Closed form solution of nonlinear oscillation of a cantilever beam using λ-symmetry linearization criteria
<p dir="ltr">A mechanical system, in general, undergoes vibrational motion when the system is subjected to a tension or an external force. One of the examples of such a system is a cantilever beam when it is exposed to a bending action. When the tension is released, the cantilever be...
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| مؤلفون آخرون: | , , |
| منشور في: |
2022
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إضافة وسم
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| _version_ | 1864513541591007232 |
|---|---|
| author | Raed Ali Mara'Beh (17337892) |
| author2 | Ahmad Y. Al-Dweik (14158875) B.S. Yilbas (17337895) M. Sunar (17337898) |
| author2_role | author author author |
| author_facet | Raed Ali Mara'Beh (17337892) Ahmad Y. Al-Dweik (14158875) B.S. Yilbas (17337895) M. Sunar (17337898) |
| author_role | author |
| dc.creator.none.fl_str_mv | Raed Ali Mara'Beh (17337892) Ahmad Y. Al-Dweik (14158875) B.S. Yilbas (17337895) M. Sunar (17337898) |
| dc.date.none.fl_str_mv | 2022-11-15T15:00:00Z |
| dc.identifier.none.fl_str_mv | 10.1016/j.heliyon.2022.e11673 |
| dc.relation.none.fl_str_mv | https://figshare.com/articles/journal_contribution/Closed_form_solution_of_nonlinear_oscillation_of_a_cantilever_beam_using_-symmetry_linearization_criteria/24501163 |
| dc.rights.none.fl_str_mv | CC BY 4.0 info:eu-repo/semantics/openAccess |
| dc.subject.none.fl_str_mv | Engineering Mechanical engineering Mathematical sciences Pure mathematics Physical sciences Atomic, molecular and optical physics Cantilever beam Non-linear oscillation Closed form solution Lie-Tresse linearization |
| dc.title.none.fl_str_mv | Closed form solution of nonlinear oscillation of a cantilever beam using λ-symmetry linearization criteria |
| dc.type.none.fl_str_mv | Text Journal contribution info:eu-repo/semantics/publishedVersion text contribution to journal |
| description | <p dir="ltr">A mechanical system, in general, undergoes vibrational motion when the system is subjected to a tension or an external force. One of the examples of such a system is a cantilever beam when it is exposed to a bending action. When the tension is released, the cantilever beam suffers from the oscillations until the strain energy is totally released through the damping characteristics of the cantilever beam. Depending on the stiffness and damping factors of the beam, the vibrational motion can be non-linear; in which case, the analytical solution becomes challenging formulating the flexural characteristics of the beam. Although numerical solution for the non-linear problem is possible, the analytical solution provides useful information between the mechanical response and the cantilever beam characteristics. In the present study, the analytical solution of the non-linear equations governing the motion of the cantilever beam is presented. The governing equation is linearized incorporating the Lie-Tresse linearization method. The closed form solution for the displacement of the cantilever beam is reduced to a linear solution after introducing the appropriate beam characteristics. The dynamic behavior of the flexural motion due to non-linear and linear cantilever beams are compared.</p><h2>Other Information</h2><p dir="ltr">Published in: Heliyon<br>License: <a href="http://creativecommons.org/licenses/by/4.0/" target="_blank">http://creativecommons.org/licenses/by/4.0/</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.1016/j.heliyon.2022.e11673" target="_blank">https://dx.doi.org/10.1016/j.heliyon.2022.e11673</a></p> |
| eu_rights_str_mv | openAccess |
| id | Manara2_cf5479de314cc8b19f8e9cd19397a14e |
| identifier_str_mv | 10.1016/j.heliyon.2022.e11673 |
| network_acronym_str | Manara2 |
| network_name_str | Manara2 |
| oai_identifier_str | oai:figshare.com:article/24501163 |
| publishDate | 2022 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| rights_invalid_str_mv | CC BY 4.0 |
| spelling | Closed form solution of nonlinear oscillation of a cantilever beam using λ-symmetry linearization criteriaRaed Ali Mara'Beh (17337892)Ahmad Y. Al-Dweik (14158875)B.S. Yilbas (17337895)M. Sunar (17337898)EngineeringMechanical engineeringMathematical sciencesPure mathematicsPhysical sciencesAtomic, molecular and optical physicsCantilever beamNon-linear oscillationClosed form solutionLie-Tresse linearization<p dir="ltr">A mechanical system, in general, undergoes vibrational motion when the system is subjected to a tension or an external force. One of the examples of such a system is a cantilever beam when it is exposed to a bending action. When the tension is released, the cantilever beam suffers from the oscillations until the strain energy is totally released through the damping characteristics of the cantilever beam. Depending on the stiffness and damping factors of the beam, the vibrational motion can be non-linear; in which case, the analytical solution becomes challenging formulating the flexural characteristics of the beam. Although numerical solution for the non-linear problem is possible, the analytical solution provides useful information between the mechanical response and the cantilever beam characteristics. In the present study, the analytical solution of the non-linear equations governing the motion of the cantilever beam is presented. The governing equation is linearized incorporating the Lie-Tresse linearization method. The closed form solution for the displacement of the cantilever beam is reduced to a linear solution after introducing the appropriate beam characteristics. The dynamic behavior of the flexural motion due to non-linear and linear cantilever beams are compared.</p><h2>Other Information</h2><p dir="ltr">Published in: Heliyon<br>License: <a href="http://creativecommons.org/licenses/by/4.0/" target="_blank">http://creativecommons.org/licenses/by/4.0/</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.1016/j.heliyon.2022.e11673" target="_blank">https://dx.doi.org/10.1016/j.heliyon.2022.e11673</a></p>2022-11-15T15:00:00ZTextJournal contributioninfo:eu-repo/semantics/publishedVersiontextcontribution to journal10.1016/j.heliyon.2022.e11673https://figshare.com/articles/journal_contribution/Closed_form_solution_of_nonlinear_oscillation_of_a_cantilever_beam_using_-symmetry_linearization_criteria/24501163CC BY 4.0info:eu-repo/semantics/openAccessoai:figshare.com:article/245011632022-11-15T15:00:00Z |
| spellingShingle | Closed form solution of nonlinear oscillation of a cantilever beam using λ-symmetry linearization criteria Raed Ali Mara'Beh (17337892) Engineering Mechanical engineering Mathematical sciences Pure mathematics Physical sciences Atomic, molecular and optical physics Cantilever beam Non-linear oscillation Closed form solution Lie-Tresse linearization |
| status_str | publishedVersion |
| title | Closed form solution of nonlinear oscillation of a cantilever beam using λ-symmetry linearization criteria |
| title_full | Closed form solution of nonlinear oscillation of a cantilever beam using λ-symmetry linearization criteria |
| title_fullStr | Closed form solution of nonlinear oscillation of a cantilever beam using λ-symmetry linearization criteria |
| title_full_unstemmed | Closed form solution of nonlinear oscillation of a cantilever beam using λ-symmetry linearization criteria |
| title_short | Closed form solution of nonlinear oscillation of a cantilever beam using λ-symmetry linearization criteria |
| title_sort | Closed form solution of nonlinear oscillation of a cantilever beam using λ-symmetry linearization criteria |
| topic | Engineering Mechanical engineering Mathematical sciences Pure mathematics Physical sciences Atomic, molecular and optical physics Cantilever beam Non-linear oscillation Closed form solution Lie-Tresse linearization |