Self-excited Microcantilevers Research Articles

Bifurcation analysis and complex phenomena in self-excited microcantilevers

Sensors based on self-excitation of microcantilevers have been proposed as effective devices for the measurement of rheological properties of the fluid where they are immersed. However, embedding microcantilevers in a feedback loop causes complex phenomena that need to be investigated. Specifically, a variable delay in the loop originates jumps in the oscillation frequency. In this paper, we study the nonlinear dynamics of a self-excited microcantilever oscillating in viscous fluids. Using DDE-Biftool, a Matlab package for numerical bifurcation analysis of DDEs, we investigate the bifurcations of periodic solutions in one and two parameters. The numerical results are compared with some experimental data of previous studies.

Self-Excited Microcantilever with Higher Mode Using Band-Pass Filter.

Microresonators have a variety of scientific and industrial applications. The measurement methods based on the natural frequency shift of a resonator have been studied for a wide range of applications, including the detection of the microscopic mass and measurements of viscosity and stiffness. A higher natural frequency of the resonator realizes an increase in the sensitivity and a higher-frequency response of the sensors. In the present study, by utilizing the resonance of a higher mode, we propose a method to produce the self-excited oscillation with a higher natural frequency without downsizing the resonator. We establish the feedback control signal for the self-excited oscillation using the band-pass filter so that the signal consists of only the frequency corresponding to the desired excitation mode. It results that careful position setting of the sensor for constructing a feedback signal, which is needed in the method based on the mode shape, is not necessary. By the theoretical analysis of the equations governing the dynamics of the resonator coupled with the band-pass filter, it is clarified that the self-excited oscillation is produced with the second mode. Furthermore, the validity of the proposed method is experimentally confirmed by an apparatus using a microcantilever.

Experimental amplitude and frequency control of a self-excited microcantilever by linear and nonlinear feedback

It is well known that the micro scale deviations of mechanical properties of a sample can be detected by measurement methods that use microcantilever as resonators. Those methods use the natural frequency shift of a resonator, thus we need to recognize the frequency shift caused by the effects of a sample on a resonator with high sensitivity and accuracy. Experimental approaches based on self-excited oscillation enable the detection of these shifts even when the resonator is immersed in a high-viscosity environment. In the present study, we experimentally and theoretically investigate the nonlinear characteristics of a microcantilever resonator and their control by nonlinear feedback. We show that the steady-state response amplitude and the corresponding response frequency can be controlled by cubic nonlinear velocity feedback and cubic nonlinear displacement feedback, respectively. Furthermore, the amplitude and frequency of the steady-state self-excited oscillation can be controlled separately. These results will expand application of measurement methods that use self-excited resonators.

Nanoscale cutting using self-excited microcantilever

The application of self-excitation is proposed to improve the efficiency of the nanoscale cutting procedure based on use of a microcantilever in atomic force microscopy. The microcantilever shape is redesigned so that it can be used to produce vibration amplitudes with sufficient magnitudes to enable the excitation force applied by an actuator to be transferred efficiently to the tip of the microcantilever for the cutting process. A diamond abrasive that is set on the tip is also fabricated using a focused ion beam technique to improve the cutting effect. The natural frequency of the microcantilever is modulated based on the pressing load. Under conventional external excitation conditions, to maintain the microcantilever in its resonant state, it is necessary to vary the excitation frequency in accordance with the modulation. In this study, rather than using external excitation, the self-excitation cutting method is proposed to overcome this difficulty. The self-excited oscillation is produced by appropriate setting of the phase difference between the deflection signal of the microcantilever and the feedback signal for the actuator. In addition, it is demonstrated experimentally that the change in the phase difference enables us to control the amplitude of the self-excitation. As a result, control of the cutting depth is achieved via changes in the phase difference.

A Versatile Mass-Sensing Platform With Tunable Nonlinear Self-Excited Microcantilevers

A versatile mass-sensing platform based on the nonlinear dynamical response of a microcantilever embedded in a self-excitation feedback loop is proposed. It is experimentally shown that the delay imposed in the feedback loop by an adjustable phase-shifter can be used to finely tune this system to work in three different modalities, according to the desired mass sensing application: 1) as a continuous mass sensor, where the oscillation frequency smoothly responds to changes in the mass added to the resonator; 2) as a threshold sensor, where a sudden change in the oscillation frequency is triggered by an arbitrarily small change of mass added to the cantilever; and 3) as a stable microresonator, whose oscillation frequency is almost not affected by environmental conditions, such as changes in added mass, or in density/viscosity of the surrounding fluid. This variety of dynamical responses was registered for a wide range of added masses, in the form of beads individually attached to the cantilever. A complete analytical model to explain the observed experimental results is derived and shows a strong agreement with the measured data. The high resolution and signal-to-noise ratio, as well as the threshold and stable sensing modalities obtained with this closed-loop technique, are not available in the current open-loop microcantilever-based mass sensors.

Measuring viscosity with nonlinear self-excited microcantilevers

A viscosity sensor based on the nonlinear behaviour of a microcantilever embedded in a self-excitation loop with an adjustable phase-shifter is proposed. The self-sustained oscillation frequencies of the cantilever are experimentally and theoretically investigated as functions of the fluid viscosity and of the imposed phase shift of the signal along the self-excitation loop. The sensor performance is validated experimentally using different water-glycerol solutions. In contrast to existing rheological sensors, the proposed platform can be tuned to work in two different modes: a high-sensitivity device whose oscillation frequency changes smoothly with the rheological properties of the fluid or a critical viscosity threshold detector, where, for small changes in fluid viscosity, there is a step change in oscillation frequency.

Nonlinear behaviour of self-excited microcantilevers in viscous fluids

Microcantilevers are increasingly being used to create sensitive sensors for rheology and mass sensing at the micro- and nano-scale. When operating in viscous liquids, the low quality factor of such resonant structures, translating to poor signal-to-noise ratio, is often manipulated by exploiting feedback strategies. However, the presence of feedback introduces poorly-understood dynamical behaviours that may severely degrade the sensor performance and reliability. In this paper, the dynamical behaviour of self-excited microcantilevers vibrating in viscous fluids is characterized experimentally and two complementary modelling approaches are proposed to explain and predict the behaviour of the closed-loop system. In particular, the delay introduced in the feedback loop is shown to cause surprising non-linear phenomena consisting of shifts and sudden-jumps of the oscillation frequency. The proposed dynamical models also suggest strategies for controlling such undesired phenomena.

Van der Pol-Type Self-Excited Microcantilever Probe for Atomic Force Microscopy

A control method is proposed in order to reduce the steady-state amplitude of a self-excited cantilever probe in atomic force microscopy. The control method induces van der Pol oscillation by applying both linear and nonlinear feedback. Oscillation of the controlled cantilever cannot easily be stopped, even with the modulation of the viscous damping effect in the measurement environment, because the self-excited oscillation is produced far from the Hopf bifurcation point by high-gain linear feedback. Also, high-gain nonlinear feedback realizes a low steady-state amplitude to enable noncontact measurement. Finally, the feasibility of the practical application of a van der Pol-type self-excited microcantilever probe to nanoscale imaging is examined.

MP-53 非線形自励発振するマイクロカンチレバープローブの応答振幅(ポスターセッション)

MP-53 非線形自励発振するマイクロカンチレバープローブの応答振幅(ポスターセッション)

MNM-2A-5 van der Pol type自励発振型カンチレバープローブのダイナミクスとAFMへの応用(セッション 2A MEMSデバイスを用いた熱・流体計測,マイクロ・ナノ工学における非線形力学,電気等価回路から考えるMEMS設計手法)

Micro-cantilever probe behaves as a van der Pol oscillator by linear-plus-nonlinear feedback control. The nonlinear dynamics of van der Pol-type self-excited micro-cantilever probe is investigated by considering atomic force between the tip of the probe and a sample surface. By applying the method of multiple scales to the equation of motion, we derive the amplitude equation expressing the slow time variation of the response amplitude. It is noticed from the nonlinear analysis that the response amplitude can be kept small by high-gain nonlinear feedback. The response frequency in the van der Pol-type self-excited micro-cantilever probe cannot be deviated from the effective natural frequency independent of the magnitude of amplitude response.