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Integrability Conditions in Nonlinear Beam Kinematics

[+] Author Affiliations
Hidenori Murakami

University of California, San Diego, La Jolla, CA

Paper No. IMECE2016-65293, pp. V04BT05A068; 17 pages
  • ASME 2016 International Mechanical Engineering Congress and Exposition
  • Volume 4B: Dynamics, Vibration, and Control
  • Phoenix, Arizona, USA, November 11–17, 2016
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-5055-8
  • Copyright © 2016 by ASME


In order to develop an active nonlinear beam model, the beam’s kinematics is examined by employing the kinematic assumption of a rigid cross section during deformation. As a mathematical tool, the moving frame method, developed by Élie Cartan (1869–1951) on differentiable manifolds, is utilized by treating a beam as a frame bundle on a deforming centroidal curve. As a result, three new integrability conditions are obtained, which play critical roles in the derivation of beam equations of motion. They also serve a role in a geometrically-exact finite-element implementation of beam models. These integrability conditions enable the derivation of beam models starting from the three-dimensional Hamilton’s principle and the d’Alembert principle of virtual work. Finally, the reconstruction scheme for rotation matrices for given angular velocity at each time is presented.

Copyright © 2016 by ASME
Topics: Kinematics



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