论文标题
基于替代均质解决方案的任意平面系统的数值组装技术
The Numerical Assembly Technique for arbitrary planar systems based on an alternative homogeneous solution
论文作者
论文摘要
扩展了数值组装技术以研究任意平面框架结构，重点是固有频率的计算。这使我们能够获得高度准确的结果，而无需诉诸空间离散化。为此，我们系统地将框架结构作为一组节点，梁，轴承，弹簧和外部负载，并制定相应的边界和界面条件。作为管理方程式的潜在均匀解决方案，我们使用了文献中最近提出的一种新颖方法。这大大提高了数值稳定性，并可以准确地计算出非常高的固有频率。我们通过研究系统矩阵的状况数量以及使用可变精度算术的情况下的条件数量来显示这一数字结构。
The Numerical Assembly Technique is extended to investigate arbitrary planar frame structures with the focus on the computation of natural frequencies. This allows us to obtain highly accurate results without resorting to spatial discretization. To this end, we systematically introduce a frame structure as a set of nodes, beams, bearings, springs, and external loads and formulate the corresponding boundary and interface conditions. As the underlying homogeneous solution of the governing equations, we use a novel approach recently presented in the literature. This greatly improves the numerical stability and allows the stable computation of very high natural frequencies accurately. We show this numerically at two frame structures by investigation of the condition number of the system matrix and also by the use of variable precision arithmetic.
