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Kron’s procedure for a freely vibrating spinning structure. (English) Zbl 0673.73040

Summary: In this paper Kron’s eigenvalue method is extended to the analysis of a stable spinning undamped structure. A spinning structure is complicated by the presence of Coriolis forces, centrifugal forces and the internal forces in the steady state. For a free-ended substructure, these forces render the ‘static’ stiffness matrix in general indefinite; this leads to a defective dynamic stiffness matrix, and to the possibility of substructure flutter. Extra springs are introduced to ‘earth’ free-ended substructures such that the free-ended substructures are stable (therefore the associated dynamic stiffness matrices are Hermitian), and simple diagonal canonical forms can be obtained for the free-ended substructures. The spring-addition techniques is essential: without it, the complexity of the canonical forms at substructure level is such as to preclude the application of Kron’s method on grounds of numerical complexity and cost. A Newtonian procedure is developed to solve the eigenproblems for substructures and the composite structure. Finally, truncation is introduced into Kron’s method to obtain approximate fundamental modes. Numerical examples are presented which illustrate the above procedures.

MSC:

74H45 Vibrations in dynamical problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
74E30 Composite and mixture properties
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