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To calculate the trimming mass locations, it is necessary to solve N non-linear algebraic equations.
Finally, the trimming mass is analytically predicted by the function of initially attached masses and angular positions.
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.
The concept is used to estimate the trimming mass which must be added to or removed from the ring, and at which point, in order to reduce or eliminate the frequency split in a given pair of modes.
In practice, it is likely that the trimming masses will be spaced regularly.
Once this has been achieved, the magnitude of the trimming masses can be calculated easily.
By positioning the trimming masses at pre-selected locations, it is shown that a simple set of trimming masses can be calculated easily, and from this set an infinite number of solution sets can be found.
Compared with previous work, the novel feature of this method is that the trimming masses are positioned at pre-selected locations on the ring.
By considering this trimming problem it is deduced that it is possible to trim N pairs of modes simultaneously by removing (a minimum of) 2 N trimming masses at particular locations around the 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 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.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com