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## Addressing geometric non-linearities with cantilever MEMS: beyond the Duffing model

*E. Collin, Yu.M. Bunkov and H. Godfrin*

We report on low-temperature measurements performed on microelectromechanical systems driven deeply into the nonlinear regime. The materials are kept in their elastic domain while the observed nonlinearity is purely of geometrical origin. Two techniques are used, harmonic drive and free decay. For each case, we present *an analytic* theory fitting the data. The harmonic drive is fit with a *modified Lorentzian* line shape obtained from an extended version of Landau and Lifshitz’s nonlinear theory. The evolution in the time domain is fit with an *amplitude-dependent frequency* decaying function derived from the Lindstedt-Poincaré theory of nonlinear differential equations. The technique is perfectly generic and can be straightforwardly adapted to *any* mechanical device made of ideally elastic constituents, and which can be reduced to a single degree of freedom, for an *experimental* definition of its nonlinear dynamics equation.

*Phys. Rev. B*

**82**, 235416 (2010)doi:

*10.1103/PhysRevB.82.235416*