Reference Value Selection in a Perturbation Theory Applied to Nonuniform Beams

Reference Value Selection in a Perturbation Theory Applied to Nonuniform Beams

The Lindstedt-Poincaré method is applied to a nonuniform Euler-Bernoulli beam model for the free transverse vibrations of the system. The nonuniformities in the system include spatially varying and piecewise continuous bending stiffness and mass per unit length. The expression for the natural freque...

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Main Authors: Blake Martin, Armaghan Salehian
Format: Article
Language:English
Published: Hindawi Limited 2018-01-01
Series:Shock and Vibration
Online Access:http://dx.doi.org/10.1155/2018/4627865
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spelling doaj-8a9ec599c323492793aba84c617c626a2020-11-24T23:05:55ZengHindawi LimitedShock and Vibration1070-96221875-92032018-01-01201810.1155/2018/46278654627865Reference Value Selection in a Perturbation Theory Applied to Nonuniform BeamsBlake Martin0Armaghan Salehian1Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, N2L 3G1, CanadaDepartment of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, N2L 3G1, CanadaThe Lindstedt-Poincaré method is applied to a nonuniform Euler-Bernoulli beam model for the free transverse vibrations of the system. The nonuniformities in the system include spatially varying and piecewise continuous bending stiffness and mass per unit length. The expression for the natural frequencies is obtained up to second-order and the expression for the mode shapes is obtained up to first-order. The explicit dependence of the natural frequencies and mode shapes on reference values for the bending stiffness and the mass per unit length of the system is determined. Multiple methods for choosing these reference values are presented and are compared using numerical examples.http://dx.doi.org/10.1155/2018/4627865
collection DOAJ
language English
format Article
sources DOAJ
author Blake Martin
Armaghan Salehian
spellingShingle Blake Martin
Armaghan Salehian
Reference Value Selection in a Perturbation Theory Applied to Nonuniform Beams
Shock and Vibration
author_facet Blake Martin
Armaghan Salehian
author_sort Blake Martin
title Reference Value Selection in a Perturbation Theory Applied to Nonuniform Beams
title_short Reference Value Selection in a Perturbation Theory Applied to Nonuniform Beams
title_full Reference Value Selection in a Perturbation Theory Applied to Nonuniform Beams
title_fullStr Reference Value Selection in a Perturbation Theory Applied to Nonuniform Beams
title_full_unstemmed Reference Value Selection in a Perturbation Theory Applied to Nonuniform Beams
title_sort reference value selection in a perturbation theory applied to nonuniform beams
publisher Hindawi Limited
series Shock and Vibration
issn 1070-9622
1875-9203
publishDate 2018-01-01
description The Lindstedt-Poincaré method is applied to a nonuniform Euler-Bernoulli beam model for the free transverse vibrations of the system. The nonuniformities in the system include spatially varying and piecewise continuous bending stiffness and mass per unit length. The expression for the natural frequencies is obtained up to second-order and the expression for the mode shapes is obtained up to first-order. The explicit dependence of the natural frequencies and mode shapes on reference values for the bending stiffness and the mass per unit length of the system is determined. Multiple methods for choosing these reference values are presented and are compared using numerical examples.
url http://dx.doi.org/10.1155/2018/4627865
work_keys_str_mv AT blakemartin referencevalueselectioninaperturbationtheoryappliedtononuniformbeams
AT armaghansalehian referencevalueselectioninaperturbationtheoryappliedtononuniformbeams
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