Advanced Steel Construction

Vol. 10, No. 1, pp. 14-32 (2014)



M.S. Abdel-Jaber 1, A.A. Al-Qaisia 2,* , M. Abdel-Jaber 3 and R.G. Beale 4

1Associate Professor, Department of Civil Engineering, The University of Jordan, Amman, Jordan

2Professor, Department of Mechanical Engineering, The University of Jordan, Amman, Jordan

3Associate Professor, Department of Civil Engineering, Faculty of Engineering and Technology, Applied Science University, Amman, Jordan

4Reader, Department of Mechanical Engineering and Mathematical Sciences,

Oxford Brookes University, Oxford, United Kingdom

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

Received: 4 June 2012; Revised: 2 July 2012; Accepted: 8 October 2012 




An analytical method for the study of the nonlinear forced vibrations and their stabilities of an elastically restrained tapered cantilever beam due to a direct periodic excitation is developed. The method of harmonic balance is used to study the steady state frequency response of the beam system for different values of physical parameters such as the root translational and rotational stiffness and the beam taper ratio. Results are presented for the first three modes of vibration. The stability of the frequency response for some selected values of the physical parameters is investigated, i.e. the regions on the frequency response curves at which the solution may bifurcate and then culminate into chaos. The qualitative features of the solutions are studied and identified using phase plane, Poincare maps and Fast Fourier Transform. The results are presented, discussed and conclusions on the elastically restrained tapered beam nonlinear dynamics are drawn.


Keywords: Forced vibration, tapered beam, elastically restrained, stability, period doubling, chaos


Download PDF: