Complex modes of vibration due to small-scale damping in a guitar topplate

Modal analysis is one of the preeminent methods used by scientists and engineers to study vibrating structures. The frequency response functions obtained through this method, are, in general, complex-valued. There is, however, no agreed-upon interpretation given to the real and imaginary parts of th...

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Detalles Bibliográficos
Autores: Torres, J A, Rendón, P L, Boullosa, R R
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2010
País:México
Institución:UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO
Repositorio:Journal of Applied Research and Technology
Idioma:inglés
OAI Identifier:oai:ojs2.localhost:article/487
Acceso en línea:https://jart.icat.unam.mx/index.php/jart/article/view/487
Access Level:acceso abierto
Palabra clave:Complex modes
mode shapes
damped plates
guitar
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spelling Complex modes of vibration due to small-scale damping in a guitar topplateComplex modes of vibration due to small-scale damping in a guitar topplateTorres, J ARendón, P LBoullosa, R RComplex modesmode shapesdamped platesguitarModal analysis is one of the preeminent methods used by scientists and engineers to study vibrating structures. The frequency response functions obtained through this method, are, in general, complex-valued. There is, however, no agreed-upon interpretation given to the real and imaginary parts of these functions, even though it is acknowledged that their relative magnitude for different frequencies is related to the behaviour of the corresponding modes. A simple model is deduced to describe the shape of the spectrum associated with a finite-length time-signal. There is very good agreement between results obtained using this model and numerical results obtained for, in this case, the vibration of a guitar top-plate using finite element methods. One interpretation of the relative magnitudes of the real and imaginary parts of the frequency response functions is advanced. It is found that stationary-wave behaviour is associated with the dominance of the real or imaginary part; traveling-wave behaviour, on the other hand, occurs when the real and imaginary parts are of the same order of magnitude, as long as the scale of damping is large enough and resonance peaks in the spectrum are close enough.El análisis modal es uno de los métodos utilizados con mayor frecuencia por científicos e ingenieros para estudiar estructuras vibrantes. Las funciones de respuesta de frecuencia obtenidas mediante este método tienen, en general, valores complejos. No existe, sin embargo, una interpretación universalmente aceptada asociada a las partes real e imaginaria de estas funciones, aún cuando se sabe que la magnitud relativa de estas cantidades para diferentes frecuencias está relacionada con el comportamiento de los distintos modos. Se obtiene un modelo sencillo que describe la forma del espectro asociado a una señal temporal de duración finita. Hay una muy buena concordancia enre los resultados obtenidos utilizando este modelo y aquellos obtenidos para, en este caso, la vibración de la tapa de una guitarra simulada a través de elementos finitos. Se propone una interpretación de las magnitudes relativas de las partes real e imaginaria de la función de respuesta de frecuencia. El comportamiento de onda estacionaria se asocia a la dominancia de la parte real o imaginaria; por otra parte, el comportamiento de onda viajera ocurre cuando las partes real e imaginaria son del mismo orden de magnitud, y siempre y cuando la escala del amortiguamiento sea lo suficientemente grande y los picos de resonancia en el espectro sean suficientemente cercanos.Universidad Nacional Autónoma de México2010-04-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionPeer-reviewed Articleapplication/pdfhttps://jart.icat.unam.mx/index.php/jart/article/view/48710.22201/icat.16656423.2010.8.01.487Journal of Applied Research and Technology; Vol. 8 No. 01Journal of Applied Research and Technology; Vol. 8 Núm. 012448-67361665-642310.22201/icat.24486736e.2010.8.01reponame:Journal of Applied Research and Technologyinstname:UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICOinstacron:UNAMenghttps://jart.icat.unam.mx/index.php/jart/article/view/487/483Copyright (c) 2018 Journal of Applied Research and Technologyinfo:eu-repo/semantics/openAccessoai:ojs2.localhost:article/4872024-08-16T17:54:16Z
dc.title.none.fl_str_mv Complex modes of vibration due to small-scale damping in a guitar topplate
Complex modes of vibration due to small-scale damping in a guitar topplate
title Complex modes of vibration due to small-scale damping in a guitar topplate
spellingShingle Complex modes of vibration due to small-scale damping in a guitar topplate
Torres, J A
Complex modes
mode shapes
damped plates
guitar
title_short Complex modes of vibration due to small-scale damping in a guitar topplate
title_full Complex modes of vibration due to small-scale damping in a guitar topplate
title_fullStr Complex modes of vibration due to small-scale damping in a guitar topplate
title_full_unstemmed Complex modes of vibration due to small-scale damping in a guitar topplate
title_sort Complex modes of vibration due to small-scale damping in a guitar topplate
dc.creator.none.fl_str_mv Torres, J A
Rendón, P L
Boullosa, R R
author Torres, J A
author_facet Torres, J A
Rendón, P L
Boullosa, R R
author_role author
author2 Rendón, P L
Boullosa, R R
author2_role author
author
dc.subject.none.fl_str_mv Complex modes
mode shapes
damped plates
guitar
topic Complex modes
mode shapes
damped plates
guitar
description Modal analysis is one of the preeminent methods used by scientists and engineers to study vibrating structures. The frequency response functions obtained through this method, are, in general, complex-valued. There is, however, no agreed-upon interpretation given to the real and imaginary parts of these functions, even though it is acknowledged that their relative magnitude for different frequencies is related to the behaviour of the corresponding modes. A simple model is deduced to describe the shape of the spectrum associated with a finite-length time-signal. There is very good agreement between results obtained using this model and numerical results obtained for, in this case, the vibration of a guitar top-plate using finite element methods. One interpretation of the relative magnitudes of the real and imaginary parts of the frequency response functions is advanced. It is found that stationary-wave behaviour is associated with the dominance of the real or imaginary part; traveling-wave behaviour, on the other hand, occurs when the real and imaginary parts are of the same order of magnitude, as long as the scale of damping is large enough and resonance peaks in the spectrum are close enough.
publishDate 2010
dc.date.none.fl_str_mv 2010-04-01
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Peer-reviewed Article
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://jart.icat.unam.mx/index.php/jart/article/view/487
10.22201/icat.16656423.2010.8.01.487
url https://jart.icat.unam.mx/index.php/jart/article/view/487
identifier_str_mv 10.22201/icat.16656423.2010.8.01.487
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv https://jart.icat.unam.mx/index.php/jart/article/view/487/483
dc.rights.none.fl_str_mv Copyright (c) 2018 Journal of Applied Research and Technology
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Copyright (c) 2018 Journal of Applied Research and Technology
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universidad Nacional Autónoma de México
publisher.none.fl_str_mv Universidad Nacional Autónoma de México
dc.source.none.fl_str_mv Journal of Applied Research and Technology; Vol. 8 No. 01
Journal of Applied Research and Technology; Vol. 8 Núm. 01
2448-6736
1665-6423
10.22201/icat.24486736e.2010.8.01
reponame:Journal of Applied Research and Technology
instname:UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO
instacron:UNAM
instname_str UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO
instacron_str UNAM
institution UNAM
reponame_str Journal of Applied Research and Technology
collection Journal of Applied Research and Technology
repository.name.fl_str_mv
repository.mail.fl_str_mv
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