Research Initiation Awards: A New Approach for the Analysis of Piece-Wise Periodic Structures of Finite Length

本文将开发一个程序，用于分析由离散周期单元组成的有限长度大型结构系统的动力响应和噪声传递。该方法是有限元、传递矩阵和波浪传播相结合的方法。利用波反射（由于结构模式的变化）和传输矩阵，将响应视为波运动的叠加。这使得计算只在波传播的方向上进行，因此结果在数值上总是稳定的。新方法可以处理有限长度的长分段周期加筋结构，这是传统传递矩阵由于数值困难而无法实现的。该方法可以使用周期单元的有限元公式来处理复杂几何系统，并且由于自由度降低，预计比有限元方法快得多。该方法将用于大型柔性结构的结构噪声传递预测。最后，将该方法与随机有限元公式结合使用，以减少计算时间，这是随机响应中随着单元数量增加而出现的一个明显问题。//

A procedure will be developed for the analysis of dynamic response and noise transmission of large structural systems of finite length which are composed of discretely periodic units. The method is a combination of finite elements, transfer matrices and waved propagation. The response is treated as superposition of wave motions using wave reflection (due to changes in the construction pattern) and transmission matrices. This enables the computations to proceed in the direction of wave propagation only, so that the results are always numerically stable. The new method can treat long piece-wise periodic stiffened structures of finite length, which is not possible with traditional transfer matrices, because of numerical difficulties. The method can use the finite element formulation for the periodic units to treat systems of complicated geometries and is expected to be much faster than the finite elements because the degrees of freedom are reduced. The method will be used for the prediction of the structure-borne noise transmission of large flexible structures. Finally, the method will be used with the stochastic finite element formulation to reduce computational time, which is an evident problems in stochastic response as the number of elements increases. //