工程结构多刚度尺度分析与模态理论

当前工程结构设计大多基于成熟的线性振动理论，未综合考虑非线性、多尺度等特性的影响，导致各类工程振动问题频发，减振措施失效.首先，本文以质量弹簧系统为例，对系统刚度比和质量比等关键参数开展分析，指出刚度比对系统模态具有显著影响；再者，简述大跨桥梁动力学研究现状，从系统全局动力学角度，根据非线性动力学分析和有限元分析，提出工程结构多刚度尺度概念，分析并指出多刚度尺度耦合系统的全局模态、局部模态和混合模态基于不同刚度尺度的定义.为建立桥梁全局动力学模型和理论，桥梁非线性动力学研究奠定基础.

Multiple Scale Analysis and Modal Theory of Engineering Structures

At present, the design of engineering structures is generally based on the mature linear vibration theory, without considering the influence of nonlinear and multi scale characteristics, which leads to the frequent occurrence of various vibration problems and the failure of vibration reduction measures. Firstly, this paper takes the mass-spring system as an example, and carries out the parametric influence of the stiffness ratio and mass ratio on the system vibration, of which the result points out that the stiffness ratio has a significant influence on the system modal property. In addition, the research overview on the long-span bridge dynamics is briefly discussed. From the perspective of system global dynamics, the concept of a multi stiffness scale of engineering structure is proposed based on nonlinear dynamics analysis and finite element analysis. The global modes, local modes and mixed modes of multi-stiffness scale coupling systems based on different stiffness scales are analyzed and pointed out. The research may lay the foundation for establishing the global dynamic model and theory of bridge and studying the nonlinear dynamics of the bridge.