The Use of Trigonometric Series for the Study of Isotropic Beam Deflection
The average deformed fiber is a continuous and smooth function of the fourth order. The deflection and rotation of beams can be determined by various methods available in the literature. Thus, in this paper, the expression of the average deformed fiber is defined in advance, then it is considered an...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/6/1426 |
| _version_ | 1797610269587800064 |
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| author | Adrian Ioan Botean |
| author_facet | Adrian Ioan Botean |
| author_sort | Adrian Ioan Botean |
| collection | DOAJ |
| description | The average deformed fiber is a continuous and smooth function of the fourth order. The deflection and rotation of beams can be determined by various methods available in the literature. Thus, in this paper, the expression of the average deformed fiber is defined in advance, then it is considered an infinite sum of sinusoidal functions that are successively evaluated using sinusoidal trigonometric series if it is considered a periodic function, or using Fourier series if it is considered a non-periodic function. The method is examined by solving several beam problems. The results indicate that the method can be used with confidence for solving any bending beam problem. |
| first_indexed | 2024-03-11T06:13:01Z |
| format | Article |
| id | doaj.art-15e0930346554db18b56681d87b106ed |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T06:13:01Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-15e0930346554db18b56681d87b106ed2023-11-17T12:28:26ZengMDPI AGMathematics2227-73902023-03-01116142610.3390/math11061426The Use of Trigonometric Series for the Study of Isotropic Beam DeflectionAdrian Ioan Botean0Mechanical Engineering Department, Faculty of Road Vehicles, Mechatronics and Mechanics, Technical University of Cluj-Napoca, 28 Memorandumului, 400114 Cluj-Napoca, RomaniaThe average deformed fiber is a continuous and smooth function of the fourth order. The deflection and rotation of beams can be determined by various methods available in the literature. Thus, in this paper, the expression of the average deformed fiber is defined in advance, then it is considered an infinite sum of sinusoidal functions that are successively evaluated using sinusoidal trigonometric series if it is considered a periodic function, or using Fourier series if it is considered a non-periodic function. The method is examined by solving several beam problems. The results indicate that the method can be used with confidence for solving any bending beam problem.https://www.mdpi.com/2227-7390/11/6/1426beambendingstatic loadaverage deformed fiberdeformationssinusoid |
| spellingShingle | Adrian Ioan Botean The Use of Trigonometric Series for the Study of Isotropic Beam Deflection Mathematics beam bending static load average deformed fiber deformations sinusoid |
| title | The Use of Trigonometric Series for the Study of Isotropic Beam Deflection |
| title_full | The Use of Trigonometric Series for the Study of Isotropic Beam Deflection |
| title_fullStr | The Use of Trigonometric Series for the Study of Isotropic Beam Deflection |
| title_full_unstemmed | The Use of Trigonometric Series for the Study of Isotropic Beam Deflection |
| title_short | The Use of Trigonometric Series for the Study of Isotropic Beam Deflection |
| title_sort | use of trigonometric series for the study of isotropic beam deflection |
| topic | beam bending static load average deformed fiber deformations sinusoid |
| url | https://www.mdpi.com/2227-7390/11/6/1426 |
| work_keys_str_mv | AT adrianioanbotean theuseoftrigonometricseriesforthestudyofisotropicbeamdeflection AT adrianioanbotean useoftrigonometricseriesforthestudyofisotropicbeamdeflection |