Mechanical Resonance Frequency Research Articles

Magnetic actuator driver system for laser scanning capsule endoscopy

This paper focuses on designing and implementing a power and area-efficient magnetic actuator driver interface integrated circuit for laser scanning capsule endoscopy. The proposed system contains a 3D-printed focus-adjusting actuator embarking a lens, multiple magnets, an external coil, battery, laser, and actuator driver integrated circuit with off-chip components. The actuator features multiple pantograph springs connected to the lens, as well as multiple magnets, enabling precise focusing capability through electromagnetic actuation. A magnetic actuator driver integrated circuit implemented in a commercial 180 nm CMOS process drives the coil at 32 Hz, which is the mechanical resonance frequency of the actuator. A novel control methodology for the driver has been devised, aimed at enhancing driving efficiency and mitigating total harmonic distortion. Simulations and measurements substantiate that the actuator can induce a 3.22 mm focal point displacement while the driver circuit delivers 9.62 mA (RMS) current to the 7.7 mH coil. Under these conditions, the system exhibits an aggregate power consumption of 11.48 mW, thereby achieving a power efficiency of 85.5%.

Optomechanics Driven by Noisy and Narrowband Fields

AbstractWe report a study of a cavity optomechanical system driven by narrowband electromagnetic fields, which are applied either in the form of uncorrelated noise, or as a more structured spectrum. The bandwidth of the driving spectra is smaller than the mechanical resonant frequency, and thus we can describe the resulting physics using concepts familiar from regular cavity optomechanics in the resolved-sideband limit. With a blue-detuned noise driving, the noise-induced interaction leads to anti-damping of the mechanical oscillator, and a self-oscillation threshold at an average noise power that is comparable to that of a coherent driving tone. This process can be seen as noise-induced dynamical amplification of mechanical motion. However, when the noise bandwidth is reduced down to the order of the mechanical damping, we discover a large shift of the power threshold of self-oscillation. This is due to the oscillator adiabatically following the instantaneous noise profile. In addition to blue-detuned noise driving, we investigate narrowband driving consisting of two coherent drive tones nearby in frequency. Also in these cases, we observe deviations from a naive optomechanical description relying only on the tones’ frequencies and powers.

Comparison of Multifrequency Narrow-Band CE-Chirp and Tone Burst Evoked Cervical Vestibular Evoked Myogenic Potentials.

Cervical vestibular evoked myogenic potentials (cVEMPs) are inhibitory myogenic responses that have commonly been elicited using a variety of stimuli. Yet the comparison of the effects of multifrequency tone bursts and narrow-band Claus Elberling chirps (NB CE-chirps) on cVEMPs has never been studied in homogeneous age groups. The present study focused on comparing the effect of multifrequency NB CE-chirps and tone bursts on the various parameters of cVEMP responses in normal-hearing younger adults. A within-group study design was applied, and purposive sampling was utilized for the collection of the data sample. The present study involved the elicitation of NB CE-chirp and tone burst-evoked cVEMPs across four-octave frequencies in 25 normal-hearing younger adults. NB CE-chirp and tone burst evoked cVEMPs were found to have a 100% response rate for all frequencies except 4,000 Hz. Across frequencies, P1 and N1 latencies were seen to be significantly shorter for NB CE-chirps than tone bursts at 500 Hz and 1,000 Hz stimulation. No differences were seen in the P1N1 amplitudes and interaural asymmetry ratio between the two stimuli across all four-octave frequencies. Furthermore, we found a significantly higher number of ears tuned to NB CE-chirps than tone bursts at 500 Hz. Comparative differences in the latencies of cVEMP responses between and within stimuli could be due to the variation in stimuli duration. Also, the difference in amplitudes across stimulation frequencies might have resulted due to the predominance of saccular responses at lower mechanical resonance frequencies. Thus, the tuning was also seen at 500 Hz and was relatively higher for NB CE-chirps than tone bursts.

Design and Analysis of MEMS-Based Capacitive Power Inverter Using Electrostatic Transduction

In this study, a capacitive microelectromechanical system (MEMS) based DC/AC power inverter design for renewable energy applications is proposed, modeled, and analyzed. In the proposed approach, electrostatic actuation is preferred to develop a DC/AC power inverter with varying phase overlap lengths for solar energy systems. The operating voltage required during the analysis is applied to the active part as the tensile stress. Thus, the maximum displacement is achieved with less instability. The developed inverter is based on MEMS to achieve miniaturized performances, producing smooth sine wave output, efficiently obtaining the signal frequency, and low power consumption. The proposed inverter has a thickness of 325 μm, an active settlement area of 45x45x0.585 mm3, and an initial capacitance value of 2.9 pF. In addition, a 50 Hz mechanical resonance frequency was used to be compatible with the frequency of the city network. It can convert voltage values between 0.5V and 24V DC with a MEMS power inverter. Since the inverter is based on a capacitive structure, it provides near-zero power consumption. The frequency and waveform of the converted DC/AC signal match the AC signal of a power grid with an efficiency of 5%.

Online Mechanical Resonance Frequency Identification Method Based on an Improved Second-Order Generalized Integrator—Frequency-Locked Loop

To address the issue of mechanical resonance frequency detection in dual-inertia servo systems, this paper proposes an online identification method for mechanical resonance frequency using a low-pass filter and cascaded second-order generalized integrator—frequency-locked loop (LPF-CSOGI-FLL). Initially, the cascaded second-order generalized integrator—frequency-locked loop (CSOGI-FLL) is employed to eliminate the interference of direct current (DC) bias in resonance frequency identification. From a dual-stage structural perspective, the first second-order generalized integrator (SOGI-FLL) acts as a band-pass pre-filter to extract the mechanical resonance signal from the signal to be tested. The second SOGI-FLL generates a signal with equal amplitude and frequency to the mechanical resonance and obtains the frequency of the resonance signal through the frequency-locked loop. Subsequently, a low-pass filter (LPF) is applied to the frequency feedback loop of the second-stage SOGI-FLL, effectively reducing the oscillation of the estimated frequency. Finally, combining the CSOGI-FLL with an LPF forms a novel structure, namely, LPF-CSOGI-FLL. The results demonstrate that the proposed method significantly improves the detection accuracy of mechanical resonance frequency under various conditions. Compared to traditional offline techniques, this method overcomes the impact of resonance frequency drift and enhances system stability.

Elucidation of the “jumping and dropping” phenomena of piezoelectric vibrators in high-amplitude operations in the vicinity of their mechanical resonance frequencies

The peculiar events called the “jumping and dropping” phenomena of piezoelectric ceramic vibrators in high amplitude operation have been widely known. The phenomena, that occur solely in the vicinity of the mechanical resonance frequencies of the vibrators, are due to the emergence of hysteresis in the frequency domain with an abrupt increase and decrease of the vibratory amplitude. It has long been believed that the nonlinearity of the piezoelectric materials is the dominant cause of the unstable vibratory behaviors. Nevertheless, the authors have found that they can be attributed to the local piezoelectric polarization reversals due to the electric field concentration caused by its conspicuous distortion inside the vibrators in mechanical resonance. This hypothesis has been examined by numerical and experimental investigations for hard-type piezoelectric ceramic disks vibrating in axisymmetric radially pulsating mode.

Quantifying stress distribution in ultra-large graphene drums through mode shape imaging

Suspended drums made of 2D materials hold potential for sensing applications. However, the industrialization of these applications is hindered by significant device-to-device variations presumably caused by non-uniform stress distributions induced by the fabrication process. Here, we introduce a methodology to determine the stress distribution from their mechanical resonance frequencies and corresponding mode shapes as measured by a laser Doppler vibrometer (LDV). To avoid limitations posed by the optical resolution of the LDV, we leverage a manufacturing process to create ultra-large graphene drums with diameters of up to 1000 μm. We solve the inverse problem of a Föppl–von Kármán plate model by an iterative procedure to obtain the stress distribution within the drums from the experimental data. Our results show that the generally used uniform pre-tension assumption overestimates the pre-stress value, exceeding the averaged stress obtained by more than 47%. Moreover, it is found that the reconstructed stress distributions are bi-axial, which likely originates from the transfer process. The introduced methodology allows one to estimate the tension distribution in drum resonators from their mechanical response and thereby paves the way for linking the used fabrication processes to the resulting device performance.

Selective cooling and squeezing in a lossy optomechanical closed loop embodying an exceptional surface

A closed-loop, lossy optomechanical system consisting of one optical and two degenerate mechanical resonators is computationally investigated. This system constitutes an elementary synthetic plaquette derived from the loop phase of the intercoupling coefficients. In examining a specific quantum attribute, we delve into the control of quadrature variances within the resonator selected through the plaquette phase. An amplitude modulation is additionally applied to the cavity-pumping laser to incorporate mechanical squeezing. Our numerical analysis relies on the integration-free computation of steady-state covariances for cooling and the Floquet technique for squeezing. We provide physical insights into how non-Hermiticity plays a crucial role in enhancing cooling and squeezing in proximity to exceptional points. This enhancement is associated with the behavior of complex eigenvalue loci as a function of the intermechanical coupling rate. Additionally, we demonstrate that the parameter space embodies an exceptional surface, ensuring the robustness of exceptional point singularities under experimental parameter variations. However, the pump laser detuning breaks away from the exceptional surface unless it resides on the red-sideband by an amount sufficiently close to the mechanical resonance frequency. Finally, we show that this disparate parametric character entitles frequency-dependent cooling and squeezing, which is of technological importance.

Johnson-noise-limited cancellation-free microwave impedance microscopy with monolithic silicon cantilever probes

Microwave impedance microscopy (MIM) is an emerging scanning probe technique for nanoscale complex permittivity mapping and has made significant impacts in diverse fields. To date, the most significant hurdles that limit its widespread use are the requirements of specialized microwave probes and high-precision cancellation circuits. Here, we show that forgoing both elements not only is feasible but also enhances performance. Using monolithic silicon cantilever probes and a cancellation-free architecture, we demonstrate Johnson-noise-limited, drift-free MIM operation with 15 nm spatial resolution, minimal topography crosstalk, and an unprecedented sensitivity of 0.26 zF/√Hz. We accomplish this by taking advantage of the high mechanical resonant frequency and spatial resolution of silicon probes, the inherent common-mode phase noise rejection of self-referenced homodyne detection, and the exceptional stability of the streamlined architecture. Our approach makes MIM drastically more accessible and paves the way for advanced operation modes as well as integration with complementary techniques.

Nano-optomechanical fiber-tip sensing

Nano-optomechanical sensors exploit light confinement at the nanoscale to enable very precise measurements of displacement, force, acceleration, and mass. Their application is hampered by the complex optical set-ups or packaging schemes required to couple light to and from the nano-optomechanical resonator. In this work, we present a fiber-coupled nano-optomechanical sensor that requires no coupling optics. This is achieved by directly placing a nano-optomechanical structure, a double membrane photonic crystal (DM-PhC), on the facet of a fiber, using a simple and scalable wafer-to-fiber transfer method. The device is probed in reflection and has a resonance at telecom wavelengths with a relatively broad spectral width of 3–10 nm, which is advantageous for a simple read-out and achieves a displacement imprecision of 10fm/Hz\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10\\,{{\\rm{fm}}}/{\\sqrt{{\\rm{Hz}}}}$$\\end{document}. Using resonant driving and a ringdown measurement, we can induce and monitor mechanical oscillations with an nm-scale amplitude via the fiber, which allows for tracking the mechanical resonant frequency and the mechanical linewidth with imprecisions of 79 and 12 Hz, respectively, at integration times of 4.5 s. We further demonstrate the application of this fiber-tip sensor to the measurement of pressure, using the effect of collisional damping on the mechanical linewidth, leading to the imprecision of 9×10−4mbar\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$9\ imes {10}^{-4}\\,{\\rm{mbar}}$$\\end{document} with an integration time of 290 s. This combination of optomechanics and fiber-tip sensing may open the way to a new generation of fiber sensors with unprecedented functionality, ultrasmall footprint, and low-cost readout.

Squeeze film absolute pressure sensors with sub-millipascal sensitivity

We report on the realization of ultrasensitive absolute pressure sensors based on silicon nitride membrane sandwiches. These sandwiches consist in a pair of highly-pretensioned, ultrathin (50 nm), large area (0.25 mm2) films, suspended parallel to each other and forming an ultrashort (500 nm) open cavity. The compression of a gas in this cavity leads to a strong squeeze film force, resulting in an increase in the membrane mechanical resonance frequencies, which is directly proportional to the absolute gas pressure. These sandwiches show a record high responsivity of >300 Hz/Pa in terms of squeeze film-induced frequency shift in the range 10−3-100 Pa, which, combined with high quality factor mechanical resonances (Q>106), allows for bringing the sensitivity of absolute squeeze film pressure sensors down to the sub-millipascal level.

A wide drive frequency matching method for harmonic suppression and voltage stabilization of ultrasonic motors.

To reduce harmonic components, balance system impedance, and stabilize driving voltage, an additional matching circuit is required for ultrasonic motors (USMs) driver. However, the performance of inductor or capacitor matching can be seriously weakened with changes in driving frequency. Therefore, this paper presents a simple and effective LC matching method against driving frequency adjustment for USMs. First, the driving scheme of the USM is proposed and the electromechanical coupling model is analyzed. Subsequently, the output characteristics of the full-bridge inverter are derived theoretically when the driving frequency deviates from the mechanical resonant frequency. Then, the impedance circular transform method is proposed, which can intuitively analyze the effect of matching parameters on the voltage amplitude. A matching objective function is established that can consider both the voltage stabilization and harmonic suppression. The matching parameters are solved using random weight particle swarm optimization. Simulations and experiments demonstrate that within the operating frequency of the USM, the proposed matching method can effectively prevent overvoltage and suppress harmonic components. Furthermore, compared with the existing resonant matching method, the proposed matching method can realize more stable driving capability at different frequencies. The proposed method could be useful for USMs' variable-frequency driver design.

Ultrasensitive optomechanical strain sensor

We demonstrate an ultrasensitive optomechanical strain sensor based on a SiN membrane and a Fabry-Perot cavity, enabling the measurements of both static and dynamic strain by monitoring reflected light fluctuations using a single-frequency laser. The SiN membrane offers high-quality-factor mechanical resonances that are sensitive to minute strain fluctuations. The two-beam Fabry-Perot cavity is constructed to interrogate the motion state of the SiN membrane. A static strain resolution of 4.00 nɛ is achieved by measuring mechanical resonance frequency shifts of the SiN membrane. The best dynamic resolution is 4.47 pɛHz-1/2, which is close to that of the sensor using high-finesse cavity and optical frequency comb, overcoming the dependence of ultrasensitive strain sensors on narrow-linewidth laser and high-finesse cavity with frequency locking equipment. This work opens up a promising avenue for a new generation of ultrasensitive strain sensors.

Effect of air-loading on the performance limits of graphene microphones

As a consequence of their high strength, small thickness, and high flexibility, ultrathin graphene membranes show great potential for pressure and sound sensing applications. This study investigates the performance of multi-layer graphene membranes for microphone applications in the presence of air-loading. Since microphones need a flatband response over the full audible bandwidth, they require a sufficiently high mechanical resonance frequency. Reducing membrane thickness facilitates meeting this bandwidth requirement, and therefore, also allows increasing compliance and sensitivity of the membranes. However, at atmospheric pressure, air-loading effects can increase the effective mass, and thus, reduce the bandwidth of graphene and other 2D material-based microphones. To assess the severity of this performance-limiting effect, we characterize the acoustic response of multi-layer graphene membranes with a thickness of 8 nm in the pressure range from 30 to 1000 mbar, in air and helium environments. A bandwidth reduction by a factor ∼2.8× for membranes with a diameter of 500 μm is observed. These measurements show that air-loading effects, which are usually negligible in conventional microphones, can lead to a substantial bandwidth reduction in ultrathin graphene microphones. With analytical and finite element models, we further analyze the performance limits of graphene microphones in the presence of air-loading effects.

Sample-tracking vibration isolation with rigid negative stiffness for broad bandwidth

Sample-tracking vibration isolators position their mover such that the distance to a targeted sample is constant to provide a vibration-free environment, for example, for inline metrology with high resolution. To achieve high vibration isolation and rejection especially at low frequencies, this paper proposes a sample-tracking vibration isolator that integrates a flexure-guided hybrid reluctance actuator (HRA) with a negative stiffness for quasi-zero stiffness (QZS). The negative stiffness cancels the flexure stiffness for QZS, by which vibrations transmitted from the actuator’s stator can be significantly reduced. Unlike conventional QZS systems, the negative stiffness is magnetically realized with rigid components such as a permanent magnet and ferromagnetic cores. Consequently, the proposed vibration isolator has mechanical resonant frequencies of around 2.5kHz and higher. This hardware design with a feedback controller realizes a motion with nanometer resolution and a high closed-loop control bandwidth of 991Hz for further vibration isolation and sample tracking. To evaluate the performances of the proposed vibration isolator, the negative stiffness is tuned to cancel a flexure stiffness at experiments. Experimental results show that the fine tuning decreases transmissibility from −30dB to −62dB by a factor of 40 at a low frequency of 10Hz. Furthermore, the tracking error of the mover position is measured for a demonstration of the vibration rejection performance in the time domain. The results also show that the stiffness cancellation decreases the tracking error with feedback control from 2.7 nm (rms) to 1.3 nm (rms) by 52% at a steady state. The proposed sample-tracking vibration isolator successfully demonstrates high vibration isolation performance by utilizing the rigid negative stiffness of the HRA.

Design, fabrication, and characterization of kinetic-inductive force sensors for scanning probe applications.

We describe a transducer for low-temperature atomic force microscopy based on electromechanical coupling due to a strain-dependent kinetic inductance of a superconducting nanowire. The force sensor is a bending triangular plate (cantilever) whose deflection is measured via a shift in the resonant frequency of a high-Q superconducting microwave resonator at 4.5 GHz. We present design simulations including mechanical finite-element modeling of surface strain and electromagnetic simulations of meandering nanowires with large kinetic inductance. We discuss a lumped-element model of the force sensor and describe the role of an additional shunt inductance for tuning the coupling to the transmission line used to measure the microwave resonance. A detailed description of our fabrication is presented, including information about the process parameters used for each layer. We also discuss the fabrication of sharp tips on the cantilever using focused electron beam-induced deposition of platinum. Finally, we present measurements that characterize the spread of mechanical resonant frequency, the temperature dependence of the microwave resonance, and the sensor's operation as an electromechanical transducer of force.

Optical coupling control of isolated mechanical resonators

We present a Hamiltonian model describing two pairs of mechanical and optical modes under standard optomechanical interaction. The vibrational modes are mechanically isolated from each other and the optical modes couple evanescently. We recover the ranges for variables of interest, such as mechanical and optical resonant frequencies and naked coupling strengths, using a finite element model for a standard experimental realization. We show that the quantum model, under this parameter range and external optical driving, may be approximated into parametric interaction models for all involved modes. As an example, we study the effect of detuning in the optical resonant frequencies modes and optical driving resolved to mechanical sidebands and show an optical beam splitter with interaction strength dressed by the mechanical excitation number, a mechanical bidirectional coupler, and a two-mode mechanical squeezer where the optical state mediates the interaction strength between the mechanical modes.

Beat phenomena of oscillating readouts.

To demonstrate slowly varying, erroneous magnetic field gradients for oscillating readouts due to the mechanically resonant behavior of gradient systems. Projections of a static phantom were acquired using a one-dimensional (1D) EPI sequence with varying EPI frequencies ranging from 1121 to 1580 Hz on clinical 3T systems (30 mT/m, 200 T/m/s). Phase due to static B0 inhomogeneities was eliminated by a complex division of two separate scans with different polarities of the EPI readout. The temporal evolution of phase was evaluated and related to the mechanical resonances of the gradient systems derived from the gradient modulation transfer function. Additionally, the impact of temporally varying mechanical resonance effects on EPI was evaluated using an echo-planar spectroscopic imaging sequence. A beat phenomenon resulting in a slowly varying phase was observed. Its temporal frequency was given by the difference between the EPI frequency and the mechanical resonance frequency of the activated gradient axis. The maximum erroneous, oscillating phase during phase encoding was ±0.5 rad for an EPI frequency of 1281 Hz. Echo-planar spectroscopic imaging images showed the resulting time-dependent stretching/compression of the FOV. Oscillating readouts such as those used in EPI can result in low-frequency, erroneous phase contributions, which are explained by the beat phenomenon. Therefore, EPI phase-correction approaches may need to include beat effects for accurate image reconstruction.

Measurement of web tension using ambient vibrations in roll-to-roll manufacturing of flexible and printed electronics

Abstract Web tension measurement and control are important for the quality control of flexible and printed electronics fabricated by roll-to-roll (R2R) manufacturing. The distribution of tension within a R2R web can be calculated from the values of the web’s mechanical resonance frequencies. Typically, such measurements require an active external forcing to be generated and applied to the web. In this work, we show it is possible to obtain the web’s resonance frequencies from forcing due to ambient noise present in the test environment. This result broadens the applicability of noncontact resonance methods for computing web tension as currently available methods of active external forcing cannot be applied to all web materials and all R2R operating environments. We validate the ambient excitation method by comparing it to speaker-based acoustic excitation at atmospheric pressure and find the two methods agree within 0.5%. A calculation of the experimental motion of the web due to finite temperature effects suggests the observed vibration is generated from air-borne or structure-borne noise in the test environments. To show the effectiveness of the approach, we demonstrate the use of ambient excitation at five externally applied tensions, on three different web materials, and at both atmospheric and vacuum pressures.

Structural–fluidic–acoustic computational modelling and experimental validation of piezoelectric synthetic jet actuators

In this study, coupled structural–fluidic–acoustic modelling of piezoelectric diaphragm driven synthetic jet actuators is conducted computationally for the first time. The aim is to demonstrate the importance of piezoelectric diaphragm structural modelling and the effects of acoustics coupling to compute accurate synthetic jet exit jet velocity. Two different synthetic jet actuator orifice–diaphragm configurations are studied in which the orifice is parallel and adjacent to the diaphragm, namely, opposite and adjacent synthetic jet actuators, respectively. In investigating the aforementioned configurations, cavity acoustic and mechanical resonance frequencies are identified within ± 100 Hz, compared to in-house experimental measurements of laser vibrometry and hot-wire anemometry. The numerical peak jet velocity differs from the experimental value at the diaphragm mechanical resonance by 5.4% and 0.3% for opposite and adjacent synthetic jets, respectively. Further analysis of velocity and vorticity fields showed that no vortex formation is observed in the cavity of the adjacent synthetic jets, despite having similar exit jet velocity of the opposite synthetic jet configuration.