Mechanical Resonance Research Articles

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.

Phonon pumping by modulating the ultrastrong vacuum

The vacuum (i.e., the ground state) of a system in ultrastrong light-matter coupling contains particles that cannot be emitted without any dynamical perturbation and is thus called virtual. We propose a protocol for inducing and observing real mechanical excitations of a mirror enabled by the virtual photons in the ground state of a tripartite system, where a resonant optical cavity is ultrastrongly coupled to a two-level system (qubit) and, at the same time, optomechanically coupled to a mechanical resonator. Real phonons are coherently emitted when the frequency of the two-level system is modulated at a frequency comparable to that of the mechanical resonator and, therefore much lower than the optical frequency. We demonstrate that this hybrid effect is a direct consequence of the virtual photon population in the ground state. Within a classical physics analogy, attaching a weight to a spring only changes its resting position, whereas dynamically modulating the weight makes the system oscillate. In our case, however, the weight is the vacuum itself. We propose and accurately characterize a hybrid superconducting-optomechanical setup based on available state-of-the-art technology, where this effect can be experimentally observed.

Controlling surface acoustic waves (SAWs) via temporally graded metasurfaces

In this manuscript, the temporal rainbow effect for surface acoustic waves (SAWs) is illustrated through a temporal analog of space metagradings. We show that a time-modulated array of mechanical resonators induces a wavenumber-preserving frequency transformation which, in turn, dictates Rayleigh-to-Shear wave conversion. The process is unfolded through the adiabatic theorem, which allows us to delineate the transition between a solely frequency-converted wave packet and a temporally-driven mode conversion. In other words, our paper explores the role of time modulation in the context of elastic metasurfaces, and we envision our implementation to be suitable for designing a new family of SAW devices with frequency conversion, mode conversion, and unusual transport capabilities.

Designing gram-scale resonators for precision inertial sensors

Recent advances in glass fabrication technology have allowed for the development of high-precision inertial sensors in devices weighing of the order of grams. Gram-scale inertial sensors can be used in many applications with tight space or weight requirements. A key element of these devices’ performance is the behavior of a mechanical resonator. We present a detailed study on the design of resonators for such sensors. First, we consider how the mechanical parameters of a resonator couple with an inertial sensor’s performance. Then, we look at how to geometrically design resonators to achieve specific mechanical behavior without undergoing brittle failure. Both analytic tools and finite element analysis are used to this end. We then derive expressions that can be used to optimize the performance of an inertial sensor for a specific sensitive bandwidth. A simple geometry used throughout the field is studied as an example. However, the results are presented in a general form so that they can be easily adapted to any required geometry and use case. Ultimately, the results presented here guide the design of gram-scale inertial sensors and will improve the performance of devices that follow them. Published by the American Physical Society 2024

Integration of High‐Tc Superconductors with High‐Q‐Factor Oxide Mechanical Resonators

AbstractMicro‐mechanical resonators are building blocks of a variety of applications in basic science and consumer electronics. This device technology is mainly based on well‐established and reproducible silicon‐based fabrication processes with outstanding performances in term of mechanical Q‐factor and sensitivity to external perturbations. Broadening the functionalities of micro‐electro‐mechanical systems (MEMS) by the integration of functional materials is a key step for both applied and fundamental science. However, combining functional materials with silicon‐based devices is challenging. An alternative approach is directly fabricating MEMS based on compounds inherently showing non‐trivial functional properties, such as transition metal oxides. Here, a full‐oxide approach is reported, where a high‐ superconductor YBa2Cu3O7 (YBCO) is integrated with high Q‐factor micro‐bridge resonators made of single‐crystal LaAlO3 (LAO) thin films. LAO resonators are tensile strained, with a stress of about 350 MPa, show a Q‐factor above 200k, and have low roughness. YBCO overlayers are grown ex situ by pulsed laser deposition and YBCO/LAO bridges show zero resistance below 78 K and mechanical properties similar to those of bare LAO resonators. These results open new possibilities toward the development of advanced transducers, such as bolometers or magnetic field detectors, as well as experiments in solid state physics, material science, and quantum opto‐mechanics.

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.

Design of a Two-Degree-of-Freedom Mechanical Oscillator for Multidirectional Vibration Energy Harvesting to Power Wireless Sensor Nodes.

Converting otherwise wasted kinetic energy present in the environment into usable electrical energy to power wireless sensor nodes, is a green strategy to avoid the use of batteries and wires. Most of the energy harvesters presented in the literature are based on the exploitation of a one-degree-of-freedom arrangement, consisting of a tuned spring-mass system oscillating in the main direction of the exciting vibration source. However, if the direction of excitation changes, the efficiency of the harvester decreases. This paper thus proposes the idea of a curved cantilever beam with a two-degree-of-freedom arrangement, where the two bending natural frequencies of the mechanical resonator are designed to be equal. This is thought to lead to a configuration design that can be used in practical circumstances where excitation varies its direction in the plane. This, in turn, may possibly lead to a more effective energy-harvesting solution to power nodes in a wireless sensor network.

Adaptive Disturbance Suppression Method for Servo Systems Based on State Equalizer.

Disturbances in the aviation environment can compromise the stability of the aviation optoelectronic stabilization platform. Traditional methods, such as the proportional integral adaptive robust (PI + ARC) control algorithm, face a challenge: once high-frequency disturbances are introduced, their effectiveness is constrained by the control system's bandwidth, preventing further stability enhancement. A state equalizer speed closed-loop control algorithm is proposed, which combines proportional integral adaptive robustness with state equalizer (PI + ARC + State equalizer) control algorithm. This new control structure can suppress high-frequency disturbances caused by mechanical resonance, improve the bandwidth of the control system, and further achieve fast convergence and stability of the PI + ARC algorithm. Experimental results indicate that, in comparison to the control algorithm of PI + ARC, the inclusion of a state equalizer speed closed-loop compensation in the model significantly increases the closed-loop bandwidth by 47.6%, significantly enhances the control system's resistance to disturbances, and exhibits robustness in the face of variations in the model parameters and feedback sensors of the control object. In summary, integrating a state equalizer speed closed-loop with PI + ARC significantly enhances the suppression of high-frequency disturbances and the performance of control systems.

Regulation of near-infrared absorbing property for the absorptive short-wave pass filter based on Ag:1st/Si3N4/SiO2/Si3N4/Ag:2nd/Si3N4/W-WOx quasi-optical microcavity

Regulation of the near-infrared absorbing property in the different spectral ranges has been a challenge for absorptive short-wave pass filters (ASPFs) to meet the increasing application demands. In this paper, the multi-layer ASPF with the film structure of substrate(quartz)/Si3N4/ Ag:1st/Si3N4/SiO2/Si3N4/Ag:2nd/Si3N4/W-WOx/SiO2 is designed and prepared by magnetron sputtering. We get an optimal spectral selectivity in that the transmissive band ranges from 380-700 nm with a peak transmittance of 72.9 %, and the absorptive band ranges from 700-1400 nm with a peak absorptance of 84.1 %. As the main part of the ASPF, the quasi-optical microcavity (QOM) is creatively constructed with the film structure of Ag:1st/Si3N4/SiO2/Si3N4/Ag:2nd/Si3N4/W-WOx, integrating the interference mechanism and surface plasmon resonance mechanism with the intrinsic spectral selectivity of the W-WOx and silver layers, achieving the good selective absorbing property. The absorptive band is widened from 700-1400 nm to 700–2500 nm by regulating the interference effect and the intrinsic property via changing the thickness of the W-WOx layer, realizing much more significant regulation. The optical property remains stable after heat treatment at 200 °C for 72 h in the air, showing better thermal stability than other ASPFs. The outdoor thermal insulation experiments show that the temperature of black paint under the ASPF is about 17 °C lower than that under quartz glass. The microscopic and optical mechanisms for regulating the optical properties have been analyzed in-depth, providing a new strategy for the development of ASPFs.

Toward Programmable Quantum Processors Based on Spin Qubits with Mechanically Mediated Interactions and Transport.

Solid-state spin qubits are promising candidates for quantum information processing, but controlled interactions and entanglement in large, multiqubit systems are currently difficult to achieve. We describe a method for programmable control of multiqubit spin systems, in which individual nitrogen-vacancy (NV) centers in diamond nanopillars are coupled to magnetically functionalized silicon nitride mechanical resonators in a scanning probe configuration. Qubits can be entangled via interactions with nanomechanical resonators while programmable connectivity is realized via mechanical transport of qubits in nanopillars. To demonstrate the feasibility of this approach, we characterize both the mechanical properties and the magnetic field gradients around the micromagnet placed on the nanobeam resonator. We demonstrate coherent manipulation of a spin qubit in the proximity of a transported micromagnet by utilizing nuclear spin memory and use the NV center to detect the time-varying magnetic field from the oscillating micromagnet, extracting a spin-mechanical coupling of 7.7(9)Hz. With realistic improvements, the high-cooperativity regime can be reached, offering a new avenue toward scalable quantum information processing with spin qubits.

Quantum squeezing in a nonlinear mechanical oscillator

Mechanical degrees of freedom are natural candidates for continuous-variable quantum information processing and bosonic quantum simulations. However, these applications require the engineering of squeezing and nonlinearities in the quantum regime. Here we demonstrate squeezing below the zero-point fluctuations of a gigahertz-frequency mechanical resonator coupled to a superconducting qubit. This is achieved by parametrically driving the qubit, which results in an effective two-phonon drive. In addition, we show that the resonator mode inherits a nonlinearity from the off-resonant coupling with the qubit, which can be tuned by controlling the detuning. We, thus, realize a mechanical squeezed Kerr oscillator, in which we demonstrate the preparation of non-Gaussian quantum states of motion with Wigner function negativities and high quantum Fisher information. This shows that our results can also have applications in quantum metrology and sensing.

Merging mechanical bound states in the continuum in high-aspect-ratio phononic crystal gratings

Mechanical bound states in the continuum (BICs) present an alternative avenue for developing high-frequency, high-Q mechanical resonators, distinct from the conventional band structure engineering method. While symmetry-protected mechanical BICs have been realized in phononic crystals, the observation of accidental mechanical BICs—whose existence is independent of mode symmetry and tunable by structural parameters—has remained elusive. This challenge is primarily attributed to the additional radiation channel introduced by the longitudinal component of elastic waves. Here, we employ a coupled wave theory to predict and experimentally demonstrate mechanical accidental BICs within a high-aspect-ratio gallium arsenide phononic crystal grating. We observe the merging process of accidental BICs with symmetry-protected BICs, resulting in reduced acoustic radiation losses compared to isolated BICs. This finding opens up new possibilities for phonon trapping using BIC-based systems, with potential applications in sensing, transduction, and quantum measurements.

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.

Spectroscopy of substrate thermal vibrational modes using an optomechanical sensor

We used an optomechanical sensor to record the vibrational spectrum of its own fused silica substrate. The coupling of the substrate modes was greatly enhanced by covering the sensor with an appropriately sized ethylene glycol droplet, and in that case even thermally populated modes could be clearly detected. We observed a rich spectrum of high-quality flexural modes for frequencies less than ∼ 10 MHz, in good agreement with analytical theory and finite element simulations. We also observed signatures of acoustic waves resonantly confined by the droplet, over the entire ∼ 0–40 MHz range of the experiment. This work could inform efforts to increase the quality factor of mechanical resonators, and the use of substrate phonon modes as information channels.

Near-field optomechanical transduction enhanced by Raman gain.

Raman-gain-enhanced near-field optomechanical transduction between a movable optical cavity and SiN-membrane resonator is demonstrated. The Raman gain compensates for the intrinsic loss of the cavity and amplifies the optomechanical transduction, through which the membrane vibration is sensed using a high-Q whispering-gallery-mode optical cavity evanescently. The optical Q of the cavity resonance is improved with respect to the optical pump power, which results in an increase in the optomechanically transduced vibration signals of the mechanical resonator. Our near-field optomechanical coupling approach with optical gain realizes highly sensitive displacement measurement in nano- and micro-mechanical resonators consisting of arbitrary materials and structures.

Quantum Mechanical Quantitative Nuclear Magnetic Resonance Enables Digital Reference Standards at All Magnetic Fields and Enhances qNMR Sustainability.

Quantum mechanics (QM)-driven 1H iterative functionalized spin analysis produces HifSA profiles, which encode the complete 1H spin parameters ("nuclear genotype") of analytes of interest. HifSA profiles enable the establishment of digital reference standards (dRS) that are portable, FAIR (findable - accessible - interoperable - reusable), and fit for the purpose of quantitative 1H NMR (qHNMR) analysis at any magnetic field. This approach enhances the sustainability of analytical standards. Moreover, the analyte-specific complete chemical shift and J-coupling information in HifSA-based dRS enable computational quantitation of substances in mixtures via QM-total-line-shape fitting (QM-qHNMR). We present the proof of concept for HifSA-based dRS by resolving the highly overlapping NMR resonances in the experimental spectra ("nuclear phenotypes") of the diastereomeric mixture of (2RS, 4RS)- and (2RS, 4SR)-difenoconazole (DFZ), a widely used antifouling food additive. The underlying 1H spin parameters are highly conserved in various solvents, are robust against variation in measurement temperature, and work across a wide range of magnetic fields. QM-qHNMR analysis of DFZ samples at 80, 400, 600, and 800 MHz showed high congruence with metrological reference values. Furthermore, this study introduces QM-qHNMR combined with chiral shift reagents for the analysis of all four DFZ stereoisomers: (2R, 4R)-, (2S, 4S)-, (2R, 4S)-, and (2S, 4R)-DFZ to perform chiral qHNMR measurements.

A piezoelectric transducer for bone conduction implants designed using finite element analysis

AbstractThis study describes the design of a transducer for bone conduction implants that combines a piezoelectric element and a displacement amplifier. To develop a displacement amplifier with the maximum possible amplification ratio, theoretical analysis was performed to derive the parameters that affect the amplification ratio. Parametric sweep analysis was conducted to calculate the amplification ratio according to changes in the various parameters. The resulting optimal displacement amplifier afforded the maximum amplification ratio when the beam thickness, depth, inclination angle, and length were 0.15 mm, 1.2 mm, 6.5°, and 4 mm, respectively. The displacement amplifier with these optimal parameter values amplified the piezoelectric element displacement by approximately 7.7‐fold. Frequency characteristic analysis by weight was performed to derive a mechanical resonance location with frequency characteristics that appropriately compensated for hearing loss. As a result of this analysis, when a weight of 0.7 g was applied to the displacement amplifier, the mechanical resonance was that required for bone conduction implant transducers.

Propagation of elastic waves in correlated dispersions of resonant scatterers.

The propagation of coherent longitudinal and transverse waves in random distributions of spherical scatterers embedded in an elastic matrix is studied. The investigated frequency range is the vicinity of the resonance frequencies of the translational and rotational motion of the spheres forced by the waves, where strong dispersion and attenuation are predicted. A technique for making samples made of layers of carbide tungsten beads embedded in epoxy resin is presented, which allows control of the scatterers distribution, induce short-range positional correlations, and minimize the anisotropy of samples. Comparison between phase velocity and attenuation measurements and a model based on multiple scattering theory (MST) shows that bulk effective properties accurately described by MST are obtained from three beads layers. Besides, short-range correlations amplify the effect of mechanical resonances on the propagation of longitudinal and transverse coherent waves. As a practical consequence, the use of short-range positional correlations may be used to enhance the attenuation of elastic waves by disordered, locally resonant, elastic metamaterials, and MST globally correctly predicts the effect of short-range positional order on their effective properties.

Exploring regenerative coupling in phononic crystals for room temperature quantum optomechanics

Quantum technologies play a pivotal role in driving transformative advancements across diverse fields, surpassing classical approaches and empowering us to address complex challenges more effectively; however, the need for ultra-low temperatures limits the use of these technologies to particular fields. This work comes to alleviate this problem. We present a way of phononic bandgap engineering using FEM by which the radiative mechanical energy dissipation of a nanomechanical oscillator can be significantly suppressed through coupling with a complementary oscillating mode of a defect of the surrounding phononic crystal (PnC). Applied to an optomechanically coupled nanobeam resonator in the megahertz regime, we find a mechanical quality factor improvement of up to four orders of magnitude compared to conventional PnC designs. As this method is based on geometrical optimization of the PnC and frequency matching of the resonator and defect mode, it is applicable to a wide range of resonator types and frequency ranges. Taking advantage of the, hereinafter referred to as, “regenerative coupling” in phononic crystals, the presented device is capable of reaching f × Q products exceeding 10E16 Hz with only two rows of PnC shield. Thus, stable quantum states with mechanical decoherence times up to 700 μs at room temperature can be obtained, offering new opportunities for the optimization of mechanical resonator performance and advancing the room temperature quantum field across diverse applications.

Resonant Electro-Mechanical Coupling – A Possible Renewable Energy Source

This paper looks at a simple Electro-Mechanical System that is tuned to resonate with both mechanical and electrical resonance. The intention is to couple the system resonance such that the amplitude of the output voltage is increased. The basic setup consists of a forced Mass-Spring System consisting of a speaker driving a mass attached to a tension-spring. The mass is a Neodymium cylindrical magnet. The vertically driven system couples to a magnet coil which sits over the magnet. Thus, by induction a voltage is generated within the coil. The coil is connected in series with a set of electrolytic capacitors. The resulting Resistor-Capacitor-Inductor (RCL) circuit is so designed as to resonate. The idea behind this coupling is to increase the output voltage of the circuit, thereby creating a voltage supply that could be boosted via transformer action, if necessary. Noting that the resulting circuit provides a source of single-phase electricity, such a setup could be used to charge small electronic devices like cellphones and mobile earphone sets. Mechanical resonance is indicated by the erratic vibration of the speaker, spring and magnet system. Knowing the magnet mass and measured resonant frequency the approximate spring constant can be calculated. The resonant frequency is then used as the driving frequency for the electrical circuit consisting of the RCL components. Noting the electric circuit resonance frequency, the approximate capacitance needed can be calculated using the driving frequency and the inductance of the said magnet coil. Using the circuit capacitance and appropriate circuit resistance, the maximised quality factor is sought, therefore the objective of the electric circuit design is to maximise the output voltage. The power generated by the device was found to be less than ~1 W. This system can be optimized to deliver maximum power output at the required resonant frequency, by greatly increasing the coil turns, using closer tolerances between the moving magnet and the wound coil and/or using materials that would ensure added magnetic coupling. Such a system can be used as a possible source of renewable energy especially on reciprocating engines, where exciting forces are available.