In order to develop an active nonlinear beam model, the beam's kinematics is examined in this paper, by employing the kinematic assumption of a rigid cross section during deformation. As a mathematical tool, the moving frame method, developed by 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. These integrability conditions enable the derivation of beam models in Part II, starting from the three-dimensional Hamilton's principle and the d'Alembert's principle of virtual work. To illustrate the critical role played by the integrability conditions, the variation of kinetic energy is computed. Finally, the reconstruction scheme for rotation matrices for given angular velocity at each time is presented.
Development of an Active Curved Beam Model—Part I: Kinematics and Integrability Conditions
Manuscript received December 16, 2016; final manuscript received March 18, 2017; published online April 18, 2017. Assoc. Editor: Yihui Zhang.
Murakami, H. (April 18, 2017). "Development of an Active Curved Beam Model—Part I: Kinematics and Integrability Conditions." ASME. J. Appl. Mech. June 2017; 84(6): 061002. https://doi.org/10.1115/1.4036308
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