Vibrations of the Euler–Bernoulli Beam Under a Moving Force based on Various Versions of Gradient Nonlocal Elasticity Theory: Application in Nanomechanics
Two models of vibrations of the Euler–Bernoulli beam under a moving force, based on two different versions of the nonlocal gradient theory of elasticity, namely, the Eringen model, in which the strain is a function of stress gradient, and the nonlocal model, in which the stress is a function of stra...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Sciendo
2020-06-01
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| Series: | Studia Geotechnica et Mechanica |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/sgem-2019-0049 |
| _version_ | 1818652936989835264 |
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| author | Paweł Śniady Misiurek Katarzyna Szyłko-Bigus Olga Rafał Idzikowski |
| author_facet | Paweł Śniady Misiurek Katarzyna Szyłko-Bigus Olga Rafał Idzikowski |
| author_sort | Paweł Śniady |
| collection | DOAJ |
| description | Two models of vibrations of the Euler–Bernoulli beam under a moving force, based on two different versions of the nonlocal gradient theory of elasticity, namely, the Eringen model, in which the strain is a function of stress gradient, and the nonlocal model, in which the stress is a function of strains gradient, were studied and compared. A dynamic response of a finite, simply supported beam under a moving force was evaluated. The force is moving along the beam with a constant velocity. Particular solutions in the form of an infinite series and some solutions in a closed form as well as the numerical results were presented. |
| first_indexed | 2024-12-17T02:29:56Z |
| format | Article |
| id | doaj.art-e09263abb4e8482d9023f22d84e0f4c7 |
| institution | Directory Open Access Journal |
| issn | 2083-831X |
| language | English |
| last_indexed | 2024-12-17T02:29:56Z |
| publishDate | 2020-06-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Studia Geotechnica et Mechanica |
| spelling | doaj.art-e09263abb4e8482d9023f22d84e0f4c72022-12-21T22:07:00ZengSciendoStudia Geotechnica et Mechanica2083-831X2020-06-0142430631810.2478/sgem-2019-0049sgem-2019-0049Vibrations of the Euler–Bernoulli Beam Under a Moving Force based on Various Versions of Gradient Nonlocal Elasticity Theory: Application in NanomechanicsPaweł Śniady0Misiurek Katarzyna1Szyłko-Bigus Olga2Rafał Idzikowski3Faculty of Environmental Engineering and Geodesy, Wroclaw University of Environmental and Life Science, ul. Grunwaldzka 55, 50-357Wroclaw, PolandFaculty of Civil Engineering, Wroclaw University of Science and Technologypl. Grunwaldzki 11, 50-377Wroclaw, PolandFaculty of Civil Engineering, Wroclaw University of Science and Technologypl. Grunwaldzki 11, 50-377Wroclaw, PolandFaculty of Environmental Engineering and Geodesy, Wroclaw University of Environmental and Life Science, ul. Grunwaldzka 55, 50-357Wroclaw, PolandTwo models of vibrations of the Euler–Bernoulli beam under a moving force, based on two different versions of the nonlocal gradient theory of elasticity, namely, the Eringen model, in which the strain is a function of stress gradient, and the nonlocal model, in which the stress is a function of strains gradient, were studied and compared. A dynamic response of a finite, simply supported beam under a moving force was evaluated. The force is moving along the beam with a constant velocity. Particular solutions in the form of an infinite series and some solutions in a closed form as well as the numerical results were presented.https://doi.org/10.2478/sgem-2019-0049vibrationbeammoving forcenonlocal elasticity |
| spellingShingle | Paweł Śniady Misiurek Katarzyna Szyłko-Bigus Olga Rafał Idzikowski Vibrations of the Euler–Bernoulli Beam Under a Moving Force based on Various Versions of Gradient Nonlocal Elasticity Theory: Application in Nanomechanics Studia Geotechnica et Mechanica vibration beam moving force nonlocal elasticity |
| title | Vibrations of the Euler–Bernoulli Beam Under a Moving Force based on Various Versions of Gradient Nonlocal Elasticity Theory: Application in Nanomechanics |
| title_full | Vibrations of the Euler–Bernoulli Beam Under a Moving Force based on Various Versions of Gradient Nonlocal Elasticity Theory: Application in Nanomechanics |
| title_fullStr | Vibrations of the Euler–Bernoulli Beam Under a Moving Force based on Various Versions of Gradient Nonlocal Elasticity Theory: Application in Nanomechanics |
| title_full_unstemmed | Vibrations of the Euler–Bernoulli Beam Under a Moving Force based on Various Versions of Gradient Nonlocal Elasticity Theory: Application in Nanomechanics |
| title_short | Vibrations of the Euler–Bernoulli Beam Under a Moving Force based on Various Versions of Gradient Nonlocal Elasticity Theory: Application in Nanomechanics |
| title_sort | vibrations of the euler bernoulli beam under a moving force based on various versions of gradient nonlocal elasticity theory application in nanomechanics |
| topic | vibration beam moving force nonlocal elasticity |
| url | https://doi.org/10.2478/sgem-2019-0049 |
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