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Nonlinear superharmonic resonance analysis of a nonlocal beam on a fractional visco-Pasternak foundation
,
Goran Janevski
Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Volume: 235, Issue: 20, Start page: 095440622093632
Swansea University Author:
Danilo Karlicic
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DOI (Published version): 10.1177/0954406220936322
Abstract
This paper investigates the dynamic behavior of a geometrically nonlinear nanobeam resting on the fractional visco-Pasternak foundation and subjected to dynamic axial and transverse loads. The fractional-order governing equation of the system is derived and then discretized by using the single-mode...
| Published in: | Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science |
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| ISSN: | 0954-4062 2041-2983 |
| Published: |
SAGE Publications
2020
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa54763 |
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| Abstract: |
This paper investigates the dynamic behavior of a geometrically nonlinear nanobeam resting on the fractional visco-Pasternak foundation and subjected to dynamic axial and transverse loads. The fractional-order governing equation of the system is derived and then discretized by using the single-mode Galerkin discretization. Corresponding forced Mathieu-Duffing equation is solved by using the perturbation multiple time scales method for the weak nonlinearity and by the semi-numerical incremental harmonic balance method for the strongly nonlinear case. A comparison of the results from two methods is performed in the validation study for the weakly nonlinear case and a fine agreement is achieved. A parametric study is performed and the advantages and deficiencies of each method are discussed for order two and three superharmonic resonance conditions. The results demonstrate a significant influence of the fractional-order damping of the visco-Pasternak foundation as well as the nonlocal parameter and external excitation load on the frequency response of the system. The proposed methodology can be used in pre-design procedures of novel energy harvesting and sensor devices at small scales exhibiting nonlinear dynamic behavior. |
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| Keywords: |
Nanobeams, nonlocal elasticity, fractional damping, nonlinear vibration, multiple scales method, incremental harmonic balance |
| College: |
Faculty of Science and Engineering |
| Issue: |
20 |
| Start Page: |
095440622093632 |