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    Three-dimensional Modeling and Simulation of a Tuning Fork

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    Thesis
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    Type
    Thesis
    Authors
    Larisch, Lukas cc
    Advisors
    Wittum, Gabriel
    Committee members
    Michels, Dominik L.
    Keyes, David E. cc
    Program
    Computer Science
    KAUST Department
    Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
    Date
    2018-09-16
    Permanent link to this record
    http://hdl.handle.net/10754/628716
    
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    Abstract
    The mathematical characterization of the sound of a musical instrument still follows Schumann’s laws [1]. According to this theory, the resonances of the instrument body, “the formants”, filter the oscillations of the sound generator (e.g., strings) and produce the characteristic “timbre” of an instrument. This is a strong simplification of the actual situation. It applies to a point source and does not distinguish between a loudspeaker and a three-dimensional instrument. In this work we investigate Finite-Element-based numerical simulations of eigenfrequencies and eigenmodes of a tuning fork in order to capture the oscillation behavior of its eigenfrequencies. We model the tuning fork as an elastic solid body and solve an eigenvalue equation derived from a system of coupled equations from linear elasticity theory on an unstructured three-dimensional grid. The eigenvalue problem is solved using the preconditioned inverse iteration (PINVIT) method with an efficient geometric multigrid (GMG) preconditioner. The latter allows us to resolve the tuning fork with a high resolution grid, which is required to capture fine modes of the simulated eigenfrequencies. To verify our results, we compare them with measurement data obtained from an experimental modal analyses of a real reference tuning fork. It turns out that our model is sufficient to capture the first eight eigenmodes of a reference tuning fork, whose identification and reproduction by simulation is novel to the knowledge of the author.
    Citation
    Larisch, L. (2018). Three-dimensional Modeling and Simulation of a Tuning Fork. KAUST Research Repository. https://doi.org/10.25781/KAUST-2243L
    DOI
    10.25781/KAUST-2243L
    ae974a485f413a2113503eed53cd6c53
    10.25781/KAUST-2243L
    Scopus Count
    Collections
    MS Theses; Computer Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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