由两组模态及相应频率构造Enler梁

ON THE CONSTRUCTION OF THE EULEK-BERNOULI BEAM VIA TWO SETS OF MODES AND THE CORRESPONDING FREQUENCIES

本文以悬臂梁和两端铰支梁为例,讨论了由部分频率及相应的位移模态或应变模态确定Euler梁的截面物理参数这类问题,建立了解存在唯一的充要条件,提出了一种算法并做了算例,分析和计算都表明,求解这一问题用应变模态比用位移模态有利得多。

In this paper the problem was discussed in which the flextural rigidity and density of the Euler-Bernoulli Beam were solved from some of the displacement modes or the strain modes and the corresponding frequencies of a cantilever or a pinned-pinned beam. The necessary and sufficient conditions for the unique ex istence of a solution to the problem have been set up. An algorithm was proposed and numerical calculations were carried out. Examples and analysis both showed that much better results could be attained if the strain modes instead of the displacement modes were employed in the calculations. Although the investigations were made only on the cantilever and the pinned-pinned beam, the ideas in this paper worked equally well in the study of the mode inverse problem of beams subject to other boundary restraints.