Electrically tunable collective response in a coupled micromechanical array

Abstract

Abstract-We employ optical diffraction to study the mechanical properties of a grating array of suspended doubly clamped beams made of Au. The device allows application of electrostatic coupling between the beams that gives rise to formation of a band of normal modes of vibration (phonons). We parametrically excite these collective modes and study the response by measuring the diffraction signal. The results indicate that nonlinear effects strongly affect the dynamics of the system. Further optimization will allow employing similar systems for real-time mechanical spectrum analysis of electrical waveforms.[756]

Nonlinear Dynamics of Nanomechanical Resonators

“…Solid curves indicate stable solutions, and dashed curves are solutions that are unstable to small perturbations. Thin curves show the response without nonlinear damping (η D 0), which grows indefinitely with frequency Ω P and is therefore incompatible with experimental observations [8,66,71] as well as the assumptions of our calculation. As we saw for the saturation below threshold, without nonlinear damping and with linear damping being small, one would have to go to higher orders of perturbation theory to search for a physical mechanism that could provide saturation.…”

“…Such arrays have already exhibited interesting nonlinear dynamics, ranging from the formation of extended patterns [8,38], as one commonly observes in analogous continuous systems such as Faraday waves, to that of intrinsically localized modes [39,[58][59][60]. Thus, nanomechanical resonator arrays are perfect for testing dynamical theories of discrete nonlinear systems with many degrees of freedom.…”

“…We first consider the linear part of the equation, which has the form of (8.5) with T 0 in place of T, separate the variables, 8) and find its spatial eigenmodes φ n (z). For the eigenmodes, we use the convention that the local maximum of the eigenmode φ n (z) that is nearest to the center of the beam is scaled to 1.…”

“…The last two sections of this review describe theoretical work that was motivated directly by the experimental work of Buks and Roukes [8]. They fabricated an array of nonlinear micromechanical doubly-clamped gold beams, and excited them parametrically by modulating the strength of an externally controlled electrostatic coupling between neighboring beams.…”

“…The equations of motion for particular experimental implementations might have different terms, although we expect all will have linear and nonlinear damping, linear coupling, and parametric drive. For example, to model the experimental setup of Buks and Roukes [8], LC supposed that both linear and nonlinear dissipation terms involved the difference of neighboring displacements, that is, the terms involving P u n in our equations of motion (8.89) are replaced with terms involving u nC1 u n in the equations of motion (8.88) used by LC. This was to describe the physics of electric current damping, with the currents driven by the varying capacitance between neighboring resonators depending on the change in separation and the fixed DC voltage.…”