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Al-Ansari, L.S., Al-Hajjar, A.M.H. and Jawad, H. (2018) Calculating the Natural Frequency of Cantilever Tapered Beam Using Classical Rayleigh, Modified Rayleigh and Finite Element Methods. International Journal of Engineering & Technology, 7, 4866-4872.

has been cited by the following article:

• TITLE: Mathematical Model of the Tapered Cantilever Beam Based on the Geometrically Exact Beam Theory

  AUTHORS: Yumei Luo, Yundong Li, Linyan Li, Zhongxiang Li

  KEYWORDS: Geometrically Exact Beam Theory, The Tapered Cantilever Beam, Natural Frequency

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.13 No.2, February 20, 2025

  ABSTRACT: Based on the geometrically exact beam theory, the mathematical model of the tapered cantilever beam is built, and analysis of the structures under load is completed. With the stress-strain relationship of geometrically exact beam theory, and the principle of virtual displacement and D’Alembert principle, the virtual work balance equation of the tapered cantilever beam element is derived. The internal force, external force, and inertial force virtual work of the beam element is discretized by weak form quadrature element method. The numerical results show the variation of the natural frequency of the beam with the taper when the tapered cantilever beam is not subjected to the load and the free end is subjected to the concentrated load and bending moment.