Q-factor control of a microcantilever by mechanical sideband excitation

We demonstrate the coupling between the fundamental and second flexural mode of a microcantilever. A mechanical analogue of cavity-optomechanics is then employed, where the mechanical cavity is formed by the second vibrational mode of the same cantilever, coupled to the fundamental mode via the geometric nonlinearity. By exciting the cantilever at the sum and difference frequencies between fundamental and second flexural mode, the motion of the fundamental mode of the cantilever is amplified and damped. This concept makes it possible to enhance or suppress the Q-factor over a wide range.Comment: 9 pages, 3 figure

Atomic force microscope cantilever with reduced second harmonic frequency during tip-surface contact

We describe an atomic force microscope cantilever design for which the second flexural mode frequency can be tailored relative to the first mode frequency, for operation in contact with a substrate. A freely-resonating paddle internal to the cantilever reduces the stiffness of the second flexural mode relative to the first while nearly maintaining the mass of the original cantilever. This strategy allows the ratio of the first two resonant modes f2/f1 to be controlled over the range 1.6 ??? 4.5. The ability to vary f2/f1 could improve a variety of dynamic contact-mode measurements

Amplitude dependence of image quality in atomically-resolved bimodal atomic microscopy

In bimodal FM-AFM, two flexural modes are excited simultaneously. The total vertical oscillation deflection range of the tip is the sum of the peak-to-peak amplitudes of both flexural modes (sum amplitude). We show atomically resolved images of KBr(100) in ambient conditions in bimodal AFM that display a strong correlation between image quality and sum amplitude. When the sum amplitude becomes larger than about 200 pm, the signal-to-noise ratio (SNR) is drastically decreased. We propose this is caused by the temporary presence of one or more water layers in the tip-sample gap. These water layers screen the short range interaction and must be displaced with each oscillation cycle. Further decreasing the sum amplitude, however, causes a decrease in SNR. Therefore, the highest SNR in ambient conditions is achieved when the sum amplitude is slightly less than the thickness of the primary hydration layer.Comment: 3000 words, 3 Figures, 3 supplimentary figure

Influence of the Second Flexural Mode on the Response of High-Speed Bridges

This paper deals with the assessment of the contribution of the second flexural mode to the dynamic behaviour of simply supported railway bridges. Alluding to the works of other authors, it is suggested in some references that the dynamic behaviour of simply supported bridges could be adequately represented taking into account only the contribution of the fundamental flexural mode. On the other hand, the European Rail Research Institute (ERRI) proposes that the second mode should also be included whenever the associated natural frequency is lower than 30 Hz]. This investigation endeavours to clarify the question as much as possible by establishing whether the maximum response of the bridge, in terms of displacements, accelerations and bending moments, can be computed accurately not taking account of the contribution of the second mode. To this end, a dimensionless formulation of the equations of motion of a simply supported beam traversed by a series of equally spaced moving loads is presented. This formulation brings to light the fundamental parameters governing the behaviour of the beam: damping ratio, dimensionless speed $\alpha$=VT/L, and L/d ratio (L stands for the span of the beam, V for the speed of the train, T represents the fundamental period of the bridge and d symbolises the distance between consecutive loads). Assuming a damping ratio equal to 1%, which is a usual value for prestressed high-speed bridges, a parametric analysis is conducted over realistic ranges of values of $\alpha$ and L/d. The results can be extended to any simply supported bridge subjected to a train of equally spaced loads in virtue of the so-called Similarity Formulae. The validity of these formulae can be derived from the dimensionless formulation mentioned above. In the parametric analysis the maximum response of the bridge is obtained for one thousand values of speed that cover the range from the fourth resonance of the first mode to the first resonance of the second mode. The response at twenty-one different locations along the span of the beam is compared in order to decide if the maximum can be accurately computed with the sole contribution of the fundamental mode

Observation of second flexural mode enhancement in graphene resonators

The enhancement of the second flexural mode in a monolayer graphene resonator by an inhomogeneous electrostatic actuation force has been observed. The devices have been fabricated by transferring the graphene onto a poly-Si/SiO2/Si substrate whereby the poly-Si has been released to produce graphene resonators. Enhancement of the second harmonic has been demonstrated by varying the actuation voltage, achieving an amplitude enhancement of up to 95% of the fundamental mode. The reported findings open new perspectives for graphene resonant sensors with enhanced sensitivity.</p

Finite element reduced order models for nonlinear vibrations of piezoelectric layered beams with applications to NEMS

This article presents a finite element reduced order model for the nonlinear vibrations of piezoelectric layered beams with application to NEMS. In this model, the geometrical nonlinearities are taken into account through a von Kármán nonlinear strain–displacement relationship. The originality of the finite element electromechanical formulation is that the system electrical state is fully described by only a couple of variables per piezoelectric patches, namely the electric charge contained in the electrodes and the voltage between the electrodes. Due to the geometrical nonlinearity, the piezoelectric actuation introduces an original parametric excitation term in the equilibrium equation. The reduced-order formulation of the discretized problem is obtained by expanding the mechanical displacement unknown vector onto the short-circuit eigenmode basis. A particular attention is paid to the computation of the unknown nonlinear stiffness coefficients of the reduced-order model. Due to the particular form of the von Kármán nonlinearities, these coefficients are computed exactly, once for a given geometry, by prescribing relevant nodal displacements in nonlinear static solutions settings. Finally, the low-order model is computed with an original purely harmonic-based continuation method. Our numerical tool is then validated by computing the nonlinear vibrations of a mechanically excited homogeneous beam supported at both ends referenced in the literature. The more difficult case of the nonlinear oscillations of a layered nanobridge piezoelectrically actuated is also studied. Interesting vibratory phenomena such as parametric amplification or patch length dependence of the frequency output response are highlighted in order to help in the design of these nanodevices.This research is part of the NEMSPIEZO project, under funds from the French National Research Agency (Project ANR-08-NAN O-015-04), for which the authors are grateful

A comparison of NASTRAN (Cosmic) and experimental results for the vibration of thick open cylindrical cantilevered shells

The natural frequencies and associated mode shapes for three thick open cantilevered cylindrical shells were determined both numerically and experimentally. The shells ranged in size from moderately to very thick with length to thickness ratios of 16, 8 and 5.6, the independent dimension being the shell thickness. The shell geometry is characterized by a circumferential angle of the 142 degrees and a ratio of length to inner radii arc length near 1.0. The finite element analysis was performed using NASTRAN's (COSMIC) triangular plate bending element CTRIA2, which includes membrane effects. The experimental results were obtained through holographic interferometry which enables one to determine the resonant frequencies as well as mode shapes from photographs of time-averaged holograms

Multiple impact regimes in liquid environment dynamic atomic force microscopy

A canonical assumption in dynamic atomic force microscopy is that the probe tip interacts with the sample once per oscillation cycle. We show this key ansatz breaks down for soft cantilevers in liquid environments. Such probes exhibit drum roll like dynamics with sequential bifurcations between oscillations with single, double, and triple impacts that can be clearly identified in the phase of the response. This important result is traced to a momentary excitation of the second flexural mode induced by tip-sample forces and low quality factors. Experiments performed on supported biological membranes in buffer solutions are used to demonstrate the findings. (C) 2008 American Institute of Physics