Vibration Analysis of Circular Plate with Continuously Varying Thickness

가변두께를 가지는 원판의 진동해석에 관한 연구

  • Received : 2005.11.01
  • Accepted : 2006.02.10
  • Published : 2006.02.27

Abstract

paper presents the results of the use of the differential transformation technique in analyzing the free vibration of circular plates.calculations were carried out and were compared with previously published results. The results that were obtained when this method was used coincide with the results of The present analysis shows the usefulness and validity of differential transformation in solving a solid-circular and annular-plate problem in terms of free-vibration responses.

Acknowledgement

Supported by : 안동대학교

References

  1. 권경문, 신영재, 유영순,(2001) 미분변환에 의한 비균질 보의 진동 해석, 한국소음진동공학회 2001년도 추계학술대회 논문집, pp. 617-621
  2. Chen, C. K and HO, S. H.(1999) Transverse vibration of a rotating twisted Timoshenko Beams under Axial Loading using Differential Transform, International Journal of Mechanical Sciences, vol.41, pp. 1339-1356 https://doi.org/10.1016/S0020-7403(97)00086-6
  3. Kovacs, B.(2001) Free Vibration of a Laminated circular Ring Segment, Journal of Sound and Vibration, vol. 245(4), pp. 653-667 https://doi.org/10.1006/jsvi.2000.3552
  4. Mehmet Utku, Ergin Citipitioglu and Ilker, Inceleme (2000), Circular plates on elastic foundations modelled with annular plates, Computers and Structures , vol. 78, pp. 365-374 https://doi.org/10.1016/S0045-7949(00)00063-8
  5. Selmane, A and Lakis, A. A.(1999) Nature Frequencies of Transverse Vibrations of Non-uniform Circular and Annular Plates, Journal of Sound and Vibration, vol. 220(2), pp. 255-249
  6. Zhou, J. K.(1986) Differential Transformation and its Application for Electrical Circuits, Huazhong University Press, Wuhan China(in Chinese)
  7. Laura, P. A. A. and Gutierrez, R. H.(2001) Transverse Vibration of a Damaged Circular Annular Plate with a Free Edge, Journal of Sound and Vibration, vol. 241(4), pp. 720-724 https://doi.org/10.1006/jsvi.2000.3271
  8. Arthur H. B. Mechanical Analysis and Design, Elsevier
  9. Laura, P. A. A. and Gutierrez, R. H.(1995) Analysis of Vibration Circular Plates of Nonuniform Thickness by the Method of Differential Quadrature, Ocean Engng. vol. 22, no. 1, pp. 97-100 https://doi.org/10.1016/0029-8018(94)00042-5
  10. Malik. Moinuddin and Dang. H. H.(1998) Vibration Analysis of Continuous Systems by Differential Transformation, Applied Mathematics and Computation, vol. 96, pp. 17-26 https://doi.org/10.1016/S0096-3003(97)10076-5
  11. Thomas, O. and Chaigne, A.(2002) Asymmeric Non-liner Forced Vibratin of Free-Edge Circular Plates. Part 1:Theory, Journal of Sound and Vibration, vol. 258(4), pp. 649-676 https://doi.org/10.1006/jsvi.2002.5143
  12. Zhou, Y. H.(2001) Shooting Method for Non-linear Vibration and Thermal Buckling of Heated Orthotropic Circular Plates, Journal of Sound and Vibration , vol. 248(2), pp. 379-386 https://doi.org/10.1006/jsvi.2001.3727
  13. 유영찬, 신영재,(2003) 조합하중을 받는 전단변형 기둥의 좌굴 후 거동 해석, 한국강구조학회 논문집, 제15권 3호, pp. 313-320
  14. Wu, T. Y. and Liu, G. R.(2001) Free Vibration Analysis of Circular Plates with variable Thickness by the Generalized Differential Quadrature Rule, International Journal of Solids and Structures, vol. 38, pp. 7967-7980 https://doi.org/10.1016/S0020-7683(00)00007-X
  15. Zhou, D., Au, F. T .K., Cheung, Y. K. and Lo, S. H.(2003) Three- dimensional vibration analysis of circular and annular plates via the Chebyshev Ritz method, International Journal of Solids and Structures, vol. 40, pp. 3089-3105 https://doi.org/10.1016/S0020-7683(03)00114-8
  16. Chen, C. K and WU, W. J.(1994) Application of the Taylor Differential Transformation Method to Viscous Damped Vibration of Hard and Soft spring System, Computer and Structures, vol. 59, no. 4, pp. 631-639 https://doi.org/10.1016/0045-7949(95)00158-1
  17. Gutirrez, R. H., Romanelli, E. and Laura, P. A. A.(1996) Vibrations and Elastic Stablity of Thin Circular Plates with Variable Profile, Journal of Sound and Vibration, vol. 195(3), pp. 391-399 https://doi.org/10.1006/jsvi.1996.0400
  18. 신영재, 권경문, 윤종학, 유영찬, 이주형,(2004) 미분변환법과 일반 화 미분구적법을 이용한 가변단면 원호 아치의 진동해석, 한국 강구조학회 논문집, 제16권 1호, pp. 81-89
  19. Celep, Z. and Gencoglu, M.(2003) Forced vibrations of a rigid circular plate on a tensionless Winkler edge support, Journal of Sound and Vibration, vol. 263, pp. 945-953 https://doi.org/10.1016/S0022-460X(02)01472-4
  20. Wang, C. Y. and Wang, C. M.(2003) Fundamental frequencies of circular plates with internal elastic ring support, Journal of Sound and Vibration, vol. 263, pp. 1071-1078 https://doi.org/10.1016/S0022-460X(02)01016-7
  21. 신영철, 신영재,(2001) Differential Transformation방법에 의한 가변단면을 갖는 봉의 진동해석, 한국해양공학회 2001년도 춘계학술대회 논문집, pp. 229-233