Abstract

Modal analysis is an often-used method for the solution of dynamical problems in engineering practice. In the case of continuous systems and discretization methods (e.g., FEM) with a large number of degrees of freedom, the reduced modal analysis is used, where only a selected number of modes are applied, while the higher modes are neglected. A piecewise linear elastic structure has state-dependent stiffness and as such, state-dependent vibration modes. During the dynamic modal analysis of such systems, one has to switch between the modes. During the switch a part of the kinetic and potential energy is transferring into modes, which are neglected in the reduced modal analysis. Thus, using the reduced modal analysis for the numerical calculation of the dynamic behavior of piecewise linear elastic structures introduces the modal truncation damping. In this paper, we present on a continuous system, how this modal truncation damping can be characterized, what are the upper and lower limits of that damping and how the characteristics of the free vibration of a piecewise linear elastic structure can be predicted.

摘要

模态分析是解决工程实践中动力学问题的常用方法。在具有大量自由度的连续系统和离散化方法（例如FEM）的情况下，使用简化的模态分析，其中仅应用选定数量的模式，而忽略较高的模式。分段线性弹性结构具有状态相关的刚度，因此具有状态相关的振动模式。在这种系统的动态模态分析期间，必须在模式之间进行切换。在切换期间，动能和势能的一部分转换为模式，在简化的模式分析中忽略了这些模式。因此，将简化的模态分析用于分段线性弹性结构动力学行为的数值计算中，会引入模态截断阻尼。