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• W2000624188 abstract "This paper proposes a method for trimming the natural frequencies of an imperfect ring to simultaneously eliminate certain of the frequency splits present. Initially, the effect of the addition of a number of imperfection masses on a perfect ring is considered. This is achieved by using a Rayleigh–Ritz approach in which it is assumed that the mode shapes are identical to those of a perfect ring. By considering the inverse (the so-called trimming) problem it is deduced that it is possible to trim N pairs of modes simultaneously by removing (a minimum of) N trimming masses at particular locations around the ring. To calculate the trimming mass locations, it is necessary to solve N non-linear algebraic equations. Once this has been achieved, the magnitude of the trimming masses can be calculated easily. For the special case of trimming a single pair of modes, analytic solutions for the magnitude and position of the single required trimming mass are available. To trim two pairs of modes, it is shown that a simple analytic relationship exists between the angular positions of the two required trimming masses and that the magnitude of these masses can be obtained easily. To trim more pairs of modes, numerical techniques are required and for this purpose a numerical procedure is proposed. Validation of the derived analytic results and the proposed numerical procedure is achieved by studying a number of theoretical examples." @default.
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• W2000624188 date "2001-12-01" @default.
• W2000624188 modified "2023-10-03" @default.
• W2000624188 title "MULTI-MODE TRIMMING OF IMPERFECT RINGS" @default.
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• W2000624188 doi "https://doi.org/10.1006/jsvi.2001.3811" @default.
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