Reference Type:  Journal Article
Record Number: 1
Author: Abdel-Jaber, M., Al-Qaisia , A. A. and Abdel-Jaber, M. S.
Year: 2008
Title: Nonlinear natural frequencies of a tapered cantilever beam
Journal: Advanced Steel Construction
Volume: 5
Issue: 3
Pages: 14
Start Page: 259
Short Title: Nonlinear natural frequencies of a tapered cantilever beam
DOI: 10.18057/IJASC.2009.5.3.3
Keywords: Nonlinear, free vibration, harmonic balance, tapered beam, cantilever beam
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.
Author Address: Department of Mechanical Engineering, Faculty of Engineering and Technology, University of Jordan, Amman, Jordan