Authors: Nešić, Nikola
Cajić, Milan 
Karličić, Danilo 
Janevski, Goran
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Nonlinear superharmonic resonance analysis of a nonlocal beam on a fractional visco-Pasternak foundation
Journal: Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science
Issue Date: 2-Jul-2020
Rank: M23
ISSN: 0954-4062
DOI: 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 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.
Keywords: fractional damping | incremental harmonic balance | multiple scales method | Nanobeams | nonlinear vibration | nonlocal elasticity
Publisher: SAGE Journals

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