Author(s)

Yumei Luo¹, Yundong Li^1,2*, Linyan Li¹, Zhongxiang Li¹

¹School of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong, China.
²South Sichuan Center for Applied Mathematics, Sichuan University of Science and Engineering, Zigong, China.

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.

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

Luo, Y. , Li, Y. , Li, L. and Li, Z. (2025) Mathematical Model of the Tapered Cantilever Beam Based on the Geometrically Exact Beam Theory. Journal of Applied Mathematics and Physics, 13, 490-505. doi: 10.4236/jamp.2025.132027.