Contribution to the free vibration problem of a free-free beam with large end masses
Abstract
Free vibration of an Euler-Bernoulli beam with rigid bodies connected to the beam ends by both revolute joints and torsional springs is considered. The mass centers of rigid bodies have both the transverse and the axial eccentricity relative to the neutral axis of the undeformed beam. The coupling of the partial differential equations of axial and bending vibrations of the beam due to boundary conditions is considered. The frequency equation and the mode shape orthogonality condition of the system are derived. In order to illustrate the effect of the transverse and the axial eccentricity on the vibration behavior of the beam, a numerical example is provided.
Keywords:
mode orthogonality condition / free-free beam / free vibration / euler-bernoulli beam / end rigid bodiesSource:
Zamm-Zeitschrift Fur Angewandte Mathematik Und Mechanik, 2018, 98, 5, 840-847Publisher:
- Wiley-V C H Verlag Gmbh, Weinheim
Funding / projects:
- Sustainability and improvement of mechanical systems in energetic, material handling and conveying by using forensic engineering, environmental and robust design (RS-MESTD-Technological Development (TD or TR)-35006)
- Software development and national database for strategic management and development of transportation means and infrastructure in road, rail, air and inland waterways transport using the European transport network models (RS-MESTD-Technological Development (TD or TR)-36027)
DOI: 10.1002/zamm.201600300
ISSN: 0044-2267
WoS: 000431684500010
Scopus: 2-s2.0-85040533986
Collections
Institution/Community
Mašinski fakultetTY - JOUR AU - Šalinić, Slaviša AU - Obradović, Aleksandar AU - Dunjić, Momčilo AU - Sekulić, Dragan AU - Lazarević, Željko PY - 2018 UR - https://machinery.mas.bg.ac.rs/handle/123456789/2838 AB - Free vibration of an Euler-Bernoulli beam with rigid bodies connected to the beam ends by both revolute joints and torsional springs is considered. The mass centers of rigid bodies have both the transverse and the axial eccentricity relative to the neutral axis of the undeformed beam. The coupling of the partial differential equations of axial and bending vibrations of the beam due to boundary conditions is considered. The frequency equation and the mode shape orthogonality condition of the system are derived. In order to illustrate the effect of the transverse and the axial eccentricity on the vibration behavior of the beam, a numerical example is provided. PB - Wiley-V C H Verlag Gmbh, Weinheim T2 - Zamm-Zeitschrift Fur Angewandte Mathematik Und Mechanik T1 - Contribution to the free vibration problem of a free-free beam with large end masses EP - 847 IS - 5 SP - 840 VL - 98 DO - 10.1002/zamm.201600300 ER -
@article{ author = "Šalinić, Slaviša and Obradović, Aleksandar and Dunjić, Momčilo and Sekulić, Dragan and Lazarević, Željko", year = "2018", abstract = "Free vibration of an Euler-Bernoulli beam with rigid bodies connected to the beam ends by both revolute joints and torsional springs is considered. The mass centers of rigid bodies have both the transverse and the axial eccentricity relative to the neutral axis of the undeformed beam. The coupling of the partial differential equations of axial and bending vibrations of the beam due to boundary conditions is considered. The frequency equation and the mode shape orthogonality condition of the system are derived. In order to illustrate the effect of the transverse and the axial eccentricity on the vibration behavior of the beam, a numerical example is provided.", publisher = "Wiley-V C H Verlag Gmbh, Weinheim", journal = "Zamm-Zeitschrift Fur Angewandte Mathematik Und Mechanik", title = "Contribution to the free vibration problem of a free-free beam with large end masses", pages = "847-840", number = "5", volume = "98", doi = "10.1002/zamm.201600300" }
Šalinić, S., Obradović, A., Dunjić, M., Sekulić, D.,& Lazarević, Ž.. (2018). Contribution to the free vibration problem of a free-free beam with large end masses. in Zamm-Zeitschrift Fur Angewandte Mathematik Und Mechanik Wiley-V C H Verlag Gmbh, Weinheim., 98(5), 840-847. https://doi.org/10.1002/zamm.201600300
Šalinić S, Obradović A, Dunjić M, Sekulić D, Lazarević Ž. Contribution to the free vibration problem of a free-free beam with large end masses. in Zamm-Zeitschrift Fur Angewandte Mathematik Und Mechanik. 2018;98(5):840-847. doi:10.1002/zamm.201600300 .
Šalinić, Slaviša, Obradović, Aleksandar, Dunjić, Momčilo, Sekulić, Dragan, Lazarević, Željko, "Contribution to the free vibration problem of a free-free beam with large end masses" in Zamm-Zeitschrift Fur Angewandte Mathematik Und Mechanik, 98, no. 5 (2018):840-847, https://doi.org/10.1002/zamm.201600300 . .