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Natural Frequencies of Beams with Step Change in Cross-Section

Kim, Yong-Cheul   (School of Mechanical Engineering, Yeungnam UniversityUU0000951  ); Nam, Alexander-V.    (School of Mechanical Engineering, Yeungnam University  );
  • 초록

    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.


  • 주제어

    Natural Frequencies .   Asymptotic Closed Form Solution .   WKB method .   Variable Properties .   Step Change in Cross-Section.  

  • 참고문헌 (11)

    1. Karnovsky,I.A.;Lebed,O.I. , Formulas for Structural Dynamics / v.,pp.,
    2. Natural Frequencies of a Beam on Inhomogeneous Foundation , Kim,Y.C. , Journal of Ocean Engineering and Technology / v.6,pp.60-77,
         
    3. Nonlinear Vibrations of Long Slender Beams , Kim,Y.C. , Ph.D.Thesis, Department of Ocean Engineering, M.I.T. / v.,pp.,
    4. Vibration of an Euler-Bernoulli Beam on Elactic End Supports and with up to Three Step Changes in Cross-Section , Naguleswaran,S. , International Journal of Mechanical Sciences / v.44,pp.2541-2555,
    5. Geradin,M.;Rixen,D. , Mechanical Vibration, Theory and Application to Structural Dynamics / v.,pp.,
    6. Free Vibrations of Stepped Beams: Higher Mode Frequencies and Effects of Steps on Frequency , Jang,S.K.;Bert,C.W. , Journal of Sound and Vibration / v.132,pp.164-168,
    7. Natural frequencies and Critical Buckling Loads of Marine Risers , Kim,Y.C. , Transactions of the ASME / v.110,pp.2-8,
    8. Vibration of Stepped Strings and Beams , Levinson,M. , Journal of Sound and Vibration / v.49,pp.287-291,
    9. Free Vibrations of Stepped Beams: Exact and Numerical Solutions , Jang,S.K.;Bert,C.W. , Journal of Sound and Vibration / v.130,pp.342-346,
    10. Natural Frequencies,Sensitivity and Mode Shape Details of an Euler-Bernoulli Beam with One-Step Change in Cross-Section and with Ends on Classical Supports , Naguleswaran,S. , Journal of Sound and Vibration / v.252,pp.751-767,
    11. The Nonlinear Dynamics of Long Slender Cylinders , Kim,Y.C.;Triantafyllou,M.S. , ASME Journal of Energy Resources Technology / v.106,pp.250-256,

 저자의 다른 논문

  • Kim, Yong-Cheul (1)

    1. 2010 "An Asymptotic Solution and the Green's Function for the Transverse Vibration of Beams with Variable Properties" 韓國海洋工學會誌 = Journal of ocean engineering and technology 24 (1): 34~38    

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