ON THE FORESHORTENING EFFECTS OF A ROTATING FLEXIBLE BEAM USING DIFFERENT MODELING METHODS
This paper presents six methods of modeling a flexible beam rotating in the vertical plane. The first three methods, Hamilton's principle, Lagrange's equations for quasi-coordinates, and Newton-Euler equations, give a continuous model. The last three methods, Lagrange's equations, Jou...
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| Published in | Mechanics of structures and machines Vol. 30; no. 1; pp. 83 - 102 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Taylor & Francis Group
01.02.2002
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| Subjects | |
| Online Access | Get full text |
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| Abstract | This paper presents six methods of modeling a flexible beam rotating in the vertical plane. The first three methods, Hamilton's principle, Lagrange's equations for quasi-coordinates, and Newton-Euler equations, give a continuous model. The last three methods, Lagrange's equations, Jourdain's principle, and Newton-Euler equations, give a discrete model. The main conclusion of the paper is that, if foreshortening is not properly included in the beam model, then different methods give different equations. The paper also discusses several issues concerning symbolic modeling of mechanical structures within Maple.
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Communicated by J. McPhee. |
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| AbstractList | This paper presents six methods of modeling a flexible beam rotating in the vertical plane. The first three methods, Hamilton s principle, Lagrange's equations for quasi-coordinates, and Newton-Euler equations, give a continuous model. The last three methods, Lagrange's equations, Jourdain's principle, and Newton-Euler equations, give a discrete model. The main conclusion of the paper is that, if foreshortening is not properly included in the beam model, then different methods give different equations. The paper also discusses several issues concerning symbolic modeling of mechanical structures within Maple. This paper presents six methods of modeling a flexible beam rotating in the vertical plane. The first three methods, Hamilton's principle, Lagrange's equations for quasi-coordinates, and Newton-Euler equations, give a continuous model. The last three methods, Lagrange's equations, Jourdain's principle, and Newton-Euler equations, give a discrete model. The main conclusion of the paper is that, if foreshortening is not properly included in the beam model, then different methods give different equations. The paper also discusses several issues concerning symbolic modeling of mechanical structures within Maple. * Communicated by J. McPhee. |
| Author | Piedbœuf, Jean-Claude Moore, Brian |
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| CitedBy_id | crossref_primary_10_1016_j_ijnonlinmec_2013_07_002 crossref_primary_10_1080_15397734_2020_1766980 crossref_primary_10_1016_j_ijmecsci_2022_107195 crossref_primary_10_1016_j_tws_2017_06_018 crossref_primary_10_1016_j_jsv_2022_117526 crossref_primary_10_1017_S0263574709990282 crossref_primary_10_1007_s11044_018_9627_6 crossref_primary_10_1016_j_asr_2013_05_031 crossref_primary_10_1177_1081286516629768 crossref_primary_10_1080_15397734_2019_1624174 |
| Cites_doi | 10.2514/3.21447 10.2514/3.21473 10.1080/02681118908806073 10.1002/rob.4620121102 10.2514/4.862076 10.1177/027836498400300305 |
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| References | Piedbœuf J.-C. (CIT1478-3) 1998 CIT1478-9 CIT1478-7 CIT1478-1 Piedbœuf J.-C. (CIT1478-4) 1996; 3 CIT1478-2 Sincarsin G.B. (CIT1478-12) 1989; 4 Moore B. (CIT1478-14) 2000 L’Archevêque R. (CIT1478-13) 2000 Meirovitch L. (CIT1478-5) 1967 CIT1478-11 Bremer H. (CIT1478-10) 1994 Junkins J.L. (CIT1478-6) 1993 Pilkey W.D. (CIT1478-8) 1994 |
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| Snippet | This paper presents six methods of modeling a flexible beam rotating in the vertical plane. The first three methods, Hamilton's principle, Lagrange's equations... This paper presents six methods of modeling a flexible beam rotating in the vertical plane. The first three methods, Hamilton s principle, Lagrange's equations... |
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| StartPage | 83 |
| SubjectTerms | Beams and girders Differential equations Hamiltonians Model structures |
| Title | ON THE FORESHORTENING EFFECTS OF A ROTATING FLEXIBLE BEAM USING DIFFERENT MODELING METHODS |
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