Mechanical stiffening, bistability, and bit operations in a microcantilever

Abstract

We investigate the nonlinear dynamics of microcantilevers. We demonstrate mechanical stiffening of the frequency response at large amplitudes, originating from the geometric nonlinearity. At strong driving the cantilever amplitude is bistable. We map the bistable regime as a function of drive frequency and amplitude, and suggest several applications for the bistable microcantilever, of which a mechanical memory is demonstrated. © 2010 American Institute of Physics. ͓doi:10.1063/1.3511343͔Microcantilevers are widely applied as transducers in sensitive instrumentation, 1,2 with scanning probe microscopy as a clear example. Typically, the cantilever is operated in the linear regime, i.e., it is driven by a harmonic force at moderate strength, and its response is modulated by the parameter to be measured. In clamped-clamped mechanical resonators, additional applications have been proposed based on nonlinear behavior. Nonlinearity in clamped-clamped resonators is due to the extension of the beam, which results in frequency pulling and bistability at strong driving, and can be described by a Duffing equation.3 Applications which employ this bistability are, e.g., elementary mechanical computing functions. 4,5 Since a cantilever beam is clamped only at one side, it can have a nonzero displacement without extending. One would therefore not expect a Duffing-like behavior for a cantilever beam. Nonlinear effects of a different origin have been observed in scanning probe microscopy, due to interactions between the cantilever and its environment. Tipsample interactions either weaken or stiffen the cantilever response, depending on the strength of the softening Van der Waals forces and electrostatic interactions and the hardening short range interactions. 6,7 Weakening also occurs when the cantilever is driven by an electrostatic force.8 Besides nonlinear interactions with the environment, theoretical studies predict intrinsic nonlinear behavior of cantilever beams, [8][9][10][11] of which indications have been reported. 11,12 In this paper, we report a detailed experimental analysis on the nonlinear mechanics of microcantilevers. It is shown that a hardening geometric nonlinearity dominates over softening nonlinear inertia, which effectively leads to a stiffening frequency response for the fundamental mode. At large amplitudes, the mechanical stiffening results in frequency pulling and ultimately in intrinsic bistability of the cantilever. We study the bistability in detail by measuring the cantilever response as a function of the frequency and amplitude, and compare the experimental observations with theory. A good agreement is found. We suggest several applications for the bistable cantilever, and as an example we demonstrate that bit operations can be implemented in the bistable cantilever.Experiments are performed on thin cantilevers with a rectangular cross section, w ϫ h, fabricated from lowpressure chemical vapor deposited silicon nitride using electron beam lithography and an isotropic reactive ion etching release p...

Nonlinear behaviour of self-excited microcantilevers in viscous fluids

“…Potential sources of nonlinearities include: nonlinear electronic components required for signal conditioning [11,12], nonlinear stress-strain relation of the cantilever material subject to large deformations [15,16] and nonlinear forces between the probe and the sample or surrounding viscous fluids [17]. As a result, the dynamics of these systems are often very complex and several cases of chaos [18] and bifurcations [19,20] on the response of the resonators have been reported.…”

Q-factor control of a microcantilever by mechanical sideband excitation

“…19 This geometric change has a small but measurable effect on the resonance frequency of all the other vibrational modes. The effect of the cantilever amplitude on its own resonance frequency was recently analyzed in detail; 20 for the first few modes, any nonzero amplitude stiffens the frequency response, and this gives rise to frequency pulling. Recently, we also presented a detailed study on the coupling mechanism between the vibrational modes in clamped-clamped resonators.…”

Minimal energy control of a nanoelectromechanical memory element

“…The feasibility of the use of a nanoelectromechanical system (NEMS) as a memory element has been demonstrated in a number of experimental investigations [1][2][3][4][5][6][7][8] . It has been suggested that in order to increase the frequency of operation, oscillatory states (cycles) should be used as the stationary states of memory elements, with consequential switching between two cycles.…”