Dynamic model and behavior of viscoelastic beam based on the absolute nodal coordinate formulation

Abstract

Viscoelastic material is widely used in mechanisms and its properties have a great influence on the dynamic behaviors of structures. In this study, a modified viscoelastic constitutive model is developed by introducing the nonlinear strain–displacement relation of materials to the classical Kelvin–Voigt model. The new model can be implemented into the finite element absolute nodal coordinate formulation directly, which can be applied to investigate the large rotation and the large deformation problem. The mass matrix and the viscoelastic stiffness matrix of a two-dimensional viscoelastic beam with shear deformation are derived with the absolute nodal coordinate formulation. The dynamic model of the beam is presented based on Newton equations. The dynamic equations are transformed from a set of differential algebraic equations to a set of first-order ordinary differential equations, which are calculated by using the fourth-order explicit Runge–Kutta method. A free falling flexible pendulum is employed to study the correlation between the dynamic behaviors of structures and the mechanical behaviors of materials. The results indicate that the modified constitutive model is able to describe the nonlinear deformation behavior of the structure, which undergoes large rotation and large deformation. The flexible deformation of the beam is related to the elastic modulus, the density and the viscosity coefficient of the material. The viscous behavior of material reduces the elastic deformation of the structure during its movement, which is beneficial to the kinematic accuracy of the multibody system.