• Coupled systems mechanics
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• v.12 no.2
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• pp.127-149
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• 2023

A theoretical method is developed to analyze the free vibration of an elastic annular plate in contact with an ideal liquid. The displacement potential functions of the contained liquid are expressed as a combination of the Bessel functions that satisfy the Laplace equation and the liquid boundary conditions. The compatibility condition along the interface between the annular plate and the contained liquid is taken into account to consider the fluid-structure coupling. The dynamic displacement of the wet annular plate is assumed to be a combination of dry eigenfunctions, allowing for prediction of the natural frequencies using the Rayleigh-Ritz method. The study investigates the effect of radial liquid boundary conditions on the natural frequencies of the wet annular plate, considering four types of liquid bounding: outer container bounded, outer and inner bounded, inner bounded, and radially unbounded. The proposed theoretical method is validated by comparing the predicted wet natural frequencies with those obtained from finite element analysis, showing excellent accuracy. The results indicate that the radial liquid bounding effect on the natural frequencies is negligible for the axisymmetric vibrational mode, but relatively significant for the mode with one nodal diameter (n =1) and no nodal circle (m' = 0). Furthermore, the study reveals that the wet natural frequencies are the largest for the plate with an inner bounded cylinder among the radial liquid boundary cases, regardless of the vibration mode.

• Structural Engineering and Mechanics
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• v.51 no.6
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• pp.893-907
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• 2014

Meshless local collocation method produces much better conditioned matrices than meshless global collocation methods. In this paper, the meshless local collocation method based on thin plate spline radial basis function and first-order shear deformation theory are used to calculate the natural frequencies and mode shapes of laminated composite shells. Through numerical experiments, the accuracy and efficiency of present method are demonstrated.

• Journal of Ocean Engineering and Technology
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• v.18 no.2
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• pp.46-51
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• 2004

Natural frequencies of the transverse vibration of beams with step change in cross-section are obtained by using the asymptotic closed form solution. This closed form solution is found by using WKB method under the assumption of slowly varying properties, such as mass, cross-section, tension etc., along the beam length. However, this solution is found to be still very accurate even in the case of large variation in cross-section and tension. Therefore, this result can be easily applied to many engineering problems.

• International Journal of Highway Engineering
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• v.15 no.3
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• pp.23-29
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• 2013

PURPOSES: This paper aims to give a guideline and the way to apply the advanced composite materials theory to the road structures with different cross sections to the practicing engineers. METHODS: To simple but exact method of calculating natural frequencies corresponding to the modes of vibration of road structures with different cross sections and arbitrary boundary conditions. The effect of the $D_{22}$ stiffness on the natural frequency is rigorously investigated. RESULTS: Simple method of vibration analysis for calculating the natural frequency of the different cross sections is presented. CONCLUSIONS: Simple method of vibration analysis for calculating the natural frequency of the different cross sections is presented. This method is a simple but exact method of calculating natural frequencies of the road structures with different cross sections. This method is extended to be applied to two dimensional problems including composite laminated road structures.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.7
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• pp.2108-2117
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• 1996

The purpose of this paper is to investigate the influence of the exciter attached for the measurement of natural frequencies when extracting the frequency response functions of the test structure in experimental modal analysis. The procedure is first to model the attached exciter as an additional degree of freedom system and next to verify the suggested model by experimentally extracting the natural frequencies of the test structure with various values of exciter mass, stinger stiffness and attachment position of the exciter on the test structure. It is concluded that as additional degree of freedom system which includes the natural frequency of the exciter itself and axial stiffness of stinger should be considered to quantatively define the coupling effects of structure-exciter interaction on the measured natural frequencies. It is not the mass of the exciter itself but the coupling effect of the additional degree of freedom mass-spring system consisting of exciter body and armature coil that characterizes the natural frequency deviation. Therefore, when the natural frequency of this additional mass-spring system is outside of the test frequency range, the coupling effect of structure-exciter interaction can be minimized.

• Proceedings of the KSR Conference
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• 2001.10a
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• pp.304-309
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• 2001

Natural frequencies are studied for dynamic analysis of plate girder bridges which are made up about 34% in the existing railway bridges in Korea. In this study, standard plate girder bridges designed by L-22, a standard load type of the railway specification in Korea, are modeled for finite element method analysis. SAP2000n, a commercial finite element method analysis tool, is used for structural analyses and evaluations. Span lengths of Plate girders have 7 types : 6m, 9m, 12m, 15m, 22m, 24m, and 30m. Natural frequencies are considered in mass rations and span lengths and they are compared with a recommendation of UIC 776-1R for alterations, from now on, in train conditions of operation. For changes of natural frequencies in plate girders by damages of structures, Parameter studies are accomplished.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.22 no.1
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• pp.49-57
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• 1986

The vibrations problem of thin orthotropic skew plates of linearly varying thickness is analyzed using the small deflection theory of plates. Using dimensionless oblique coordinates, the deflection surface can be expressed as a polyonmial series satisfying the boundary conditions. For orthotropic plates which is clamped on all the four edges, numerical results for the first two natural frequencies are presented for various combinations of aspect ratio, skew angle and taper parameter. The properties of material used are one directional glass fibre reinforced plastic GFRP. The results obtained may be summarised as follows: 1. In case of the first mode vibration of plates with increase in the skew angle, the natural frequencies of plates decrease. 2. As the aspect ratio decrease, the natural frequencies of plates decrease. 3. For the identical skew angle, natural frequencies of plates increase with the taper parameter of thickness.

• Magazine of the Korean Society of Agricultural Engineers
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• v.34 no.1
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• pp.57-65
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• 1992

The main purpose of this paper is to present both the natural frequencies and mode shapes of tapered beams under tensile axial force. The differential equation governing planar free vibration for tapered beams under tensile axial force is derived as nondimensional form. The three kinds of cross sectional shape are considered in differential equation. The Runge-Kutta method and Determinant Search method are used to perform the integration of the differential equation and to determine the natural frequencies, respectively. The hinged-hinged, hinged-clamped, clamped-clamped and constraints are applied in numerical examples. The lowest four nondimensional natural frequencies are reported as the function of nondimensional tensile axial force. The fundamental natural frequencies are presented when section ratios and nondimensional axial forces are varied. The effects of cross sectional shapes are reported and some typical mode shapes are also presented.

• Journal of KSNVE
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• v.3 no.3
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• pp.259-269
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• 1993

For efficient use of composite materials in engineering applications the dynamic behavior, that is, natural frequencies, nodal patterns should be informed. This study presents the experimental and FEM results for the free vibration of cantilevered, symmetrically and antisymmetrically laminated composite triangular plates. The natural frequencies and nodal patterns of a number of CFRP, GFRP, composite-Aluminum and CFRP-GFRP hybrid composite plates are experimentally obtained. A method for the determination of the Young's modulus and test procedures are described. The natural frequencies are determined for a wide range of parameters: e.g., composite material constants, fiber angles and stacking sequences. Natural frequency and nondimensional frequency parameter results are compared with the finite element analysis and existing literatures. Agreement between experimental and calculated frequencies is excellent.

• Journal of Environmental Science International
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• v.5 no.1
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• pp.1-6
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• 1996

The genetic variabilities of second chromosomes of Drosophila melanogaster concealed in On-yang natural Population have been analyzed by the Cy/Pm method and an allelism test during two years(1993-1994). The mean frequencies of deleterious(lethal and semilethal) genes in On-yang natural population were estimated to be 23.97% in 1993 and 27.15% in 1994, respectively. The allelism rates between lethal genes in the population were 0.654%(1993) and 1.429%(1994). The mean values of elimination by frequencies of deleterious genes and allelism rates were 0.0004(1993) and 0.0010(1994), respectively. The frequencies of phenotypic sterility of males in 1994 were estimated to be 1.95%, and thoses of genotypic sterility of females and males were estimated to be 1.54% and 2.31%, respectively.