Journal of KSNVE (소음진동)

The Korean Society for Noise and Vibration Engineering (한국소음진동공학회)
권호 표지

Double Fourier Sine Series Method for The Free Vibration of a Rectangular Plate

이중 사인 시리즈법에 의한 직사각형 평판의 자유 진동해석

  • 윤종욱 (서울대학교, 정밀기계설계공동연구소) ;
  • 이장무 (서울대학교 공과대학 기계설계학과)
  • Published : 1996.12.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, double Fourier sine series is used as a modal displacement functions of a rectangular plate and applied to the free vibration analysis of a rectangular plate under various boundary conditions. The method of stationary potential energy is used to obtain the modal displacements of a plate. To enhance the flexibility of the double Fourier sine series, Lagrangian multipliers are utilized to match the geometric boundary conditions, and Stokes' transformation is used to handle the displacements that are not satisfied by the double Fourier sine series. The frequency parameters and mode shapes obtained by the present method are compared with those obtained by MSC/NASTRAN and other analysis.

Keywords

References

  1. Formulas for Natural Frequency and Mode Shape Blevins, R. D.
  2. Energy and Variational Methods in Applied Mechanics Reddy, J. N.
  3. Table of Integrals, Series and Products Gradshteyn, I. S.;Ryzhik, I. M.
  4. Vibrations of Shells and Plates Soedel, W.
  5. Fourier Methods for Mathematicians, Scientists and Engineers Catwright M.
  6. MSC/NASTRAN User's Manual
  7. 한국 소음진동공학회 '94 춘계학술대회 논문집 경사진 내부 직선상에서 변위가 구속된 평판에 대한 이중푸리에 사인시리즈 방법의 자유 진동해석 윤종욱;이장무;김윤영
  8. Nuclear Engineering and Design v.63 Analysis Method for Calculating Vibration Characteristics of Beams with Intermediate Supports Chung, H.
  9. Free Vibration Analysis of Rectangular Plates Gorman, D. J.
  10. Vibration of Plates, NASA Sp, 160 Leissa, A. W.
  11. Engineering Thesis, Stanford University The Application of the FFT to the Analysis of Large Deflections of Beams and Plates Almeida, M. C. V.
  12. 서울대학교 공학 박사 학위 논문 경사진 방향으로 보강재 및 구속조건을 갖는 평판의 자유진동 해석에 관한 연구 윤종욱