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

建立了有限长离散周期单元组成的大型结构系统的动力响应和噪声传递分析程序。该方法是有限元、传递矩阵和波动传播的结合。响应被处理为使用波浪反射(由于结构模式的改变)和传输矩阵的波浪运动的叠加。这使得计算只能沿着波的传播方向进行，因此结果总是数值稳定的。这种新方法可以处理有限长的分段周期加筋结构，这是传统传递矩阵所不能处理的，因为数值上的困难。该方法可以利用周期单元的有限元格式来处理复杂几何结构的体系，并且由于自由度的减少，有望比有限元快得多。该方法将用于预测大型柔性结构的结构噪声传播。最后，该方法将与随机有限元格式一起使用，以减少计算时间，这是随机响应中随着单元数量增加而明显存在的问题。//

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. //