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

机译:基于绝对节点坐标公式的粘弹性梁动力学模型与行为

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摘要

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.
机译:粘弹性材料被广泛用于机制中,其性质对结构的动力学行为有很大的影响。在这项研究中,通过将材料的非线性应变-位移关系引入经典的Kelvin-Voigt模型,开发了一种改进的粘弹性本构模型。该模型可以直接应用到有限元绝对节点坐标公式中,可以用于研究大旋转和大变形问题。利用绝对节点坐标公式推导了具有剪切变形的二维粘弹性梁的质量矩阵和粘弹性刚度矩阵。基于牛顿方程,给出了梁的动力学模型。将动力学方程从一组微分代数方程组转换为一组一阶常微分方程,这些方程组是使用四阶显式Runge-Kutta方法计算的。使用自由下落的柔性摆来研究结构的动态行为与材料的力学行为之间的相关性。结果表明,改进的本构模型能够描述结构的非线性变形行为,该结构经历了大的旋转和大的变形。梁的柔性变形与材料的弹性模量,密度和粘度系数有关。材料的粘性行为减少了结构在运动过程中的弹性变形,这有利于多体系统的运动学精度。

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