Browse > Article

Eigenvalue Analysis of Symmetrically Stepped Beams by Equivalent Beam Transformation  

Jung Jae-Chul (국민대학교 건축학과)
Moon Sang-Pil (국민대학교 건축학과)
Publication Information
Journal of the Computational Structural Engineering Institute of Korea / v.19, no.1, 2006 , pp. 55-62 More about this Journal
Abstract
The natural frequency of a beam plays a critical role in the dynamic analysis of beams. Especially it is a complicated and difficult task to analyse the natural frequency of a stepped beam with an irregularly varying section. The lumped mass methods, multi-degree of freedom analyses, are mainly used for the analysis of this kind of stepped beams. The accuracy of these methods are determined by the number of the partitions of elements, the number of the iterations in calculation, and the accuracy of assumed mode shapes. This study presents a method of transformation from symmetrically stepped beams to an equivalent beam and a method of the eigenvalue analysis. Appropriateness and utility of this method are demonstrated by comparing examples from other literatures and various models.
Keywords
stepped beam; equivalent stiffness; equivalent mass; equivalent beam; eigenvalue analysis;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Belytschko, T., Midle, W.L.(1980) Flexural Wave Propagation Behavior of Lumped Mass Approximations, Computer and Structures, 12, pp.805-812   DOI   ScienceOn
2 Hurty, W.C., Rubinstein, M.F. (1967) Dynamics of structures, Prentice-Hall of India Private Limited, New Delhi
3 Snowdon, J.C.(1968) Vibration and Shock in Damped Mechanical Systems, John Wiley and Sons, New York
4 Paz, M.(1997) Structural Dynamics Theory and Comuutation(4th ED.), CHAPMAN & HALL, New York
5 Thomson, W.T.(1981) Theory of Vibration with Application (2nd ED), Prentice-Hall, New Jersey
6 Church, A.H.(1963) Mechanical Vibration (2nd ED.), John Wiley and Sons, New York
7 Biggs, J.M.(1982) Structural Dynamics, Mcgraw Hill Book Co., New York
8 Timoshenko, S.P.(1921) On the correction for shear of the differential equation for transverse of prismatic bars, Pil mag, pp.744-746
9 김광식 외 5인 공저(1985) 기계진동학, 보성문화사
10 Clough, R.W., Penzien, J.(1982) Dynamics of Structures, Mcgraw Hill Book Co