Parametric excitation can occur when the value of a parameter of an oscillator is modulated at twice the natural frequency of the oscillator. The response grows exponentially and is only limited by a nonlinearity of the system, so large response amplitudes typically occur. However, there is no response unless the parametric drive amplitude is above a threshold value that is dictated by the damping. We investigate parametric excitation in three physical systems. The first involves an acoustic standing wave in a pipe that is driven by a piston at one end. An analysis shows that parametric excitation is not feasible in this system unless one uses a very large-excursion piston (for example, from an aircraft engine). The second system is an inductor-capacitor circuit which can undergo oscillations of the current. An analysis of capacitance modulation with a bank of alternate rotating and stationary parallel plates shows that parametric excitation would be very difficult to achieve. Finally, we describe the construction of a torsional oscillator whose length is modulated. Parametric excitation is successfully demonstrated in this system. A comparison of data to predictions of the standard theory of parametric excitation reveals significant deviations.

Thesis (M.S. in Engineering Acoustics)--Naval Postgraduate School, June 2005. / Thesis Advisor(s): Includes bibliographical references (p. 59). Also available online.

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published_or_final_version / Electrical Engineering / Master / Master of Science in Engineering

published_or_final_version / Electrical and Electronic Engineering / Master / Master of Philosophy

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Modular building systems that use only prefabricated parts, sometimes known as building “kits”, first emerged in the 1830s and 1840s in the form of glass and iron roof systems for urban transportation and distribution centers and multi-storey facade systems. Kit systems are still used widely today in the form of curtain wall assemblies for office and condominium towers, yet in all this time the formal flexibility of these systems (their ability to form complex shapes) has not increased greatly. This is in large part due to the fact that the systems still rely on mass-produced components. This lack of flexibility limits the degree to which these systems can be customized for particular contexts and optimized for such things as daylighting or energy efficiency. Digital design and fabrication tools now allow us to create highly flexible building facade systems that can be customized for different contexts as well as optimized for particular performance objectives. This thesis develops a prototype for a flexible facade system using parametric modeling tools. The first part of the thesis looks at how parametric modeling can be used to facilitate building customization and optimization by integrating the acts of design, analysis, fabrication and construction. The second part of the thesis presents the facade system prototype and documents key aspects of its development. The facade system is modeled in Grasshopper 3D, a parametric modeling plug-in for Rhinoceros 3D. The model has built-in analysis tools to help the user optimize the facade for daylighting, energy efficiency, or views within any given context, as well as tools that alert the designer when fabrication or construction constraints are being violated.