Flexible body dynamics in a local frame with explicitly predicted motion

Abstract

SUMMARYThis paper deals with formulation of dynamics of a moving flexible body in a local frame of reference. In a conventional approach the local frame is normally fixed to the corresponding body and always represents the positions and angles of the body: the positions and angles are represented by Cartesian coordinates and Euler angles or Euler parameters, respectively. The elastic degrees of freedom are expressed by, e.g. nodal coordinates in a finite element analysis, modal coordinates, etc. However, the choice of these variables as the generalized coordinates makes the resulting equations of motion extremely complicated. This is because the representation of the rotation of a body is highly non-linear and this non-linearity makes the coefficient matrices dependent on the coordinates themselves. In this paper, we propose an alternative way of treating the issue by explicitly predicting the body motions and regularly updating the local frame. First, the motion of the local frame is assumed to explicitly follow the associated moving body. Then, the equations of motion are derived in a set of generalized coordinates that express both rigid-body and elastic degrees of freedom in the local frame. These equations are solved by a time integration with a given time interval. The motion of the local frame in the interval is estimated from a prediction of the rigid-body motions. Then, the gap between the predicted and the actual motions is evaluated. Finally, the predictions are iteratively corrected by the obtained responses in the rigid-body motions so that the gap should remain within an imposed tolerance.

63881 Coupling Analysis of Dynamics and Oil Film Lubrication on Rotor : Floating Bush Bearing System(Vehicle Dynamics & Control including Tire Dynamics)

“…The analysis method of the flexible multibody dynamics is based on the formulation proposed in former works by Kawamoto(1999Kawamoto( , 2009.…”

Hybrid state‐space time integration in a rotating frame of reference

“…This equivalence for isoparametric elements was used in [19]. However, for non-isotropic interpolation or models including rotation degrees of freedom there will in general be a difference between the resulting equations of motion, and the direct differentiation approach will lead to additional mass matrices [18].…”

“…The factor X D x multiplying the internal force g(u) constitutes an infinitesimal rigid body rotation, and thus the work of the internal forces through this displacement vanishes as explained in connection with the angular momentum equation (19). For isoparametric models the mass matrix consists of 3×3 blocks in the form M i j = m i j I, where m i j is the mass coefficient and I is the unit matrix.…”

Dynamic modeling of flexible multibody system using a meshing method

“…Wang 31 used the Ritz method and the Krylov subspace method to reduce the dimension of structural dynamic equations. Kawamoto et al 32 proposed a simple method for calculations explicitly predicting the body motions and regularly updating the local frame. Hence, the conventional flexible multibody dynamics methods are still difficult to be used because of their complexity.…”