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.

Sensorless Self-Excited Vibrational Viscometer with Two Hopf Bifurcations Based on a Piezoelectric Device.

In this study, we propose a high-sensitivity sensorless viscometer based on a piezoelectric device. Viscosity is an essential parameter frequently used in many fields. The vibration type viscometer based on self-excited oscillation generally requires displacement sensor although they can measure high viscosity without deterioration of sensitivity. The proposed viscometer utilizes the sensorless self-excited oscillation without any detection of the displacement of the cantilever, which uses the interaction between the mechanical dynamics of the cantilever and the electrical dynamics of the piezoelectric device attached to the cantilever. Since the proposed viscometer has fourth-order dynamics and two coupled oscillator systems, the systems can produce different self-excited oscillations through different Hopf bifurcations. We theoretically showed that the response frequency jumps at the two Hopf bifurcation points and this distance between them depends on the viscosity. Using this distance makes measurement highly sensitive and easier because the jump in the response frequency can be easily detected. We experimentally demonstrate the efficiency of the proposed sensorless viscometer by a macro-scale measurement system. The results show the sensitivity of the proposed method is higher than that of the previous method based on self-excited oscillation with a displacement sensor.

Ultra-Sensitive Minute Mass Sensing Using a Microcantilever Virtually Coupled with a Virtual Cantilever.

Mass sensors based on the eigenmode shift of coupled cantilevers achieve much higher sensitivity than those based on the single cantilever's eigenfrequency shift. In the former sensors, two identical cantilevers and a weak coupling stiffness between them are required to achieve high sensitivity. However, conventional coupled cantilevers cannot satisfy these requirements because of machining accuracy. To satisfy both requirements, a virtual coupling between a real macrocantilever and a virtual cantilever, whose dynamics was calculated using a digital computer, was proposed in our previous research. The sensitive mass sensing of mg-order masses was achieved. In the present work, for minute mass sensing, we replace the real macrocantilever with a real microcantilever. The calculation speed of a digital computer is not fast enough to calculate the virtual cantilever's dynamics because the natural frequency of the microcantilver is much higher than that of the macrocantilever. Therefore, we use an analog circuit instead of a digital computer to achieve virtual coupling with the virtual cantilever. The proposed system enables us to tune the virtual cantilever's parameters to satisfy both requirements for high sensitivity by changing the analog circuit parameters. We verified experimentally that the proposed system achieved high sensitivity for mass sensing of the order of nanograms.

Nonlinear Dynamic Response of Nanocomposite Microbeams Array for Multiple Mass Sensing.

A nonlinear MEMS multimass sensor is numerically investigated, designed as a single input-single output (SISO) system consisting of an array of nonlinear microcantilevers clamped to a shuttle mass which, in turn, is constrained by a linear spring and a dashpot. The microcantilevers are made of a nanostructured material, a polymeric hosting matrix reinforced by aligned carbon nanotubes (CNT). The linear as well as the nonlinear detection capabilities of the device are explored by computing the shifts of the frequency response peaks caused by the mass deposition onto one or more microcantilever tips. The frequency response curves of the device are obtained by a pathfollowing algorithm applied to the reduced-order model of the system. The microcantilevers are described by a nonlinear Euler-Bernoulli inextensible beam theory, which is enriched by a meso-scale constitutive law of the nanocomposite. In particular, the microcantilever constitutive law depends on the CNT volume fraction suitably used for each cantilever to tune the frequency bandwidth of the whole device. Through an extensive numerical campaign, the mass sensor sensitivity estimated in the linear and nonlinear dynamic range shows that, for relatively large displacements, the accuracy of the added mass detectability can be improved due to the larger nonlinear frequency shifts at resonance (up to 12%).

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.