多梁复合结构的动力学建模及全局解析振型分析

多梁复合结构广泛用于工程领域，其动力学特性对相关装备的工作状况有着重要影响，建立准确适用的动力学模型对后续的动力学响应参数影响规律研究有决定性作用。针对工程中常见的多梁复合结构，给出了位移场的一般表达式，利用哈密顿原理得出多梁复合结构的运动控制方程和边界条件，对其全局解析振型进行理论计算，给出了计算多梁复合结构数值振型的一般过程，基于数值分析和实验分析以L型梁和Z型梁为例利用频率相对误差、振型定性比较和MAC定量分析说明了全局解析振型的求解验证方法，利用伽辽金方法和全局解析振型给出了截断原系统得到离散系统运动方程的一般形式。提出的多梁复合结构的建模方法和全局解析振型求解验证方法，对工程中此类结构动力学响应的参数影响规律研究有重要意义。

Dynamic Modeling and Global Analytical Mode Shapes of Multi-Beam Composite Structures

Abstract: Multi-beam composite structures are widely used in the engineering fields, whose dynamic characteristics have an important influence on the working conditions of related equipment. The establishment of accurate and applicable dynamic models has an indispensable role in subsequently investigating the parametric influence on dynamic responses. The general expressions of displacement fields of multi-beam composite structures are given. The governing equation of motion and the corresponding boundary conditions of multi-beam composite structures are obtained by using the Hamilton principle. The global analytical mode shapes are calculated theoretically. The general process of calculating the numerical mode shapes of multi-beam composite structures is presented. Based on numerical and experimental analyses, taking L-shaped beams and Z-shaped beams as examples, the frequency relative error, qualitative comparison of mode shapes, and quantitative analysis of MAC are used to illustrate the method of solving and verifying global analytical mode shapes. Using the Galerkin method and the global analytical mode to truncate the original system, the general form of the governing equation of motion for the discrete system is obtained. The proposed method for modeling multi-beam composite structures and the method for solving and verifying global analytical mode shapes are of great significance for studying the parametric influences on the dynamic responses of such structures in engineering.