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A dynamic stiffness-based modal analysis method for a double-beam system with elastic supports

机译：弹性支架双梁系统的基于动态刚度的模态分析方法

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摘要

The double-beam system with several elastic supports is one of most significant mechanical models in engineering structures. Its dynamic characteristics are crucial for structural design, vibration control, health monitoring, and other dynamic issues. In the dynamic analysis of double-beam systems, since existing researches often need to make some assumptions or approximations to the displacement function, the accuracy and application range of the analysis results are limited. In view of this, this article proposes an exact modal analysis method for the double-beam system based on the dynamic stiffness method. It can consider the effect of boundary conditions, the differences in the material and structural of the two beams, the axial forces and other factors simultaneously without any approximation. During the analysis, the accuracy of the proposed method is verified first by comparing with finite element solutions. Then, the influence of elastic supports on modal characteristic is discussed, and the variation law of the dynamic stiffness in frequency domain is investigated. Finally, a dynamic stiffness-based method for determining the contributions of the two beams to each mode of the system is provided. The method can be extended to quickly obtain the frequency and mode shape information of the system without solving the frequency equation or characteristic equation.
机译：具有多个弹性支撑件的双光束系统是工程结构中最重要的机械模型之一。其动态特性对于结构设计，振动控制，健康监测和其他动态问题至关重要。在双光束系统的动态分析中，由于现有研究通常需要对位移函数进行一些假设或近似，因此分析结果的精度和应用范围是有限的。鉴于此，本文提出了一种基于动态刚度法的双光束系统的精确模态分析方法。它可以考虑边界条件的影响，两个梁的材料和结构的差异，轴向力和其他因子同时没有任何近似。在分析期间，通过与有限元解决方案进行比较首先验证所提出的方法的准确性。然后，讨论了弹性支撑对模态特性的影响，研究了频域中的动态刚度的变化律。最后，提供了一种基于动态刚度的方法，用于确定两个光束到系统的每个模式的贡献。该方法可以扩展以快速获得系统的频率和模式形状信息而不求解频率方程或特性方程。

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