Equipartition of modal energy in an ideal string vibrating in the presence of a boundary obstacle

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Nonlinear Dynamics vol. 112, no. 1 (Jan 2024), p. 215
1. Verfasser: Mandal, Ashok K.
Weitere Verfasser: Wahi, Pankaj
Veröffentlicht:
Springer Nature B.V.
Schlagworte:
Online-Zugang:Citation/Abstract
Full Text - PDF
Tags: Tag hinzufügen
Keine Tags, Fügen Sie das erste Tag hinzu!

MARC

LEADER 00000nab a2200000uu 4500
001 2903728821
003 UK-CbPIL
022 |a 0924-090X 
022 |a 1573-269X 
024 7 |a 10.1007/s11071-023-09046-w  |2 doi 
035 |a 2903728821 
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