The exact natural frequency solution of a free axialbending vibration problem of a non-uniform AFG cantilever beam with a tip body
2019
Download 🢃
Authors
Tomović, AleksandarŠalinić, Slaviša
Obradović, Aleksandar
Lazarević, Mihailo
Mitrović, Zoran
Conference object (Published version)
Metadata
Show full item recordAbstract
In this paper we present the solution of exact equations of motion for coupled axial and
bending vibrations of a non-uniform axially functionally graded (AFG) cantilever beam with a
body of which mass center is eccentrically displaced in axial and transverse direction with respect
to the beam’s end. The Euler-Bernoulli beam theory is implemented to model behavior of the
beam under axial and transverse in-plane vibrations. Based on the paper [1], that is supported by
results publish in the paper [2] authors confirm the obtained results of natural frequencies of the
AFG cantilever beam, when boundary conditions define the vibration coupling. The modified
symbolic-numeric method of initial parameters presented in [3] is implemented in computing
natural frequencies of the beam. This method is expanded to solve axial-bending vibration
problems, with respect to the one presented in the literature [3] for the problem of the vibration of
a cantilever beam. Some minor deviations in th...e obtained results may be noticed with respect to
those obtained in [1], yet all within a tolerance domain due to the computational precision.
Keywords:
coupled vibrations / boundary conditions / natural frequency / functionally graded materials / modified symbolic-numeric method of initial parameters / cantilever beamSource:
Proceeding of 7th International Congress of Serbian Society of Mechanics Sremski Karlovci, Serbia, June 24-26, 2019, 2019, M4c-Publisher:
- Beograd : Srpsko društvo za mehaniku
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)
Collections
Institution/Community
Mašinski fakultetTY - CONF AU - Tomović, Aleksandar AU - Šalinić, Slaviša AU - Obradović, Aleksandar AU - Lazarević, Mihailo AU - Mitrović, Zoran PY - 2019 UR - https://machinery.mas.bg.ac.rs/handle/123456789/4028 AB - In this paper we present the solution of exact equations of motion for coupled axial and bending vibrations of a non-uniform axially functionally graded (AFG) cantilever beam with a body of which mass center is eccentrically displaced in axial and transverse direction with respect to the beam’s end. The Euler-Bernoulli beam theory is implemented to model behavior of the beam under axial and transverse in-plane vibrations. Based on the paper [1], that is supported by results publish in the paper [2] authors confirm the obtained results of natural frequencies of the AFG cantilever beam, when boundary conditions define the vibration coupling. The modified symbolic-numeric method of initial parameters presented in [3] is implemented in computing natural frequencies of the beam. This method is expanded to solve axial-bending vibration problems, with respect to the one presented in the literature [3] for the problem of the vibration of a cantilever beam. Some minor deviations in the obtained results may be noticed with respect to those obtained in [1], yet all within a tolerance domain due to the computational precision. PB - Beograd : Srpsko društvo za mehaniku C3 - Proceeding of 7th International Congress of Serbian Society of Mechanics Sremski Karlovci, Serbia, June 24-26, 2019 T1 - The exact natural frequency solution of a free axialbending vibration problem of a non-uniform AFG cantilever beam with a tip body SP - M4c UR - https://hdl.handle.net/21.15107/rcub_machinery_4028 ER -
@conference{ author = "Tomović, Aleksandar and Šalinić, Slaviša and Obradović, Aleksandar and Lazarević, Mihailo and Mitrović, Zoran", year = "2019", abstract = "In this paper we present the solution of exact equations of motion for coupled axial and bending vibrations of a non-uniform axially functionally graded (AFG) cantilever beam with a body of which mass center is eccentrically displaced in axial and transverse direction with respect to the beam’s end. The Euler-Bernoulli beam theory is implemented to model behavior of the beam under axial and transverse in-plane vibrations. Based on the paper [1], that is supported by results publish in the paper [2] authors confirm the obtained results of natural frequencies of the AFG cantilever beam, when boundary conditions define the vibration coupling. The modified symbolic-numeric method of initial parameters presented in [3] is implemented in computing natural frequencies of the beam. This method is expanded to solve axial-bending vibration problems, with respect to the one presented in the literature [3] for the problem of the vibration of a cantilever beam. Some minor deviations in the obtained results may be noticed with respect to those obtained in [1], yet all within a tolerance domain due to the computational precision.", publisher = "Beograd : Srpsko društvo za mehaniku", journal = "Proceeding of 7th International Congress of Serbian Society of Mechanics Sremski Karlovci, Serbia, June 24-26, 2019", title = "The exact natural frequency solution of a free axialbending vibration problem of a non-uniform AFG cantilever beam with a tip body", pages = "M4c", url = "https://hdl.handle.net/21.15107/rcub_machinery_4028" }
Tomović, A., Šalinić, S., Obradović, A., Lazarević, M.,& Mitrović, Z.. (2019). The exact natural frequency solution of a free axialbending vibration problem of a non-uniform AFG cantilever beam with a tip body. in Proceeding of 7th International Congress of Serbian Society of Mechanics Sremski Karlovci, Serbia, June 24-26, 2019 Beograd : Srpsko društvo za mehaniku., M4c. https://hdl.handle.net/21.15107/rcub_machinery_4028
Tomović A, Šalinić S, Obradović A, Lazarević M, Mitrović Z. The exact natural frequency solution of a free axialbending vibration problem of a non-uniform AFG cantilever beam with a tip body. in Proceeding of 7th International Congress of Serbian Society of Mechanics Sremski Karlovci, Serbia, June 24-26, 2019. 2019;:M4c. https://hdl.handle.net/21.15107/rcub_machinery_4028 .
Tomović, Aleksandar, Šalinić, Slaviša, Obradović, Aleksandar, Lazarević, Mihailo, Mitrović, Zoran, "The exact natural frequency solution of a free axialbending vibration problem of a non-uniform AFG cantilever beam with a tip body" in Proceeding of 7th International Congress of Serbian Society of Mechanics Sremski Karlovci, Serbia, June 24-26, 2019 (2019):M4c, https://hdl.handle.net/21.15107/rcub_machinery_4028 .