Graduate Thesis Or Dissertation
 

The violin's sound : a mathematical exploration employing principles of continuum mechanics and numerical methods

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/vd66w2443

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  • This thesis explores the vibrational behavior of the main components of sound production in the violin using a continuum mechanics approach. The author provides a mathematical description of the regions in the vibrating continuum, and begins to develop a system of equations governing their behavior, focusing on the air in the resonant chamber. Later chapters, contain discussion of issues involved in solving the system of equations, and examples involving both formal and numerical methods. The existence of a unique formal solution would allow mathematicians to make predictive models for sound waves of instruments based on physical characteristics such as size, shape, density and elasticity. This thesis explores the vibrational behavior of the main components of sound production in the violin using a continuum mechanics approach. The author provides a mathematical description of the regions in the vibrating continuum, and begins to develop a system of equations governing their behavior, focusing on the air in the resonant chamber. Later chapters, contain discussion of issues involved in solving the system of equations, and examples involving both formal and numerical methods. The existence of a unique formal solution would allow mathematicians to make predictive models for sound waves of instruments based on physical characteristics such as size, shape, density and elasticity. This thesis explores the vibrational behavior of the main components of sound production in the violin using a continuum mechanics approach. The author provides a mathematical description of the regions in the vibrating continuum, and begins to develop a system of equations governing their behavior, focusing on the air in the resonant chamber. Later chapters, contain discussion of issues involved in solving the system of equations, and examples involving both formal and numerical methods. The existence of a unique formal solution would allow mathematicians to make predictive models for sound waves of instruments based on physical characteristics such as size, shape, density and elasticity.
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  • File scanned at 300 ppi (Monochrome, 24-bit Color) using ScandAll PRO 1.8.1 on a Fi-6770A in PDF format. CVista PdfCompressor 4.0 was used for pdf compression and textual OCR.
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