• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1994.10a
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• pp.173-180
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• 1994

본 논문에서는 임의 형상의 블록 다각형 박막 고유 진동해석을 위해 파 형태의 해석해를 사용하는 새로운 기법을 제시하였다. 파 형태의 해석해를 임의 형상의 박막에 사용하는 데 있어 나타날 수 있는 시도해의 종속적인 문제점을 지적하고, 이를 극복하는 방안을 제시하였다. 여러 수치 예제를 통해 본 기법의 유용성과 타당성을 보였고, 특히 이 기법은 특정 주파수 대역에서 고유 진동수를 찾고자 할 때, 매우 효율적임을 알 수 있다. 본 논문은 기초 연구로서 제한된 모든 변이 고정된 블록 다각형 형상의 박막의 고유 진동 해석만 수행하였지만, 이 기법을 확장, 발전시켜 나가면, 어떠한 형상이나 경계조건을 갖는 박막뿐만 아니라 평판의 진동 해석에도 적용할 수 있으리라 기대하며, 이를 위한 연구가 진행중이다.

• Journal of the Korean Society for Railway
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• v.15 no.6
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• pp.588-596
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• 2012

This paper presents a new semi-analytical annular Mindlin plate element with which out-of-plane natural vibration of thick disks can be analyzed simply, efficiently, and accurately through FEM by including effects of rotary inertia and transverse shear deformation. Using static deformation modes which are exact solutions of equilibrium equations of annular Mindlin plate, the element interpolation functions, stiffness and mass matrices corresponding to each number of nodal diameters are derived. The element is capable of representing out-of-plane rigid-body motions exactly and free from shear locking. Natural frequencies of uniform and multi-step disks with or without concentric ring support are analyzed by applying the presented element. Such results are compared with theoretical predictions of previous works or FEA results obtained by using two-dimensional shell element to investigate the convergence and accuracy of the presented element.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.23 no.8
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• pp.725-733
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• 2013

An improved formulation of the MNDIF method is introduced to extract highly accurate natural frequencies of concave plates with arbitrary shape. Originally, the MNDIF method cannot yield accurate natural frequencies for concave plates. It can be applicable to only convex plates. To overcome this weak point, a new approach of dividing a concave plate into two convex domains and applying the MNDIF method to each domain is proposed and the validity and accuracy are shown in verification examples.

• Journal of Korean Society of Steel Construction
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• v.12 no.4 s.47
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• pp.363-374
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• 2000

An accurate method is presented for vibrations of rhombic plates having three different combinations of clamped, simply supported, and free edge conditions. A specific feature here is that the analysis explicitly considers the moment singularities that occur in the two opposite corners having obtuse angles of the rhombic plates. Stationary conditions of single-field Lagrangian functional are derived using the Ritz method. Convergence studies of frequencies show that the corner functions accelerate the convergence rate of solutions. In this paper, accurate frequencies and normalized contours of the vibratory transverse displacement are presented for highly skewed rhombic plates, so that a significant effect of corner stress singularities nay be understood.

• Journal of Korean Society of Steel Construction
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• v.10 no.4 s.37
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• pp.601-613
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• 1998

This paper reports the first-of-its-kind free vibration solutions for sectorial plates having re-entrant corners causing stress singularities when the circular edge is either clamped or simply supported. The Ritz method is employed with two sets of admissible functions assumed for the transverse vibratory displacements. Accurate frequencies and normalized contours of the transverse vibratory displacement are presented for the spectra of sector angles.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.22 no.9
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• pp.830-836
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• 2012

The NDIF method based on a sub-domain technique is introduced to extract highly accurate natural frequencies of arbitrarily shaped plates with the simply-supported boundary condition. The NDIF method, which was developed by the authors for the eigen-mode analysis of arbitrarily shaped plates with various boundary conditions, has the feature that it yields highly accurate natural frequencies thanks to its effective theoretical formulation, compared with other analytical methods or numerical methods(FEM and BEM). However, the NDIF method has the weak point that it can be applicable for only convex plates. It was revealed that the NDIF method offers very inaccurate natural frequencies or no solution for concave cavities. To overcome the weak point, the paper proposes the sub-domain method of dividing a concave plate into several convex domains. Finally, the validity of the proposed method is verified in various case studies, which indicate that natural frequencies obtained by the proposed method are very accurate compared to the exact method and FEM(ANSYS).

• Journal of the Society of Naval Architects of Korea
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• v.30 no.1
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• pp.134-144
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• 1993

Sandwich plate is consisted of equal two isotropic, thin, stiff and strong sheets of dense material separated symmetrically by an isotropic thick layer which may be much less stiff and strong. This study analyzed the dependency of the natural frequencies and mode shapes of sandwich plates on material properties, thicknesses of faces and cores, and various boundary conditions using Rayleigh-Ritz method. E-glass Woven Roving and another two kinds of materials were selected as a face, P.V.C. and another kinds of materials were selected as a core. Natural frequencies and mode shapes obtained by Rayleigh-Ritz method were compared with F.E.M. solutions using ADINA program.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.8
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• pp.1485-1492
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• 1992

While the vibration of circular plates were considered by many researchers, rather less attention is given to elliptical plates. In the present paper, the Rayleigh-Ritz mothod is used to obtain an eigenvalue equation for the free flexural vibration of thin elliptical plates having the classical free, simply suported or clmped boundary condition. Circular plates are included as a special case of the elliptical plates. Products of simple polynomials are used as the admissible functions and a recurrence relationship facilitates the evaluation of the necessary integrals. The analysis is developed for rectilinear orthotropic plates but the numerical results are given for isotropic plates with various aspect ratios.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.26 no.5
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• pp.602-608
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• 2016

The paper proposes a practical meshless method for the free vibration analysis of clamped plates having arbitrary shapes by extending the non-dimensional dynamic influence function (NDIF) method, which was developed by the author in 1999. In the proposed method, the domain and boundary of the plate of interest are discretized using only nodes without elements unlike FEM and the system matrices are obtained by making domain nodes and boundary nodes satisfy the governing differential equation and boundary conditions, respectively. However, since the above system matrices are not square ones, the problem of free vibrations of clamped plates is not reduced to an algebraic eigenvalue problem. An additional theoretical treatment is considered to produce an algebraic eigenvalue problem. It is revealed from case studies that the proposed method is valid and accurate.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.12 no.10
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• pp.785-791
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• 2002

A modeling method for the dynamic characteristic analysis of a translationally accelerated trapezoidal cantilever plate is presented in this paper. The equations of motion for the plate are derived and transformed into a dimensionless form. The effects of the inclination angles and the acceleration on the vibration characteristics of the plate are investigated. Incidentally, natural frequency loci veering and associated mode shape variations are observed and discussed.