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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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2018/4627865 |
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| _version_ | 1832556903386841088 |
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| author | Blake Martin Armaghan Salehian |
| author_facet | Blake Martin Armaghan Salehian |
| author_sort | Blake Martin |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-8a9ec599c323492793aba84c617c626a |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-8a9ec599c323492793aba84c617c626a2025-02-03T05:44:13ZengWileyShock 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 |
| spellingShingle | Blake Martin Armaghan Salehian Reference Value Selection in a Perturbation Theory Applied to Nonuniform Beams Shock and Vibration |
| title | 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_short | Reference Value Selection in a Perturbation Theory Applied to Nonuniform Beams |
| title_sort | reference value selection in a perturbation theory applied to nonuniform beams |
| url | http://dx.doi.org/10.1155/2018/4627865 |
| work_keys_str_mv | AT blakemartin referencevalueselectioninaperturbationtheoryappliedtononuniformbeams AT armaghansalehian referencevalueselectioninaperturbationtheoryappliedtononuniformbeams |