• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.24 no.4
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• pp.317-323
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• 2014

This study is concerned with the free vibration analysis of an inextensible uniform rope with a spring-mass system at the tip. The rope is hanged vertically in a gravitational field. This problem is related to the free vibration of an elevator rope connected to an elevator cage. The equation of motion and the corresponding boundary conditions are derived by using the Hamilton's principle. The general solution of the governing equation of motion is expressed in terms of Bessel functions. The characteristic equation was derived by applying the boundary conditions. The characteristic values which are in fact non-dimensionalized natural frequencies were obtained numerically. The effects of mass and spring constant were investigated. The numerical results show how the tip mass and spring affect the natural frequencies of the rope.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.6
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• pp.681-689
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• 2008

This paper is concerned with the free vibration analysis of a circular plate with an eccentric circular hole by the Independent coordinate coupling method(ICCM). It was proved in the previous study that the ICCM can accurately predict the natural frequencies and mode shapes of the annular plates and can also be used for the free vibration analysis of the simply-supported circular plate with an eccentric circular hole. In this study, the clamped and free boundary conditions were considered for the circular plate. The numerical results show that the ICCM can be used effectively for the free vibration problem of circular plate with an eccentric hole compared to the finite element method.

• Journal of Power System Engineering
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• v.21 no.2
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• pp.70-76
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• 2017

When Timoshenko arcs considering the shear deformation and rotatory inertia have elastic supports, the authors analyze in-plane free vibration of them by the transfer influence coefficient method. This method finds the natural frequencies of them using the transfer of influence coefficient after obtaining the transfer matrix of arc element from numerical integration of the differential equations governing the vibration of arc. In this study, two computer programs were made by the transfer influence coefficient method and the transfer matrix method for analyzing free vibration of Timoshenko arcs. From numerical results of four computational models, we confirmed that the transfer influence coefficient method is a reliable method when analyzing the free vibration of Timoshenko arcs. In particular, the transfer influence coefficient method is a effective method when analyzing the free vibration of arcs with rigid supports.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.1073-1078
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• 2003

This paper presents the vibration characteristics of a cantilever beam in contact with a fluid using a PZT actuator and PVDF film. dynamic behaviors of a flexible beam-water interaction system are examined. The effect of the liquid level on free vibration of the composite beam in a partially liquid-filled circular cylinder is investigated. The coupled system is subject to an undisturbed boundary condition un the fluid domain. In the vibration analysis of a wetted beam. the decoupled analyses between beam and fluid have been conventionally employed by considering first the composite beam vibration in the all and secondly Performing the correction taking account for surrounding fluid effects. That is, this investigation was to look at how natural frequencies, mode shapes. and damping are affected by liquid level variations. The signals from the sensor according to the applied input voltage are digitalized and filtered in order to obtain the dynamic characteristics of the composite beam in contact with fluid. It was found that the coupled natural frequencies decreased with the fluid level for the identical composite beam due to added mass effect. In case of the free-free boundary condition, the natural frequency gently decreased at fluid water level between 20% and 80% in the first tending mode and we found out the bends of stair shape for added mass effect of the fluid.

• Advances in aircraft and spacecraft science
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• v.4 no.3
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• pp.269-280
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• 2017

The natural vibration analysis of microbeams resting on visco-Pasternak's foundation is presented. The thermoelasticity theory of Green and Naghdi without energy dissipation as well as the classical Euler-Bernoulli's beam theory is used for description of natural frequencies of the microbeam. The generalized thermoelasticity model is used to obtain the free vibration frequencies due to the coupling equations of a simply-supported microbeam resting on the three-parameter viscoelastic foundation. The fundamental frequencies are evaluated in terms of length-to-thickness ratio, width-to-thickness ratio and three foundation parameters. Sample natural frequencies are tabulated and plotted for sensing the effect of all used parameters and to investigate the visco-Pasternak's parameters for future comparisons.

• Structural Engineering and Mechanics
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• v.63 no.4
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• pp.551-565
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• 2017

In this paper, an analytical approach is proposed for determining vibration characteristics of cracked non-uniform continuous Timoshenko beam carrying an arbitrary number of spring-mass systems. This method is based on the Timoshenko beam theory, transfer matrix method and numerical assembly method to obtain natural frequencies and mode shapes. Firstly, the beam is considered to be divided into several segments by spring-mass systems and support points, and four undetermined coefficients of vibration modal function are contained in each sub-segment. The undetermined coefficient matrices at spring-mass systems and pinned supports are obtained by using equilibrium and continuity conditions. Then, the overall matrix of undetermined coefficients for the whole vibration system is obtained by the numerical assembly technique. The natural frequencies and mode shapes of a cracked non-uniform continuous Timoshenko beam carrying an arbitrary number of spring-mass systems are obtained from the overall matrix combined with half-interval method and Runge-Kutta method. Finally, two numerical examples are used to verify the validity and reliability of this method, and the effects of cracks on the transverse vibration mode shapes and the rotational mode shapes are compared. The influences of the crack location, depth, position of spring-mass system and other parameters on natural frequencies of non-uniform continuous Timoshenko beam are discussed.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2002.05a
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• pp.647-651
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• 2002

This study dealt with the free vibration of two identical rectangular plates coupled with fluid. In order to investigate the vibration characteristics of fluid-coupled rectangular plates, an analytical method based on the finite Fourier series expansion and Rayleigh-Ritz method was suggested. A commercial computer code, ANSYS was used to perform finite element analysis and we investigated the vibration characteristics with mode shapes and natural frequencies. As a result, the transverse vibration modes, in-phase and out-of-phase, were observed alternately in the fluid-coupled system. The effect of fluid bounding and plate boundary condition on the fluid-coupled natural frequency were investigated. It was shown that the mode numbers increased, the normalized natural frequencies monotonically increased.

• Structural Engineering and Mechanics
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• v.7 no.1
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• pp.53-67
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• 1999

The natural frequencies and modes of free vibration of specially orthotropic elliptic and circular plates are analysed using the Rayleigh-Ritz method. The assumed functions used are two-dimensional boundary characteristic orthogonal polynomials which are generated using the Gram-Schmidt orthogonalization procedure. The first five natural frequencies are reported here for various values of aspect ratio of the ellipse. Results are given for various boundary conditions at the edges i.e., the boundary may be any of clamped, simply-supported or fret. Numerical results are presented here for several orthotropic material properties. For rectilinear orthotropic circular plates, a few results are available in the existing literature, which are compared with the present results and are found to be in good agreement.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.808-813
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• 2003

This paper is analysis of opening thick plate on foundation. This paper has the object of investigating natural frequencies of opening thick plates on pasternak foundation by means of finite element method and providing Kinematic design data for mat of building structures. In this paper, vibration analysis of rectangular opening thick plate is done by use of Serendipity finite element with 8 nodes by considering shearing strain of plate. It is shown that natural frequencies depend on not only Winkler foundation Parameter but also shear foundation parameter, opening position, opening size.

• Journal of the Korean Geophysical Society
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• v.6 no.3
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• pp.125-130
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• 2003

The aim of this paper is to investigate the dynamic characteristics of ancient stone bridges in Korea and to find the factors influencing their natural frequencies. For this end, on-site free vibration tests were performed for 18 stone arch bridges and one ancient ice storage composed of 4 arches. Test results revealed that the vertical fundamental frequencies were in the range of 10Hz to 45Hz. The damping ratios estimated from the records of free vibration tests showed a wide variety of values, that is, from 0.02 to 0.134. It has been known that the natural frequencies of stone arch bridges are mainly governed by their arch spans. Test results reveal that the presence of spandrel walls and the use of mortar for joints are also important factors influencing the natural frequencies of stone arch bridges.