基于梁理论的复杂梁式结构低阶频率快速求解方法

工程计算中常遇到纵向尺度显著大于横向的复杂梁式结构,基于此类大型复杂结构的精细有限元模型建立一个能够预测结构动力性能、实现复杂结构的快速动力分析和优化的近似降阶模型,成为这类结构设计工作者一直关心的问题。该文提出一种基于梁平截面假设和梁位移插值函数的动力模型降阶方法,建立了具有明确物理意义的降阶模型。利用降阶模型计算得到的模态向量是原结构特征向量的高精度近似,基于一次瑞利-里茨逆迭代获得了原结构高精度的低阶频率,并且与Krylov子空间法进行了对比。具体算例表明了降阶方法的有效性。

A METHOD FOR FAST ANALYSIS OF LOW-ORDER FREQUENCIES IN COMPLICATED BEAM-TYPE STRUCTURES BASED ON BEAM THEORY

In modern engineering calculations, we often have to deal with dynamic analysis, or even optimization of dynamic performance for complicated slender structures whose longitudinal dimensions are significantly larger than their transverse ones. Based on a fine FEM model of such complicated structures, constructing an approximate physical model which requires only a small amount of work and can be used to predict the structural dynamic performance and meet the requirements of design, optimization, simulation, and other tasks in the preliminary design stage is still very valuable in many design departments. This paper presents a model reduction method for these structures, which is based on the plane cross-section assumption and displacement interpolation function of beam, and results in a physical reduced model. By using the vibration modal vectors of the reduced model and constructing an initial guess of vibration modes of the original structure, one Rayleigh-Ritz iteration results in a high-accuracy estimate of vibration frequency, which is also compared with the Krylov subspace methods. The examples show the validity of this method.