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We report on low temperature measurements performed onmicro-electro-mechanical systems (MEMS) driven deeply into the non-linearregime. The materials are kept in their elastic domain, while the observednon-linearity is purely of geometrical origin. Two techniques are used,harmonic drive and free decay. For each case, we present an analytic theoryfitting the data. The harmonic drive is fit with a Lorentz-like lineshapeobtained from an extended version of Landau and Lifshitz's non-linear theory.The evolution in the time domain is fit with an amplitude-dependent frequencydecaying function derived from the Lindstedt-Poincar'e theory of non-lineardifferential equations. The technique is perfectly generic and can bestraightforwardly adapted to any mechanical device made of ideally elasticconstituents, and which can be reduced to a single degree of freedom, for anexperimental definition of its non-linear dynamics equation.

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