Nonlocal vibration of fractional order viscoelastic nanobeam with attached nanoparticle
Abstract
We propose a mathematical framework to examine the free damped transverse vibration of
nanobeams with attached nanoparticles by using the nonlocal theory of Eringen and fractional
calculus. Governing equation of nanobeam with arbitrary attached nanoparticle is derived by
considering the viscoelastic constitutive equation involving fractional order derivative and
nonlocal Euler-Bernoulli beam theory. The solution is proposed by using the method of
separation of variables. Eigenvalues and mode shapes are determined for two typical boundary
conditions. The solution of fractional order differential equation in terms of a time function is
found via Laplace transform method. The time dependent behavior is examined by observing the
time function for different values of fractional order parameter and different ratios of other
parameters in the model.
Keywords:
nanobeam / nonlocal viscoelasticity / fractional derivative viscoelasticity / nanotube mass sensorsSource:
Proceedings of the 5th International Congress of Serbian Society of Mechanics, Arandjelovac, June 15-17, 2015, I1c, 2015, 1-10Publisher:
- Belgrade: Serbian Society of Mechanics
- Novi Sad: Faculty of Technical Sciences
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)
- Dynamics of hybrid systems with complex structures. Mechanics of materials. (RS-MESTD-Basic Research (BR or ON)-174001)
- Dynamic stability and instability of mechanical systems subjected to stochastic excitations (RS-MESTD-Basic Research (BR or ON)-174011)
Collections
Institution/Community
Mašinski fakultetTY - CONF AU - Cajić, Milan AU - Karličić, Danilo AU - Lazarević, Mihailo PY - 2015 UR - https://machinery.mas.bg.ac.rs/handle/123456789/4248 AB - We propose a mathematical framework to examine the free damped transverse vibration of nanobeams with attached nanoparticles by using the nonlocal theory of Eringen and fractional calculus. Governing equation of nanobeam with arbitrary attached nanoparticle is derived by considering the viscoelastic constitutive equation involving fractional order derivative and nonlocal Euler-Bernoulli beam theory. The solution is proposed by using the method of separation of variables. Eigenvalues and mode shapes are determined for two typical boundary conditions. The solution of fractional order differential equation in terms of a time function is found via Laplace transform method. The time dependent behavior is examined by observing the time function for different values of fractional order parameter and different ratios of other parameters in the model. PB - Belgrade: Serbian Society of Mechanics PB - Novi Sad: Faculty of Technical Sciences C3 - Proceedings of the 5th International Congress of Serbian Society of Mechanics, Arandjelovac, June 15-17, 2015, I1c T1 - Nonlocal vibration of fractional order viscoelastic nanobeam with attached nanoparticle EP - 10 SP - 1 UR - https://hdl.handle.net/21.15107/rcub_machinery_4248 ER -
@conference{ author = "Cajić, Milan and Karličić, Danilo and Lazarević, Mihailo", year = "2015", abstract = "We propose a mathematical framework to examine the free damped transverse vibration of nanobeams with attached nanoparticles by using the nonlocal theory of Eringen and fractional calculus. Governing equation of nanobeam with arbitrary attached nanoparticle is derived by considering the viscoelastic constitutive equation involving fractional order derivative and nonlocal Euler-Bernoulli beam theory. The solution is proposed by using the method of separation of variables. Eigenvalues and mode shapes are determined for two typical boundary conditions. The solution of fractional order differential equation in terms of a time function is found via Laplace transform method. The time dependent behavior is examined by observing the time function for different values of fractional order parameter and different ratios of other parameters in the model.", publisher = "Belgrade: Serbian Society of Mechanics, Novi Sad: Faculty of Technical Sciences", journal = "Proceedings of the 5th International Congress of Serbian Society of Mechanics, Arandjelovac, June 15-17, 2015, I1c", title = "Nonlocal vibration of fractional order viscoelastic nanobeam with attached nanoparticle", pages = "10-1", url = "https://hdl.handle.net/21.15107/rcub_machinery_4248" }
Cajić, M., Karličić, D.,& Lazarević, M.. (2015). Nonlocal vibration of fractional order viscoelastic nanobeam with attached nanoparticle. in Proceedings of the 5th International Congress of Serbian Society of Mechanics, Arandjelovac, June 15-17, 2015, I1c Belgrade: Serbian Society of Mechanics., 1-10. https://hdl.handle.net/21.15107/rcub_machinery_4248
Cajić M, Karličić D, Lazarević M. Nonlocal vibration of fractional order viscoelastic nanobeam with attached nanoparticle. in Proceedings of the 5th International Congress of Serbian Society of Mechanics, Arandjelovac, June 15-17, 2015, I1c. 2015;:1-10. https://hdl.handle.net/21.15107/rcub_machinery_4248 .
Cajić, Milan, Karličić, Danilo, Lazarević, Mihailo, "Nonlocal vibration of fractional order viscoelastic nanobeam with attached nanoparticle" in Proceedings of the 5th International Congress of Serbian Society of Mechanics, Arandjelovac, June 15-17, 2015, I1c (2015):1-10, https://hdl.handle.net/21.15107/rcub_machinery_4248 .