• Journal of the Earthquake Engineering Society of Korea
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• v.3 no.1
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• pp.9-20
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• 1999

An accurate method is presented for flexural vibrations of rhombic plates having all combinations of clamped and free edge conditions. The prime focus here is that the analysis explicitly considers the bending stress singularities that occur in the two opposite, clamped-free corners having obtuse angles of the rhombic plates. Accurate non-dimensional frequencies and normalized contours of the vibratory transverse displacement are presented for rhombic plates having a large enough obtuse angle of 165$^{\circ}$, so that a significant influence of clamped-free corner stress singularities may be understood.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.21 no.4
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• pp.401-410
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• 2008

The natural frequency of a beam plays an important role in not only vibration analysis but also understanding its dynamic characteristics. It is complicated to analyse the natural frequency of a stepped beam with discontinuously varying section. Approximate analysis methods such as Rayleigh-Ritz method, FEM, etc. are frequently used for the vibration analysis of stepped beams. In such a case, accuracy of these methods depends upon the number of partitioned elements, the number of the iterations in calculation and the assumed mode shape. This study presents an approximate analysis method for the fundamental natural frequency analysis of stepped cantilever beam, using equivalent beam transformation technique. Validity and usefulness are verified by comparing the proposed method with FEM for several example problems.

• Journal of the Earthquake Engineering Society of Korea
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• v.16 no.3
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• pp.1-12
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• 2012

In this study, an analysis method for the earthquake response of an offshore wind turbine model is developed, considering the effects of the fluid-structure-soil interaction. The turbine is modeled as a tower with a lumped mass at the top of it. The tower is idealized as a tubular cantilever founded on flexible seabed. Substructure and Rayleigh-Ritz methods are used to derive the governing equation of a coupled structure-fluid-soil system incorporating interactions between the tower and sea water and between the foundation and the flexible seabed. The sea water is assumed to be a compressible but non-viscous ideal fluid. The impedance functions of a rigid footing in water-saturated soil strata are obtained from the Thin-Layer Method (TLM) and combined with the superstructure model. The developed method is applied to the earthquake response analysis of an offshore wind turbine model. The method is verified by comparing the results with reference solutions. The effects of several factors, such as the flexibility of the tower, the depth of the sea water, and the stiffness of the soil, are examined and discussed. The relative significance of the fluid-structure interaction over the soil-structure interaction is evaluated and vice versa.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.1A
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• pp.125-133
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• 2008

According to longer and longer span, dynamic instability of stay cable should be prevented. Dynamic instability occurs mainly symmetric 1st mode and antisymmetric 1st mode in stay cable. Especially symmetric 1st mode has a lot of influence on sag. Therefore fundamental frequency of stay cable is different from that of taut sting. Irvine, Triantafyllou, Ahn etc. analyzed dynamic behavior of taut cable with sag through analytical technical and their researches give important results for large bounds of Irvine parameter. But each research shows mutually different values out of characteristic (cross-over or mode-coupled) point and each solution of frequency equations of all researchers can be very difficultly found because of their very high non-linearity. Presented study focuses on fundamental frequency of stay cable. Generalized mechanical energy with symmetric 1st mode vibration shape satisfied boundary conditions is evolved by Rayleigh-Ritz method. It is possible to give linear analytic solution within characteristic point. Error by this approach shows only below 3% at characteristic point against existing researches. And taut cable don't exceed characteristic point. I.e. high accuracy, easy solving techniques, and a little bit limitations. Therefore presented study can be announced that it is good study ergonomically.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.3
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• pp.347-352
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• 2007

Eigenvalue reduction schemes approximate the lower eigenmodes that represent the global behavior of the structures. In the previous study, we proposed a two-level condensation scheme (TLCS) for the construction of a reduced system. In the first step, the selection of candidate elements by energy estimation, Rayleigh quotient, through Ritz vector calculation. In the second step, the primary degrees of freedom are selected by the sequential elimination method from the degrees of freedom connected to the candidate elements in the first step. In the present study, we propose TLCS combined with iterative improved reduced system (IIRS) to increase accuracy of the higher modes in the intermediate range. Also, it is possible to control the accuracy of the eigenvalues and eigenmodes of the reduced system. Finally, numerical examples demonstrate the performance of the proposed method.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.15 no.4
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• pp.609-617
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• 2002

A three-dimensional(3-D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, circular rings with isosceles trapezoidal and triangular cross-sections. Displacement components u/sub s/, u/sub z/, and u/sub θin the meridional, normal, and circumferential directions, respectively, are taken to be sinusoidal in time, periodic in θ, and algebraic polynomials in the ψ and z directions. Potential(strain) and kinetic energies of the circular ring are formulated, and upper bound values of the frequencies we obtained by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Novel numerical results are presented for the circular rings with isosceles trapezoidal and equilateral triangular cross-sections having completely free boundaries. Convergence to four-digit exactitude is demonstrated for the first five frequencies of the rings. The method is applicable to thin rings, as well as thick and very thick ones.