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• W2021882184 abstract "We study the vibration characteristics of a string with a smooth unilateral obstacle placed at one of the ends similar to the strings in musical instruments like sitar and veena. In particular, we explore the correlation between the string vibrations and some unique sound characteristics of these instruments like less inharmonicity in the frequencies, a large number of overtones and the presence of both frequency and amplitude modulations. At the obstacle, we have a moving boundary due to the wrapping of the string and an appropriate scaling of the spatial variable leads to a fixed boundary at the cost of introducing nonlinearity in the governing equation. Reduced order system of equations has been obtained by assuming a functional form for the string displacement which satisfies all the boundary conditions and gives the free length of the string in terms of the modal coordinates. To study the natural frequencies and mode-shapes, the nonlinear governing equation is linearized about the static configuration. The natural frequencies have been found to be harmonic and they depend on the shape of the obstacle through the effective free length of the string. Expressions have been obtained for the time-varying mode-shapes as well as the variation of the nodal points. Modal interactions due to coupling have been studied which show the appearance of higher overtones as well as amplitude modulations in our theoretical model akin to the experimental observations. All the obtained results have been verified with an alternate formulation based on the assumed mode method with polynomial shape functions." @default.
• W2021882184 created "2016-06-24" @default.
• W2021882184 creator A5052163644 @default.
• W2021882184 creator A5067387501 @default.
• W2021882184 date "2015-03-01" @default.
• W2021882184 modified "2023-10-16" @default.
• W2021882184 title "Natural frequencies, modeshapes and modal interactions for strings vibrating against an obstacle: Relevance to Sitar and Veena" @default.
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• W2021882184 doi "https://doi.org/10.1016/j.jsv.2014.06.010" @default.
• W2021882184 hasPublicationYear "2015" @default.
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