HB-AFT analysis of geometrically exact beams considering nodal rotational inertia and gyroscopic force

In this paper, a modified HB-AFT method applying quaternion-based geometrically exact beam (GEB) systems is proposed, considering both rotational inertia and gyroscopic terms to ensure calculation accuracy. The partial derivatives of the inertial, internal, external, and constraint forces with respect to the quaternion-based state variable are derived. It is difficult to transform the equations of motion of GEB systems into the M , C , K forms, which are typically necessary for the traditional HB-AFT method. This study uses a method to expand the residual of the equations of motion of the entire GEB system and demonstrates that it smoothly performs dynamic analysis of cantilever beam structures. The accuracy of the proposed method is verified through comparison with direct simulation and the commercial software SIMPACK. The frequency responses indicate that the rotational inertia and gyroscopic terms have a considerable effect under specific conditions, such as a high frequency of external loads, and large rotational inertia. Furthermore, for cantilever beam structures, this study indicates that rotational inertia plays a major role in dynamic characteristics compared with gyroscopic effect, and the computational efficiency of HB-AFT is 8.4–13.8 times higher than that of direct simulation.