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King Abdullah University of Science and Technology

1. Larisch, Lukas. Three-dimensional Modeling and Simulation of a Tuning Fork.

Degree: 2018, King Abdullah University of Science and Technology

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.

Subjects/Keywords: tuning fork; linear elasticity; FEM; Solid mechanics; experimental model analysis; PINVIT

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Larisch, L. (2018). Three-dimensional Modeling and Simulation of a Tuning Fork. (Thesis). King Abdullah University of Science and Technology. Retrieved from http://hdl.handle.net/10754/628716

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Larisch, Lukas. “Three-dimensional Modeling and Simulation of a Tuning Fork.” 2018. Thesis, King Abdullah University of Science and Technology. Accessed October 16, 2018. http://hdl.handle.net/10754/628716.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Larisch, Lukas. “Three-dimensional Modeling and Simulation of a Tuning Fork.” 2018. Web. 16 Oct 2018.

Vancouver:

Larisch L. Three-dimensional Modeling and Simulation of a Tuning Fork. [Internet] [Thesis]. King Abdullah University of Science and Technology; 2018. [cited 2018 Oct 16]. Available from: http://hdl.handle.net/10754/628716.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Larisch L. Three-dimensional Modeling and Simulation of a Tuning Fork. [Thesis]. King Abdullah University of Science and Technology; 2018. Available from: http://hdl.handle.net/10754/628716

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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