Observation of Locked Intrinsic Localized Vibrational Modes in a Micromechanical Oscillator Array

Abstract

The nonlinear vibrational properties of a periodic micromechanical oscillator array have been measured. For sufficiently large amplitude of the driver, the optic mode of the di-element cantilever array becomes unstable and breaks up into excitations ranging over only a few cells. A driver-induced locking effect is observed to eternalize some of these intrinsic localized modes so that their amplitudes become fixed and the modes become spatially pinned. DOI: 10.1103/PhysRevLett.90.044102 PACS numbers: 05.45.-a, 05.45.Xt, 63.20.Pw, 85.85.+j Intrinsic localized modes (ILMs) which extend over only a few lattice sites of a periodic nonlinear lattice have been examined theoretically in a variety of systems [1][2][3][4]. Although the smallest excitations would be in a quantum lattice [5], there are still interesting issues in classical models to be explored experimentally such as mobility [6], discrete lattice potential [7], and interaction among ILMs [8], as well as the long-time behavior of a driver-induced modulational instability for a dissipative system. Thus the exploration of amplitude-dependent features is one of the important experimental issues at the present time.Although some experimental studies have been reported for large scale mechanical systems [9], for somewhat smaller Josephson-junction arrays [10,11] and optical waveguides [12,13], and for nanoscale lattices [14 -16] none of these systems are, as yet, appropriate for studying the detailed motion of large numbers of ILMs in the presence of a driver. Recently, microelectro-mechanical system (MEMS) silicon technology has matured sufficiently [17] so that we can make a few hundred coupled cantilever oscillators [18]. In this Letter we describe our experimental investigation of ILM creation and locking for a cantilever array in the presence of damping, disorder, and a driver.Our cantilever array is produced from a photoresist mask over a silicon nitride layer on a silicon substrate. This is exposed and then etched via a CF 4 plasma in a reactive ion chamber. The silicon substrate is undercut using an anisotropic KOH etch, thus releasing the silicon nitride cantilevers. A 3D rendition of one unit cell of the resulting array is shown in Fig. 1(a). Such cantilevers have a hard nonlinearity. To achieve the large amplitude uniform mode instability required to produce ILMs one needs to drive the highest frequency uniform mode of the system [19]. In order to accomplish this when using a piezoelectric transducer (PZT) driver, two different length cantilevers per unit cell have been constructed as shown in Fig. 1(a). With this di-element array the dispersion curve is folded over so that the highest frequency vibrational mode is now at the zone center. The room temperature quality factor of this mode is about 8000.Figure 1(b) shows the experimental setup for measuring ILM dynamics and mobility versus time. A cylindrical lens is used to focus a He-Ne laser line image on the static array. The reflected beam is then incident on a 1-D CCD camera. The PZT is driven...

Nonlinear Dynamics of Nanomechanical Resonators

“…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.…”

Counting discrete emission steps from intrinsic localized modes in a quasi-one-dimensional antiferromagnetic lattice

“…16,17,25,26 Our more recent experimental studies of ILMs have explored the uniform mode instability of classical nonlinear micromechanical arrays and demonstrated that, after ILMs are produced, a modest amplitude cw driver can be locked to some modes, resulting in coherent ILMs with fixed amplitudes as long as the driver remains on. 12,27 In Ref. 20 and the experiments described here we apply the same locking idea to an antiferromagnet.…”

Ultrasensitive mass sensing using mode localization in coupled microcantilevers

“…While numerous studies of mode localization in coupled structures [10][11][12][13][14][15] and arrays of coupled oscillators [16][17][18] have been performed, the question of whether this phenomenon can be used in a sensing capacity has not been examined. This question is addressed in this letter both theoretically and by means of experiments using coupled gold-foil microcantilevers.…”