Complex Modal Synthesis Method for Viscoelastic Flexible Multibody System Described by ANCF

Zuqing Yu, Zhuo Liu, Yu Wang, and Qinglong Tian
J. Comput. Nonlinear Dynam. Mar 2025, 20(3): 031004
https://doi.org/10.1115/1.4067522

The viscoelastic dynamic model of flexible multibody coupled with large rotation and deformation can be described by the absolute nodal coordinate formulation (ANCF). However, with the increase of degrees-of-freedom, the computational cost of viscoelastic multibody systems will be very high. In addition, for nonproportionally viscoelastic flexible multibody systems, the orthogonality and superposition of complex modes only exist in the state space. In this investigation, a systematical procedure of model reduction method for viscoelastic flexible multibody systems described by ANCF is proposed based on the complex modal synthesis method. First, the whole motion process of the system is divided into a series of quasi-static equilibrium configurations. Then the dynamic equation is locally linearized based on the Taylor expansion to obtain the constant tangent stiffness matrix and damping matrix. The initial modes and modal coordinates need to be updated for each subinterval. A modal selection criterion based on the energy judgment is proposed to ensure the energy conservation and accuracy by the minimum number of truncations. Finally, three numerical examples are carried out as verification. Simulation results indicate that the method proposed procedure reduces the system scale and improves the computational efficiency under the premise of ensuring the simulation accuracy.

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