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On the free vibration analysis of spinning structures by using discrete or distributed mass models. (English) Zbl 0542.73082

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)

Citations:

Zbl 0227.73022

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