Homotopy analysis method: Difference between revisions

Revision as of 03:01, 17 November 2018

Revision as of 10:46, 20 July 2019

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== Frequency response analysis for nonlinear oscillators ==

The HAM has recently been reported to be useful for obtaining analytical solutions for nonlinear frequency response equations. Such solutions are able to capture various nonlinear behaviors such as hardening-type, softening-type or mixed behaviors of the oscillator,.<ref>{{cite journal|last1=Tajaddodianfar|first1=Farid|title=Nonlinear dynamics of MEMS/NEMS resonators: analytical solution by the homotopy analysis method|journal=Microsystem Technologies|volume=23|issue=6|pages=1913–1926|doi=10.1007/s00542-016-2947-7|year=2017}}</ref><ref>{{cite journal|last1=Tajaddodianfar|first1=Farid|title=On the dynamics of bistable micro/nano resonators: Analytical solution and nonlinear behavior|journal=Communications in Nonlinear Science and Numerical Simulation|volume=20|issue=3|doi=10.1016/j.cnsns.2014.06.048|url=http://www.sciencedirect.com/science/article/pii/S1007570414003116|pages=1078–1089|bibcode=2015CNSNS..20.1078T|date=March 2015}}</ref> These analytical equations are also useful in prediction of chaos in nonlinear systems.<ref>{{cite journal|last1=Tajaddodianfar|first1=Farid|title=Prediction of chaos in electrostatically actuated arch micro-nano resonators: Analytical approach|journal=Communications in Nonlinear Science and Numerical Simulation|volume=30|issue=1–3|doi=10.1016/j.cnsns.2015.06.013|url=http://www.sciencedirect.com/science/article/pii/S1007570415002142|pages=182–195|date=January 2016}}</ref>

== References ==