Advanced Steel Construction

Vol. 5, No. 3, pp. 259-272 (2009)


NONLINEAR NATURAL FREQUENCIES OF A TAPERED CANTILEVER BEAM

 

M. Abdel-Jaber 1, A.A. Al-Qaisia 2,* and M.S. Abdel-Jaber 3

1 Department of Civil Engineering, Faculty of Engineering, Applied Science University, Amman, Jordan

2 Department of Mechanical Engineering, Faculty of Engineering and Technology,

University of Jordan, Amman, Jordan

3 Department of Civil Engineering, Faculty of Engineering and Technology,

University of Jordan, Amman, Jordan

*(Corresponding author: E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.)

Received: 5 November 2007; Revised: 17 January 2008; Accepted: 23 January 2008

 

DOI:10.18057/IJASC.2009.5.3.3

 

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ABSTRACT

  The non-linear natural frequencies of the first three modes of a clamped tapered beam are investigated. The mathematical model is derived using the Euler-Lagrange method and the continuous system is discretized using the assumed mode method. The resulted uni-modal nonlinear equation of motion was solved using the harmonic balance (HB) to obtain approximate analytical expressions for the nonlinear natural frequencies. Results were obtained for two types of taper; double taper, i.e. the beam width and thickness are varied linearly along the beam axis and single taper “wedge shaped beams”, i.e. the variation is in thickness only. The effects of vibration amplitude and taper ratio on the nonlinear natural frequencies for the first three modes are obtained and presented in non-dimensional form.

 

KEYWORDS

Nonlinear, free vibration, harmonic balance, tapered beam, cantilever beam


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