Viscoelasticity plays an important role in the dynamic response of flexible multibody systems. First, single degree-of-freedom joints, such as revolute and prismatic joints, are often equipped with elastomeric components that require complex models to capture their nonlinear behavior under the expected large relative motions found at these joints. Second, flexible joints, often called force or bushing elements, present similar challenges and involve up to six degrees of freedom. Finally, flexible components such as beams, plates, and shells also exhibit viscoelastic behavior. This paper presents a number of viscoelastic models that are suitable for these three types of applications. For single degree-of-freedom joints, models that capture their nonlinear, frequency-dependent, and frequency-independent behavior are necessary. The generalized Maxwell model is a classical model of linear viscoelasticity that can be extended easily to flexible joints. This paper also shows how existing viscoelastic models can be applied to geometrically exact beams, based on a three-dimensional representation of the quasi-static strain field in those structures. The paper presents a number of numerical examples for three types of applications. The shortcomings of the Kelvin–Voigt model, which is often used for flexible multibody systems, are underlined.

粘弹性在柔性多体系统的动态响应中起着重要作用。首先，单自由度关节（例如旋转关节和棱柱形关节）通常配备有弹性体组件，这些组件需要复杂的模型才能捕获在这些关节处预期的较大相对运动下的非线性行为。其次，通常称为力或衬套元件的柔性接头也面临类似的挑战，并且涉及多达六个自由度。最后，诸如梁，板和壳之类的柔性组件也表现出粘弹性。本文介绍了适用于这三种类型应用的许多粘弹性模型。对于单自由度关节，需要捕获其非线性，与频率有关和与频率无关行为的模型。广义麦克斯韦模型是线性粘弹性的经典模型，可以轻松地扩展到挠性接头。本文还展示了如何基于这些结构中准静态应变场的三维表示，将现有的粘弹性模型应用于几何精确的梁。本文为三种类型的应用提供了许多数值示例。强调了常用于柔性多体系统的Kelvin-Voigt模型的缺点。本文为三种类型的应用提供了许多数值示例。强调了常用于柔性多体系统的Kelvin-Voigt模型的缺点。本文为三种类型的应用提供了许多数值示例。强调了常用于柔性多体系统的Kelvin-Voigt模型的缺点。