Nonlocal vibration of a fractional order viscoelastic nanobeam with attached nanoparticle
We propose a novel mathematical framework to examine the free damped transverse vibration of a nanobeam by using the nonlocal theory of Eringen and fractional derivative viscoelasticity. The motion equation of a nanobeam with arbitrary attached nanoparticle is derived by considering the non...
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| Format: | Article |
| Language: | English |
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Serbian Society of Mechanics & Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade
2015-01-01
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| Series: | Theoretical and Applied Mechanics |
| Subjects: | |
| Online Access: | http://www.doiserbia.nb.rs/img/doi/1450-5584/2015/1450-55841503167C.pdf |
| _version_ | 1818270512203169792 |
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| author | Cajić Milan Karličić Danilo Lazarević Mihailo |
| author_facet | Cajić Milan Karličić Danilo Lazarević Mihailo |
| author_sort | Cajić Milan |
| collection | DOAJ |
| description | We propose a novel mathematical framework to examine the free damped
transverse vibration of a nanobeam by using the nonlocal theory of Eringen
and fractional derivative viscoelasticity. The motion equation of a nanobeam
with arbitrary attached nanoparticle is derived by considering the nonlocal
viscoelastic constitutive equation involving fractional order derivatives and
using the Euler-Bernoulli beam theory. The solution is proposed by using the
method of separation of variables. Eigenvalues and mode shapes are determined
for three typical boundary conditions. The fractional order differential
equation in terms of a time function is solved by using the Laplace transform
method. 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. Validation study is performed by comparing the
obtained results for a special case of our model with corresponding molecular
dynamics simulation results found in the literature. [Projekat Ministarstva
nauke Republike Srbije, br. OI 174001, br. OI 174011 i br. TR 35006] |
| first_indexed | 2024-12-12T21:11:27Z |
| format | Article |
| id | doaj.art-c5877c0c84a144faa3d5c1f2b19f4607 |
| institution | Directory Open Access Journal |
| issn | 1450-5584 2406-0925 |
| language | English |
| last_indexed | 2024-12-12T21:11:27Z |
| publishDate | 2015-01-01 |
| publisher | Serbian Society of Mechanics & Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade |
| record_format | Article |
| series | Theoretical and Applied Mechanics |
| spelling | doaj.art-c5877c0c84a144faa3d5c1f2b19f46072022-12-22T00:11:53ZengSerbian Society of Mechanics & Mathematical Institute of the Serbian Academy of Sciences and Arts, BelgradeTheoretical and Applied Mechanics1450-55842406-09252015-01-0142316719010.2298/TAM1503167C1450-55841503167CNonlocal vibration of a fractional order viscoelastic nanobeam with attached nanoparticleCajić Milan0Karličić Danilo1Lazarević Mihailo2Serbian Academy of Science and Arts, Mathematical Institute, Department of Mechanics, BelgradeFaculty of Mechanical Engineering, Department of Mechanics, NišFaculty of Mechanical Engineering, Department of Mechanics, BelgradeWe propose a novel mathematical framework to examine the free damped transverse vibration of a nanobeam by using the nonlocal theory of Eringen and fractional derivative viscoelasticity. The motion equation of a nanobeam with arbitrary attached nanoparticle is derived by considering the nonlocal viscoelastic constitutive equation involving fractional order derivatives and using the Euler-Bernoulli beam theory. The solution is proposed by using the method of separation of variables. Eigenvalues and mode shapes are determined for three typical boundary conditions. The fractional order differential equation in terms of a time function is solved by using the Laplace transform method. 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. Validation study is performed by comparing the obtained results for a special case of our model with corresponding molecular dynamics simulation results found in the literature. [Projekat Ministarstva nauke Republike Srbije, br. OI 174001, br. OI 174011 i br. TR 35006]http://www.doiserbia.nb.rs/img/doi/1450-5584/2015/1450-55841503167C.pdfnanobeamnonlocal viscoelasticityfractional derivative viscoelasticitynanotube mass sensorattached mass |
| spellingShingle | Cajić Milan Karličić Danilo Lazarević Mihailo Nonlocal vibration of a fractional order viscoelastic nanobeam with attached nanoparticle Theoretical and Applied Mechanics nanobeam nonlocal viscoelasticity fractional derivative viscoelasticity nanotube mass sensor attached mass |
| title | Nonlocal vibration of a fractional order viscoelastic nanobeam with attached nanoparticle |
| title_full | Nonlocal vibration of a fractional order viscoelastic nanobeam with attached nanoparticle |
| title_fullStr | Nonlocal vibration of a fractional order viscoelastic nanobeam with attached nanoparticle |
| title_full_unstemmed | Nonlocal vibration of a fractional order viscoelastic nanobeam with attached nanoparticle |
| title_short | Nonlocal vibration of a fractional order viscoelastic nanobeam with attached nanoparticle |
| title_sort | nonlocal vibration of a fractional order viscoelastic nanobeam with attached nanoparticle |
| topic | nanobeam nonlocal viscoelasticity fractional derivative viscoelasticity nanotube mass sensor attached mass |
| url | http://www.doiserbia.nb.rs/img/doi/1450-5584/2015/1450-55841503167C.pdf |
| work_keys_str_mv | AT cajicmilan nonlocalvibrationofafractionalorderviscoelasticnanobeamwithattachednanoparticle AT karlicicdanilo nonlocalvibrationofafractionalorderviscoelasticnanobeamwithattachednanoparticle AT lazarevicmihailo nonlocalvibrationofafractionalorderviscoelasticnanobeamwithattachednanoparticle |