Authors: Cajić, Milan 
Karličić, Danilo 
Lazarević, Mihailo
Wen, Chen
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Combined resonance of a nonlocal nanobeam on fractional Pasternak-type viscoelastic foundation
First page: 1
Last page: 2
Conference: 9th European Nonlinear Dynamics Conference (ENOC 2017)
Issue Date: 2017
Rank: M30
ISBN: 978-963-12-9168-1
In this communication, we observe the interaction of fundamental parametric resonances with subharmonic resonances of order one-half of a geometrically nonlinear nonlocal nanobeam model resting on a fractional Pasternak-type viscoelastic foundation. Euler-Bernoulli beam theory and nonlinear von Karman strain-displacement relation are employed to obtained fractional order governing equation for the transverse vibration of a system. Under the assumption of small fractional damping, we used the perturbation multiplescales method to obtain an approximated analytical solution for the frequency-amplitude response. Combined parametric resonance from axial load and subharmonic resonance under external excitation are examined for different parameters of the model. Validation of the multiple scales solution against numerical solution in the phase plane and Poincare map will be provided.
Publisher: European Society of Mechanics
Project: Dynamics of hybrid systems with complex structures. Mechanics of materials. 

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