Abstract 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.

中文翻译：

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一种基于动态刚度的弹性支撑双梁系统模态分析方法

摘要 具有多个弹性支撑的双梁系统是工程结构中最重要的力学模型之一。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。在双梁系统的动力分析中，由于现有研究往往需要对位移函数进行一些假设或近似，从而限制了分析结果的准确性和适用范围。鉴于此，本文提出了一种基于动刚度法的双梁系统精确模态分析方法。它可以同时考虑边界条件的影响、两梁材料和结构的差异、轴力等因素，无需任何近似。在分析过程中，首先通过与有限元解的比较来验证所提出方法的准确性。然后讨论了弹性支撑对模态特性的影响，研究了动刚度在频域内的变化规律。最后，提供了一种基于动态刚度的方法，用于确定两个梁对系统每个模式的贡献。该方法可以扩展到无需求解频率方程或特征方程即可快速获得系统的频率和模态振型信息。提供了一种基于动态刚度的方法，用于确定两个梁对系统每个模式的贡献。该方法可以扩展，无需求解频率方程或特征方程，即可快速获得系统的频率和振型信息。提供了一种基于动态刚度的方法，用于确定两个梁对系统每个模式的贡献。该方法可以扩展到无需求解频率方程或特征方程即可快速获得系统的频率和模态振型信息。