Combined resonance of a nonlocal nanobeam on fractional Pasternak-type viscoelastic foundation
Abstract
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 multiple-scales 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
Keywords:
nanobeam / Pasternak-type viscoelastic / resonance / fractional orderSource:
Proceedings of 9th European Nonlinear Dynamics Conference (ENOC2017), edited by Gábor Stépán, Gábor Csernák. Budapest, 2017., 2017, 1-2Publisher:
- Budapest : CongressLIne Ltd.
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)
- Serbia-China bilateral project No. 3-12
Collections
Institution/Community
Mašinski fakultetTY - CONF AU - Cajić, Milan AU - Karličić, Danilo AU - Lazarević, Mihailo AU - Wen, Chen PY - 2017 UR - https://machinery.mas.bg.ac.rs/handle/123456789/4154 AB - 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 multiple-scales 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 PB - Budapest : CongressLIne Ltd. C3 - Proceedings of 9th European Nonlinear Dynamics Conference (ENOC2017), edited by Gábor Stépán, Gábor Csernák. Budapest, 2017. T1 - Combined resonance of a nonlocal nanobeam on fractional Pasternak-type viscoelastic foundation EP - 2 SP - 1 UR - https://hdl.handle.net/21.15107/rcub_machinery_4154 ER -
@conference{ author = "Cajić, Milan and Karličić, Danilo and Lazarević, Mihailo and Wen, Chen", year = "2017", abstract = "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 multiple-scales 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 = "Budapest : CongressLIne Ltd.", journal = "Proceedings of 9th European Nonlinear Dynamics Conference (ENOC2017), edited by Gábor Stépán, Gábor Csernák. Budapest, 2017.", title = "Combined resonance of a nonlocal nanobeam on fractional Pasternak-type viscoelastic foundation", pages = "2-1", url = "https://hdl.handle.net/21.15107/rcub_machinery_4154" }
Cajić, M., Karličić, D., Lazarević, M.,& Wen, C.. (2017). Combined resonance of a nonlocal nanobeam on fractional Pasternak-type viscoelastic foundation. in Proceedings of 9th European Nonlinear Dynamics Conference (ENOC2017), edited by Gábor Stépán, Gábor Csernák. Budapest, 2017. Budapest : CongressLIne Ltd.., 1-2. https://hdl.handle.net/21.15107/rcub_machinery_4154
Cajić M, Karličić D, Lazarević M, Wen C. Combined resonance of a nonlocal nanobeam on fractional Pasternak-type viscoelastic foundation. in Proceedings of 9th European Nonlinear Dynamics Conference (ENOC2017), edited by Gábor Stépán, Gábor Csernák. Budapest, 2017.. 2017;:1-2. https://hdl.handle.net/21.15107/rcub_machinery_4154 .
Cajić, Milan, Karličić, Danilo, Lazarević, Mihailo, Wen, Chen, "Combined resonance of a nonlocal nanobeam on fractional Pasternak-type viscoelastic foundation" in Proceedings of 9th European Nonlinear Dynamics Conference (ENOC2017), edited by Gábor Stépán, Gábor Csernák. Budapest, 2017. (2017):1-2, https://hdl.handle.net/21.15107/rcub_machinery_4154 .