General exact analytical expressions for rotation and displacement of a Timoshenko beam under variable loads with validation
The researchers involved in the field of applied mathematics mostly project the efficient and viable solutions of those problems in which have practical applications in science and engineering. The Timoshenko beam model (TBM) is described by a system of ordinary differential equations where the ex...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Penerbit Universiti Kebangsaan Malaysia
2024
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| Online Access: | http://journalarticle.ukm.my/25140/ http://journalarticle.ukm.my/25140/1/19.pdf |
| _version_ | 1848816279702470656 |
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| author | Hafeezullah Channa, Muhammad Mujtaba Shaikh, Kamran Malik, |
| author_facet | Hafeezullah Channa, Muhammad Mujtaba Shaikh, Kamran Malik, |
| author_sort | Hafeezullah Channa, |
| building | UKM Institutional Repository |
| collection | Online Access |
| description | The researchers involved in the field of applied mathematics mostly project the efficient and viable solutions of those
problems in which have practical applications in science and engineering. The Timoshenko beam model (TBM) is described by a system of ordinary differential equations where the expressions of rotation and displacement of the beam are ultimately required. Most of the work on analytical solutions of beam problems in literature focuses the
elastic and Euler-Bernoulli beams, whereas for the TBM the numerical solutions are usually preferred. The analytical
expressions for the TBM exist for only very basic load cases and are also not general for any load function. In this
paper, we attempt to suggest a novel protocol based on expressing a load function by a polynomial or its power series development, and then use it to develop general analytical expressions for the rotation and displacement of a fixed TBM which is not load specific. The proposed general equations can provide ease of access and handling for the
practitioners working in applied mathematics, structural engineering and mechanical vibrations as the developed
equations can be used with only constant inputs to tailor particular expressions of rotation and displacement
profiles of a fixed TBM under any variable load. For performance evaluations of the proposed general equations,
we have also obtained particular expressions for some important variable loads, like: linearly varying loads
((LVLs): triangular and trapezoidal and quadratically varying loads (QVLs): parabolic/square and circular
loads. Finally, the proposed protocol for generalization has been validated for fixed elastic beams under uniformly distributed loads (UDLs), and the results match exactly with those expressions available in literature. The contributions of this study, on one hand provide ready, direct and exact general expressions for the rotation and displacement profiles of a fixed TBM, while on the other hand the solution of such problem is achieved with quite negligible computational overhead, execution time and software implementations. |
| first_indexed | 2025-11-15T01:03:21Z |
| format | Article |
| id | oai:generic.eprints.org:25140 |
| institution | Universiti Kebangasaan Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T01:03:21Z |
| publishDate | 2024 |
| publisher | Penerbit Universiti Kebangsaan Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | oai:generic.eprints.org:251402025-05-26T08:30:21Z http://journalarticle.ukm.my/25140/ General exact analytical expressions for rotation and displacement of a Timoshenko beam under variable loads with validation Hafeezullah Channa, Muhammad Mujtaba Shaikh, Kamran Malik, The researchers involved in the field of applied mathematics mostly project the efficient and viable solutions of those problems in which have practical applications in science and engineering. The Timoshenko beam model (TBM) is described by a system of ordinary differential equations where the expressions of rotation and displacement of the beam are ultimately required. Most of the work on analytical solutions of beam problems in literature focuses the elastic and Euler-Bernoulli beams, whereas for the TBM the numerical solutions are usually preferred. The analytical expressions for the TBM exist for only very basic load cases and are also not general for any load function. In this paper, we attempt to suggest a novel protocol based on expressing a load function by a polynomial or its power series development, and then use it to develop general analytical expressions for the rotation and displacement of a fixed TBM which is not load specific. The proposed general equations can provide ease of access and handling for the practitioners working in applied mathematics, structural engineering and mechanical vibrations as the developed equations can be used with only constant inputs to tailor particular expressions of rotation and displacement profiles of a fixed TBM under any variable load. For performance evaluations of the proposed general equations, we have also obtained particular expressions for some important variable loads, like: linearly varying loads ((LVLs): triangular and trapezoidal and quadratically varying loads (QVLs): parabolic/square and circular loads. Finally, the proposed protocol for generalization has been validated for fixed elastic beams under uniformly distributed loads (UDLs), and the results match exactly with those expressions available in literature. The contributions of this study, on one hand provide ready, direct and exact general expressions for the rotation and displacement profiles of a fixed TBM, while on the other hand the solution of such problem is achieved with quite negligible computational overhead, execution time and software implementations. Penerbit Universiti Kebangsaan Malaysia 2024 Article PeerReviewed application/pdf en http://journalarticle.ukm.my/25140/1/19.pdf Hafeezullah Channa, and Muhammad Mujtaba Shaikh, and Kamran Malik, (2024) General exact analytical expressions for rotation and displacement of a Timoshenko beam under variable loads with validation. Jurnal Kejuruteraan, 36 (1). pp. 199-209. ISSN 0128-0198 https://www.ukm.my/jkukm/volume-3601-2024 |
| spellingShingle | Hafeezullah Channa, Muhammad Mujtaba Shaikh, Kamran Malik, General exact analytical expressions for rotation and displacement of a Timoshenko beam under variable loads with validation |
| title | General exact analytical expressions for rotation and displacement of a Timoshenko beam under variable loads with validation |
| title_full | General exact analytical expressions for rotation and displacement of a Timoshenko beam under variable loads with validation |
| title_fullStr | General exact analytical expressions for rotation and displacement of a Timoshenko beam under variable loads with validation |
| title_full_unstemmed | General exact analytical expressions for rotation and displacement of a Timoshenko beam under variable loads with validation |
| title_short | General exact analytical expressions for rotation and displacement of a Timoshenko beam under variable loads with validation |
| title_sort | general exact analytical expressions for rotation and displacement of a timoshenko beam under variable loads with validation |
| url | http://journalarticle.ukm.my/25140/ http://journalarticle.ukm.my/25140/ http://journalarticle.ukm.my/25140/1/19.pdf |