is mainly found in machine tools, pipeline systems and so on, has some crooked parts and subsystems. And it modeled as a distributed mass system. The superiority of the present method to the transfer matrix method in the computation accuracy and speed was confirmed by the numerical computation results. Moreover, we comfirmed that boundary and intermediate conditions have been controlled by the spring constants.

• 대한토목학회논문집
• /
• 제29권1A호
• /
• pp.19-30
• /
• 2009

본 연구에서는 CFT 트러스 거더의 자유진동실험 결과를 토대로 주요 코드에서 규정하고 있는 CFT(concrete filled tube) 합성단면의 초기 휨강성 산정식을 평가하였다. 각 코드에서 규정하는 합성단면 초기 휨강성 산정식에 의한 CFT 트러스 거더의 자유진동 해석결과와 실험결과를 비교하였으며, 그 결과 CFT 트러스 거더의 자유진동실험 결과는 ACI의 휨강성 산정식을 적용하는 경우의 해석결과와 잘 일치하는 결과를 보였다. 이를 반영하여 f/L비 변화에 따른 CFT 트러스 거더의 자유진동해석을 수행하여 f/L비가 CFT 거더의 고유진동수에 미치는 영향을 분석하였다. CFT 트러스 거더의 f/L비는 거더의 전체강성에 영향을 주기 때문에 고유진동수를 변화시킨다. 수평모드에서의 고유진동수는 f/L비가 증가하면 감소하지만, 연직 모드에서의 고유진동수는 f/L비가 증가하면 선형적으로 증가하는 경향을 보였다.

• 동력기계공학회지
• /
• 제19권6호
• /
• pp.60-67
• /
• 2015

While designing and operating machines, it is very important to understand the dynamic characteristic of the machines. Authors developed the Sylvester-transfer stiffness coefficient method in order to analyze effectively the free vibration of machines or structures. The Sylvester-transfer stiffness coefficient method was derived from the combination of the Sylvester's inertia theorem and the transfer stiffness coefficient method. In this paper, the authors formulate the computational algorithm for flexural free vibration analysis of axisymmetric annular plate using the Sylvester-transfer stiffness coefficient method. To confirm the usefulness of the Sylvester-transfer stiffness coefficient method, the natural frequencies and modes for two computational models computed using the Sylvester-transfer stiffness coefficient method are compared with those computed using the exact solution and the finite element method.

• Wind and Structures
• /
• 제32권1호
• /
• pp.11-17
• /
• 2021

In recent years, there has been a tendency towards renewable energy sources considering the damages caused by non-renewable energy resources to nature and humans. One of the renewable energy sources is wind and energy is obtained with the help of wind turbines. To determine the behavior of wind turbines under earthquake loads, dynamic characteristics are required. In this study, the differential transformation method is proposed to determine the free vibration analysis of wind turbines with a variable cross-section. The wind turbine is modeled as an equivalent variable continuous flexural beam and blade weight is considered as a point mass at the top of the structures. The differential equation representing the free vibration of the wind turbine is transformed into an algebraic equation with the help of differential transformation method and the angular frequencies and the mode shapes of the wind turbine are obtained by the help of the differential transformation method. In the study, a sample taken from the literature was solved with the presented method and the suitability of the method was investigated. The same wind turbine example also modeled by finite element modelling software, ABAQUS. Results of the finite element model and differential transformation method are compared with each other and the results are in good agreement.

• Nuclear Engineering and Technology
• /
• 제31권2호
• /
• pp.214-225
• /
• 1999

An accurate method is presented for flexural vibrations of sectorial plates having simply supported-free and free-free radial edges, when the circular edge is either clamped or simply supported. The classical Ritz method is employed with two sets of admissible functions assumed for the transverse vibratory displacements. These sets consist of : (1) mathematically complete algebraic-trigonometric polynomials which gurantee convergence to exact frequencies as sufficient terms are retained, and (2) comer functions which account for the bending moment singularities at re-entrant comer of the radial edges having arbitrary edge conditions. Accurate (at least four significant figures) frequencies and normalized contours of the transverse vibratory displacement are presented for the spectra of corner angles [90$^{\circ}$, 180$^{\circ}$(semi-circular), 270$^{\circ}$, 300$^{\circ}$, 330$^{\circ}$, 350$^{\circ}$, 355$^{\circ}$, 360$^{\circ}$ (complete circular)] causing a re-entrant comer of the radial edges. Future solutions drawn from alternative numerical procedures and finite element techniques may be compared with these accurate results.