• 소음진동
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• 제8권5호
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• pp.856-861
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• 1998

Several reactor system components, such as heat exchange tubes, fuel fins, controlrods, and various instruments are beam-like components. This study presents a simple solution method for calculating the natural frequencies and modes of beams supported by linear and torsional springs and attached concentrated mass and rotational inertia at some intermediate points. For a general multi-span beam, theoretical method is proposed to analyze the exact solution about vibrational characteristics with respect to the nondimensional parameters. And the results obtained using the numerical models are presented and discussed.

• 한국정밀공학회지
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• 제18권11호
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• pp.86-92
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• 2001

Vibrational characteristics and tension fluctuation of a translating wire in WEDM are the main problems to deteriorate the cutting accuracy and processing performance. In this paper, we analyze natural frequencies of the wire used in WEDM, both theoretically and experimentally. To reduce the tension variation of the wire, which directly affects cutting performance, we have designed a simply tension reduction device using springs and rollers. It is shown that tension fluctuation is reduced about 35% using the passive tension controller.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2003년도 추계학술대회논문집
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• pp.802-807
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• 2003

The purpose of this paper is to investigate the free vibration characteristics of tapered beams with translational and rotational springs and tip masses at the ends. The beam model is based on the classical Bernoulli-Euler beam theory. The governing differential equation for the free vibrations of linearly tapered beams is solved numerically using the corresponding boundary conditions. Numerical results are compared with existing solutions by other methods for cases in which they are available. The lowest three natural frequencies are calculated over a wide range of non-dimensional system parameters: the translational spring parameter, the rotational spring parameter, the mass ratio and the dimensionless mass moment of inertia.

• Structural Engineering and Mechanics
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• 제35권6호
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• pp.717-733
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• 2010

The dynamic stiffness matrix is formulated for an axially loaded slender double-beam element in which both beams are homogeneous, prismatic and of the same length by directly solving the governing differential equations of motion of the double-beam element. The Bernoulli-Euler beam theory is used to define the dynamic behaviors of the beams and the effects of the mass of springs and axial force are taken into account in the formulation. The dynamic stiffness method is used for calculation of the exact natural frequencies and mode shapes of the double-beam systems. Numerical results are given for a particular example of axially loaded double-beam system under a variety of boundary conditions, and the exact numerical solutions are shown for the natural frequencies and normal mode shapes. The effects of the axial force and boundary conditions are extensively discussed.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2003년도 춘계학술대회논문집
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• pp.864-869
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• 2003

The purpose of this paper is to investigate the free vibration characteristics of tapered beams with translational and rotational springs and point masses at the ends. The beam model is based on the classical Bernoulli-Euler beam theory which neglects the effects of rotatory inertia and shear deformation. The governing differential equation for the free vibrations of linearly tapered beams is solved numerically using the corresponding boundary conditions. Numerical results are compared with existing solutions by other methods for cases in which they are available. The lowest four natural frequencies are calculated over a range of non-dimensional system parameters.

• Steel and Composite Structures
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• 제8권4호
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• pp.265-280
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• 2008

An investigation on the combined effect of foundation type, foundation flexibility, axial load and PR (semi-rigid) connections on the natural frequencies of steel frames is presented. These effects were investigated using a suitable modified FE program for cases where the foundation flexibility, foundation connectivity, and semi-rigid connections could be treated as equivalent linear springs. The effect of axial load on the natural frequency of a structure was found to be significant for slender structures subjected to high axial loads. In general, if columns of medium slenderness are designed without consideration of axial load effects, the frequency of the structure will be overestimated. Studies on the 3-story Los Angeles PR SAC frame indicate that the assumption of rigid connections at beam-column and column-base interfaces, as well as the assumption of a rigid foundation, can lead to significant errors if simplified design procedures are used. These errors in an equivalent static analysis are expected to lead to even more serious problems when considering the effect of higher modes under a non-linear dynamic analysis.

• Steel and Composite Structures
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• 제33권3호
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• pp.403-432
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• 2019

Axially functionally graded (AFG) beams are a new class of composite structures that have continuous variations in material and/or geometrical parameters along the axial direction. In this study, the exact analytical solutions for the free vibration of AFG and uniform beams with general elastic supports are obtained by using Euler-Bernoulli beam theory. The elastic supports are modeled with linear rotational and lateral translational springs. Moreover, the material and/or geometrical properties of the AFG beams are assumed to vary continuously and together along the length of the beam according to the power-law forms. Accordingly, the accuracy, efficiency and capability of the proposed formulations are demonstrated by comparing the responses of the numerical examples with the available solutions. In the following, the effects of the elastic end restraints and AFG parameters, namely, gradient index and gradient coefficient, on the values of the first three natural frequencies of the AFG and uniform beams are investigated comprehensively. The analytical solutions are presented in tabular and graphical forms and can be used as the benchmark solutions. Furthermore, the results presented herein can be utilized for design of inhomogeneous beams with various supporting conditions.

• 풍력에너지저널
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• 제14권3호
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• pp.91-99
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• 2023

In research conducted on a southwestern Korean offshore meteorological tower, acceleration datasets were gathered over half a year with time-history sensors. To enhance data credibility, a parallel measurement system was used for verification. A model of the tower was configured using beam elements, and with modifications accounting for added stiffness from auxiliary structures. Ground interactions were considered as calibrated springs based on soil layer properties. The tower's dynamic attributes and mass sensitivity were discerned using eigenvalue analysis. The structural natural frequency was consistent, with variations primarily due to new equipment adding approximately 1400 kgs. With free vibration damping assumptions, a damping ratio of roughly 1 % was derived.

• Structural Engineering and Mechanics
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• 제55권3호
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• pp.655-674
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• 2015

In this paper, a new and simplified method is presented in which the natural frequencies of the uniform and non-uniform beams are calculated through simple mathematical relationships. The various vibration problems such as: Rayleigh beam under variable axial force, axial vibration of a bar with and without end discrete spring, torsional vibration of a bar with an attached mass moment of inertia, flexural vibration of the beam with laterally distributed elastic springs and also flexural vibration of the beam with effects of viscose damping are investigated. The governing differential equations are first obtained and then; according to a harmonic vibration, are converted into single variable equations in terms of location. Through repetitive integrations, the governing equations are converted into weak form integral equations. The mode shape functions of the vibration are approximated using a power series. Substitution of the power series into the integral equations results in a system of linear algebraic equations. The natural frequencies are determined by calculation of a non-trivial solution for system of equations. The efficiency and convergence rate of the current approach are investigated through comparison of the numerical results obtained with those obtained from other published references and results of available finite element software.

• Structural Engineering and Mechanics
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• 제61권6호
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• pp.785-794
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• 2017

This paper is concerned with the comparative numerical and experimental study on the natural behavior and the motion responses of a 1/75 moored scale model of a 2.5 MW spar-type floating offshore wind turbine subject to 1-D regular wave. Heave, pitch and surge motions and the mooring tensions are investigated and compared by numerical and experimental methods. The upper part of wind turbine which is composed of three rotor blades, hub and nacelle is modeled as a lumped mass and three mooring lines are pre-tensioned by means of linear springs. The numerical simulations are carried out by a coupled FEM-cable dynamics code, while the experiments are performed in a wave tank equipped with the specially-designed vision and data acquisition system. Using the both methods, the natural behavior and the motion responses in RAOs are compared and parametrically investigated to the fairlead position, the spring constant and the location of mass center of platform. It is confirmed, from the comparison, that both methods show a good agreement for all the test cases. And, it is observed that the mooring tension is influenced by all three parameters but the platform motion is dominated by the location of mass center. In addition, from the sensitivity analysis of RAOs, the coupling characteristic of platform motions and the sensitivities to the mooring parameters are investigated.