Structural Engineering and Mechanics

  • 제8권3호
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  • Pages.243-256
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  • 1999
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Flexural free vibration of cantilevered structures of variable stiffness and mass

  • Li, Q.S. (Department of Building and Construction, City University of Hong Kong)
  • 발행 : 1999.09.25
⟨ 이전 논문 다음 논문 ⟩

초록

Using appropriate transformations, the differential equation for flexural free vibration of a cantilever bar with variably distributed mass and stiffness is reduced to a Bessel's equation or an ordinary differential equation with constant coefficients by selecting suitable expressions, such as power functions and exponential functions, for the distributions of stiffness and mass. The general solutions for flexural free vibration of one-step bar with variable cross-section are derived and used to obtain the frequency equation of multi-step cantilever bars. The new exact approach is presented which combines the transfer matrix method and closed form solutions of one step bars. Two numerical examples demonstrate that the calculated natural frequencies and mode shapes of a 27-storey building and a television transmission tower are in good agreement with the corresponding experimental data. It is also shown through the numerical examples that the selected expressions are suitable for describing the distributions of stiffness and mass of typical tall buildings and high-rise structures.

키워드

참고문헌

  1. B.M. Kumar and R.l. Sujith (1997), "Exact solutions for the longitudinal vibration of non-uniform rods", Journal of Sound and Vibration, 207(5), 721-729. https://doi.org/10.1006/jsvi.1997.1146
  2. Q.S. Li, H. Cao and G. Li (1994), "Analysis of free vibrations of tall buildings", ASCE, Journal of Engineering Mechanics, 120(9), 1861-1876. https://doi.org/10.1061/(ASCE)0733-9399(1994)120:9(1861)
  3. Q.S. Li, H. Cao. and G. Li (1995), "Calculation of free vibration of high-rise structures" , Asian Journal of Structural Engineering, 1(1), 17-25.
  4. Q.S. Li, H. Cao and G. Li (1996), "Static and dynamic analysis of straight bars with variable crosssection" , International Journal of Computers & Structures, 59(6), 1185-1191. https://doi.org/10.1016/0045-7949(95)00333-9
  5. Q.S. Li, J.Q. Fang and A.P. Jeary (1998), "Free longitudidal vibration analysis of tall buildings and high-rise" , The Structural Design of Tall Buildings, 1, 167-176.
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피인용 문헌

  1. FREE VIBRATION ANALYSIS OF NON-UNIFORM BEAMS WITH AN ARBITRARY NUMBER OF CRACKS AND CONCENTRATED MASSES vol.252, pp.3, 2002, https://doi.org/10.1006/jsvi.2001.4034
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  7. Nonlinear oscillation of a cantilever FGM rectangular plate based on third-order plate theory and asymptotic perturbation method vol.42, pp.3, 2011, https://doi.org/10.1016/j.compositesb.2010.12.010
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  12. EXACT SOLUTIONS FOR FREE LONGITUDINAL VIBRATIONS OF NON-UNIFORM RODS vol.234, pp.1, 2000, https://doi.org/10.1006/jsvi.1999.2856
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