04.1 - Aerospace Grade Materials, Structural Analysis, Fatigue and Damage Tolerance
GEOMETRICALLY EXACT MODEL OF CANTILEVER BEAM UNDERGOING LARGE DEFLECTION AND LINEARIZED DYNAMICS CHARACTERIZATION
C.Y. Yang¹, R. Zhao¹, Y.S. Gu¹, Z.C. Yang¹; ¹Northwestern Polytechnical University School of Aeronautics, China
Nonlinear beam theories are widely used to study the mechanical behavior of high-aspect-ratio flexible wings, helicopter rotor blades, deep-sea risers and pipelines. However, present theoretical models usually introduce some simplifications in the research process. For example, the higher-order terms of are neglected when using Green's strain to characterize the geometric nonlinear relationship, using the axial coordinates of the beam to approximately replace the arc-length coordinates, or simplifying the structure stress or strain when using the arc-length method to characterize the structural deformation. These treatments may cause the theoretical analysis results to deviate from the finite element simulation or experimental results. In this paper, the kinetic energy and potential energy of Euler-Bernoulli beam undergoing large deformation are accurately described with arc length and curvature coordinates. The rotation angle of the beam is discretized by Galerkin method, and the control equation of the cantilever beam structure with applied load is derived based on Lagrange method. The static large deformation of the beam structure subjected to external loads is solved, and the modal frequencies in the resulting deformed state are obtained. The calculation results of the present model agree well with those by the finite element simulation and experiment, which indicates that the geometrically exact model based on curvature and arc length coordinates has high accuracy.
DOI: 10.71945/icas2026_0071