Modal Expansion Method for Eigensensitivity Calculations of Cyclically Symmetric Bladed Disks

Beck, Jeff; Brown, Jerram L.; Scott‐Emuakpor, Onome; Carper, Emily B.; Kaszynski, Alex A.

doi:10.2514/1.j057322

Cited by 8 publications

(1 citation statement)

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“…In the process of the natural vibration analysis, the multiple eigenvalues, i.e., the multiple natural frequencies for undamped systems and the multiple complex eigenvalues for damped systems, may be encountered if a mechanical system or a sub-structure system is symmetrical and its boundary conditions are also symmetric, or the system parameters are specially chosen. Determination for the frequency multiplicity is essential for these systems such as the reduced-order model [3], the optimization design [4,5], and so on.…”

Section: Introductionmentioning

confidence: 99%

Transfer Matrix Method for the Analysis of Multiple Natural Frequencies

Wang,

Rui,

et al. 2024

Mathematics

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Multiple natural frequencies may be encountered when analyzing the essential natural vibration of a symmetric mechanical system or sub-structure system or a system with special parameters. The transfer matrix method (TMM) is a useful tool for analyzing the natural vibration characteristics of mechanical or structural systems. It derives a nonlinear eigen-problem (NEP) in general, even a transcendental eigen-problem. This investigation addresses the NEP in TMM and proposes a novel method, called the determinant-differentiation-based method, for calculating multiple natural frequencies and determining their multiplicities. Firstly, the characteristic determinant is differentiated with respect to frequency, transforming the even multiple natural frequencies into the odd multiple zeros of the differentiation of the characteristic determinant. The odd multiple zeros of the first derivative of the characteristic determinant and the odd multiple natural frequencies can be obtained using the bisection method. Among the odd multiple zeros, the even multiple natural frequencies are picked out by the proposed judgment criteria. Then, the natural frequency multiplicities are determined by the higher-order derivatives of the characteristic determinant. Finally, several numerical simulations including the multiple natural frequencies show that the proposed method can effectively calculate the multiple natural frequencies and determine their multiplicities.

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Section: Introductionmentioning

confidence: 99%