Dynamic Modeling of Viscoelastic Body in Multibody System
Dynamic equations of viscoelastic bodies with fractional constitutive are derived base on the principle of virtual work and the theory of continuum mechanics. The three-dimensional fractional derivative viscoelastic constitutive model is implemented into the flexible multibody system (FMBS), using the 3D solid element based on the absolute nodal coordinate formulation (ANCF), which can exactly describe the geometric nonlinearities due to large rotation and large deformation. The BDF time integration scheme in conjunction with the Grünwald approximation of fractional derivative and the Newton-Raphson algorithm are used to solve the equations of motion. Several numerical examples are presented to demonstrate the use of the modeling procedure presented in this investigation and the effects of parameters in the fractional derivative model.
Paul P. Lin and Chunliang Zhang
D. Z. Cao et al., "Dynamic Modeling of Viscoelastic Body in Multibody System", Applied Mechanics and Materials, Vols. 105-107, pp. 587-594, 2012