一类结构的（n－3）重根及其非退化性

THE ( n -3) MULTIPLE EIGENVALUES FOR A CLASS OF STRUCTURES AND ITS NON DEFECTIVENESS

基于陀螺模态综合法，从总装阵的块式结构出发，构造性地证明了具有ｎ片桨叶的旋翼型结构陀螺特征值问题存在一系列的（ｎ－３）重特征根，得到了对应的（ｎ－３）个完备的振型．结论进而推广到有阻尼的旋翼型结构．继续研究证明过程表明：结论适用于更广泛的一类具有重复子结构的结构系统，结果表明这类结构几何上的重复性或对称性导致的重根不会引入退化性．不同类型的算例验证了所得到的解析结果．

Based on the block structure of the assembled system matrix by gyroscopic mode synthesis technique, it is proved constructively that there is a series of the ( n -3) multiple eigenvalues in the spectrum of the gyroscopic eigenvalue problem for the rotarywing type structures, corresponding to the n repeated substructures mounted on the structure. The associated complete eigenvectors or modes are also obtained. The obtained analytical results are extended to the nonrotating, undamped and damped rotarywing type structures. Further examination of the proof of the analytical results conclude that the multiple eigenvalues induced by the geometric symmetry or repetition introduce no defectiveness to the system. A variety of the numerical examples are presented to verify the results. The symmetry reaining property of the dynamic substructure method is also discussed, and it is considered to be a virtue deserved to be studied furthermore.