Optimization of Natural Frequencies for Fabrication-Aware Shape Modeling

Information

• Publication Type: Master Thesis
• Workgroup(s)/Project(s):
  • MAKE-IT-FAB: Modeling of Shapes for Personal Fabrication
• Date: September 2015
• Date (Start): 30. January 2015
• Date (End): 21. September 2015
• First Supervisor:
  • Przemyslaw Musialski
  • Michael Wimmer
• Keywords: physically based modeling, computer graphics, digital fabrication, 3D shape optmization, 3D shape processing

Abstract

Given a target shape and a target frequency, we automatically synthesize shapes that exhibit this frequency as part of their natural spectrum while resembling the target shape as closely as possible. We propose three shape parametrization methods that afford meaningful degrees of freedom in the design of instruments such as marimbas and bells. The design space is based on the representation of a solid as the volume enclosed by an outer surface and an inner offset surface. In order to evaluate the natural frequency spectrum of a solid, we employ finite element modal analysis and evaluate the suitability of different element types. We propose a fabrication method for the production of optimized instruments by an amateur craftsperson using sand or rubber molds. The efficiency of our method is demonstrated by the production of a simple tin bell and a more complicated bell in the shape of a rabbit. We achieve agreement with the predicted pitch frequencies of 2.8% and 6% respectively. These physical results are supplemented by a number of computational results that explore the optimization of harmonic ratios and the influence of mesh resolution and mesh smoothness on the accuracy of the finite element model.

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BibTeX

@mastersthesis{hafner-2015-eigf,
  title =      "Optimization of Natural Frequencies for Fabrication-Aware
               Shape Modeling",
  author =     "Christian Hafner",
  year =       "2015",
  abstract =   "Given a target shape and a target frequency, we
               automatically synthesize shapes that exhibit this frequency
               as part of their natural spectrum while resembling the
               target shape as closely as possible. We propose three shape
               parametrization methods that afford meaningful degrees of
               freedom in the design of instruments such as marimbas and
               bells. The design space is based on the representation of a
               solid as the volume enclosed by an outer surface and an
               inner offset surface. In order to evaluate the natural
               frequency spectrum of a solid, we employ finite element
               modal analysis and evaluate the suitability of different
               element types. We propose a fabrication method for the
               production of optimized instruments by an amateur
               craftsperson using sand or rubber molds. The efficiency of
               our method is demonstrated by the production of a simple tin
               bell and a more complicated bell in the shape of a rabbit.
               We achieve agreement with the predicted pitch frequencies of
               2.8% and 6% respectively. These physical results are
               supplemented by a number of computational results that
               explore the optimization of harmonic ratios and the
               influence of mesh resolution and mesh smoothness on the
               accuracy of the finite element model.",
  month =      sep,
  address =    "Favoritenstrasse 9-11/E193-02, A-1040 Vienna, Austria",
  school =     "Institute of Computer Graphics and Algorithms, Vienna
               University of Technology ",
  keywords =   "physically based modeling, computer graphics, digital
               fabrication, 3D shape optmization, 3D shape processing",
  URL =        "https://www.cg.tuwien.ac.at/research/publications/2015/hafner-2015-eigf/",
}