Wittrick, W. H.; Williams, F. W. On the free vibration analysis of spinning structures by using discrete or distributed mass models. (English) Zbl 0542.73082 J. Sound Vib. 82, 1-15 (1982). The analysis of the natural frequencies and modes of vibration of a spinning structure is in general complicated by the presence of gyroscopic or Coriolis forces, leading to a complex Hermitian dynamic stiffness (or impedance) matrix. It is shown that if the analysis is performed by using a discrete model with N degrees of freedom, the leading principal minors of the Nth order dynamic stiffness matrix exhibit a type of Sturm sequence property. This leads to a theorem which can be used for the systematic calculation of the natural frequencies of either a discrete system which is assembled from sub-structures, or an assembly of distributed mass members. In both of these cases the order n of the matrix is less than the number of degrees of freedom, and its determinant possesses poles as well as zeros. MSC: 74H45 Vibrations in dynamical problems in solid mechanics 74S30 Other numerical methods in solid mechanics (MSC2010) Keywords:natural frequencies; modes of vibration; spinning structure; complex Hermitian dynamic stiffness (or impedance) matrix; discrete model with N degrees of freedom; leading principal minors of the Nth order dynamic stiffness matrix; type of Sturm sequence property; assembled from sub- structures; assembly of distributed mass members; order n of the matrix; less than the number of degrees of freedom; poles; zeros Citations:Zbl 0227.73022 Software:PFVIBAT PDFBibTeX XMLCite \textit{W. H. Wittrick} and \textit{F. W. Williams}, J. Sound Vib. 82, 1--15 (1982; Zbl 0542.73082) Full Text: DOI