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.