Homotopy analysis method: Difference between revisions

Revision as of 20:37, 25 May 2016

Revision as of 20:49, 26 May 2016

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[[File:HomotopySmall.gif|thumb|top|200px|The two dashed paths shown above are homotopic relative to their endpoints. The animation represents one possible homotopy.]]

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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|doi=10.1007/s00542-016-2947-7|url=http://link.springer.com/article/10.1007/s00542-016-2947-7}}</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}}</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|doi=10.1016/j.cnsns.2015.06.013|url=http://www.sciencedirect.com/science/article/pii/S1007570415002142}}</ref>.

== References ==