Piezoelectrically actuated microscale resonators [1] are attractive for communication and signal processing applications. An example of a typical resonator studied in this work is shown in Figure 1. As pointed out in recent work [2]-[4], these resonators exhibit nonlinear characteristics, some of which may possibly be explained as oscillations about a non-flat equilibrium position that is caused due to buckling. The intent of the present work is to develop a model for this resonator from an experimental standpoint. To this end, the Düffing oscillator model is picked as a first prototype and parameters in this model are identified for various microscale oscillators. The basis for the parametric identification scheme is obtained from the work of Nayfeh and Balachandran [5].
Intrinsic Localized Modes (ILMs) are defined as localizations due to strong intrinsic nonlinearity within an array of perfect, periodically repeating oscillators. Such nonlinear phenomena have been studied for a number of years in the solid-state physics literature. Energy can become localized at a specific location in a discrete system as a result of the nonlinearity of the system and not due to any defects or impurities within the considered systems. Here, such mode localization is studied in the context of microcantilever arrays and microresonator arrays, and it is explored if an ILM can be realized as a forced nonlinear normal mode or nonlinear vibration mode. The method of multiple scales and methods to construct nonlinear normal modes are used to study nonlinear vibrations of microresonator arrays. Investigations reported in this article suggest that it is possible to realize an ILM as a forced nonlinear vibration mode. These results are believed to be important for future designs of microresonator arrays intended for signal processing, communication, and sensor applications.
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