Equipartition of modal energy in an ideal string vibrating in the presence of a boundary obstacle
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| Veröffentlicht in: | Nonlinear Dynamics vol. 112, no. 1 (Jan 2024), p. 215 |
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Springer Nature B.V.
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| 024 | 7 | |a 10.1007/s11071-023-09046-w |2 doi | |
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| 045 | 2 | |b d20240101 |b d20240131 | |
| 100 | 1 | |a Mandal, Ashok K. |u National Institute of Technology Jamshedpur, Mechanical Engineering Department, Jamshedpur, India (GRID:grid.444477.0) (ISNI:0000 0004 1772 7337) | |
| 245 | 1 | |a Equipartition of modal energy in an ideal string vibrating in the presence of a boundary obstacle | |
| 260 | |b Springer Nature B.V. |c Jan 2024 | ||
| 513 | |a Journal Article | ||
| 520 | 3 | |a We study the vibration characteristics of an ideal string in the presence of a curved boundary obstacle which is a common constructional feature of sitar, veena and tanpura. It has been well-established that these plucked string instruments have attractive tonal qualities like better harmonicity, presence of amplitude as well as frequency modulations, and appearance of a large number of overtones. The smooth wrapping and unwrapping of the string over the curved obstacle introduces quadratic nonlinearities whose effect on the vibration characteristics is elucidated through a perturbative analysis using the method of multiple scales. Modal interactions facilitated by the obstacle results in neutrally stable mode-locked periodic solutions in our model thereby accounting for the complex frequency and amplitude modulations. In particular, we find a mode-locked state which tends to an equipartition of energy with an increase in the number of modes. Our numerical simulations suggest that a plucked disturbance favors this state and hence, several overtones can be clearly identified in the sound of these plucked instruments. A good qualitative agreement between the results from our idealized model and the sound of these instruments highlights the role of the finite curved bridge in deciding the tonal quality of sitar, veena and tanpura. | |
| 653 | |a Qualitative analysis | ||
| 653 | |a Amplitudes | ||
| 653 | |a Mathematical models | ||
| 653 | |a Vibration analysis | ||
| 653 | |a Multiscale analysis | ||
| 653 | |a Strings | ||
| 653 | |a Barriers | ||
| 653 | |a Musical instruments | ||
| 653 | |a Partial differential equations | ||
| 653 | |a Energy | ||
| 653 | |a Harmony (Music) | ||
| 653 | |a Ordinary differential equations | ||
| 653 | |a Vibration | ||
| 653 | |a Mechanical engineering | ||
| 700 | 1 | |a Wahi, Pankaj |u Indian Institute of Technology Kanpur, Mechanical Engineering Department, Kanpur, India (GRID:grid.417965.8) (ISNI:0000 0000 8702 0100) | |
| 773 | 0 | |t Nonlinear Dynamics |g vol. 112, no. 1 (Jan 2024), p. 215 | |
| 786 | 0 | |d ProQuest |t Engineering Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/2903728821/abstract/embedded/6A8EOT78XXH2IG52?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text - PDF |u https://www.proquest.com/docview/2903728821/fulltextPDF/embedded/6A8EOT78XXH2IG52?source=fedsrch |