Dipole and quadrupole resonance excitation in linear quadrupoles

In the development of commercial quadrupole mass spectrometers, there is an interest in improving the performance characteristics such as transmission, resolution, and mass range. In particular, parametric and dipolar resonance excitation of trapping ions are used for linear quadrupole mass filters. Theoretical methods and numerical simulation of ion trajectories were applied for study of ion-optical properties. The review is devoted to description of different excitation methods to improve QMF performance and consists of three parts. The first part presents the results of a linear ion trap simulation for various operating conditions and excitation methods. The second part considers the effects of dipole excitation (DE) on the performance of the quadrupole mass filter. The last part analyzes the formation of stability islands by different methods of quadrupole excitation. To date conditions of mass separation in quadrupole mass filters with sin wave supply were described for stability islands of the first and third stability regions formed by quadrupole and DE. By complicating the electronics such methods allow to overcome the destructive influence of electric field distortions and obtain a resolving power and ion transmission efficiency comparable with commercial devices. At quadrupole resonance excitation by a two-frequency signal, it is possible to reduce the length of electrodes three times without losses in resolution and transmission, which reduces the cost of rod set production with micrometer accuracy. Dipole resonance excitation allows controlling the shape of the mass peak by changing amplitude and phase of the auxiliary AC signal. The main factors affecting the resolving power of a linear ion trap are described theoretically. The numerical modeling results are confirmed by experiment.

Dynamic Stability of Tensegrity Structures-Part II: The Periodic External Load

The paper contains a parametric analysis of tensegrity structures subjected to periodic loads. The analysis focuses on determining the main region of dynamic instability. When load parameters fall within this region, the resulting vibration amplitudes increase, posing a risk to the durability of structures. The study considers structures built using commonly used modules. The influence of the initial prestress on the distribution of the instability regions is examined. Additional prestress can significantly reduce the extent of instability regions, potentially narrowing them by up to 99%. A nondimensional parameter is introduced to accurately assess changes in the extent of the instability region. A geometrically non-linear model is employed to evaluate the behavior of the analyzed structures.

Development of an Electrostatic Comb-Driven MEMS Scanning Mirror for Two-Dimensional Raster Scanning

Microelectromechanical System (MEMS)-based scanning mirrors are important optical devices that have been employed in many fields as a low-cost and miniaturized solution. In recent years, the rapid development of Light Detection and Ranging (LiDAR) has led to opportunities and challenges for MEMS scanners. In this work, we propose a 2D electrostatically actuated micro raster scanner with relatively large aperture. The 2D scanner combines a resonant scanning axis driven by an in-plane comb and a quasistatic scanning axis driven by a vertical comb, which is achieved by raising the moving comb finger above the fixed comb finger through the residual stress gradient. The analytic formula for the resonant axis frequency, based on the mechanical coupling of two oscillation modes, is derived and compared with finite element simulation. A prototype is designed, fabricated, and tested, and an overall optical Field-of-View (FoV) of about 60° × 4° is achieved. Finally, some possibilities for further improvement or optimization are discussed.

Analysis of Parametric and Subharmonic Excitation in Push-Pull Driven Disk Resonator Gyroscopes

For micro-electromechanical system (MEMS) resonators, once the devices are fabricated and packaged, their intrinsic quality factors (Q) will be fixed and cannot be changed, which seriously limits the further improvement of the resonator’s performance. In this paper, parametric excitation is applied in a push-pull driven disk resonator gyroscope (DRG) to improve its sensitivity by an electrical pump, causing an arbitrary increase of the “effective Q”. However, due to the differential characteristics of the push-pull driving method, the traditional parametric excitation method is not applicable. As a result, two novel methods are proposed and experimentally carried out to achieve parametric excitation in the push-pull driven DRGs, resulting in a maximum “effective Q” of 2.24 × 10⁶ in the experiment, about a 7.6 times improvement over the intrinsic Q. Besides, subharmonic excitation is also theoretically analyzed and experimentally characterized. The stability boundary of parametric excitation, defined by a threshold voltage, is theoretically predicted and verified by related experiments. It is demonstrated that, when keeping the gyroscope’s vibration at a constant amplitude, the fundamental frequency driving voltage will decrease with the increasing of the parametric voltage and will drop to zero at its threshold value. In this case, the gyroscope operates in a generalized parametric resonance condition, which is called subharmonic excitation. The novel parametric and subharmonic excitation theories displayed in this paper are proven to be efficient and tunable dynamical methods with great potential for adjusting the quality factor flexibly, which can be used to further enhance the resonator’s performance.

Mass filter with phase modulation of radio frequency voltage

In this work, the parametric quadrupole resonance caused by the phase modulation of waveform potential is studied. Based on analytical and numerical description of the ion motion in the quadrupole mass filter with the phase modulation, a stability island is found with good ion optical properties such as high ion transmission efficiency (16%), high mass resolution (peak width measured at 10% of peak height, R_0.1 = 6000), the required separation time (100-150 radio frequency [RF] cycles), and good peak shape of trapezoid form. Furthermore, the analysis of the frequency spectrum of the applied potential and the quadrupole mass filter (QMF) acceptance are also presented; a resonance frequency is found from this spectrum. Finally, a suitable stability X-islands with relative modulation frequency, ν = 2 ± β , β = 1 P , 10 ≤ P ≤ 40 , is established and studied in detail. Here, β is the imaginary part of the characteristic exponent of stable solutions to the Mathieu equation.

2D Au-Coated Resonant MEMS Scanner for NIR Fluorescence Intraoperative Confocal Microscope

The electrostatic MEMS scanner plays an important role in the miniaturization of the microscopic imaging system. We have developed a new two-dimensional (2D) parametrically-resonant MEMS scanner with patterned Au coating (>90% reflectivity at an NIR 785-nm wavelength), for a near-infrared (NIR) fluorescence intraoperative confocal microscopic imaging system with a compact form factor. A silicon-on-insulator (SOI)-wafer based dicing-free microfabrication process has been developed for mass-production with high yield. Based on an in-plane comb-drive configuration, the resonant MEMS scanner performs 2D Lissajous pattern scanning with a large mechanical scanning angle (MSA, ±4°) on each axis at low driving voltage (36 V). A large field-of-view (FOV) has been achieved by using a post-objective scanning architecture of the confocal microscope. We have integrated the new MEMS scanner into a custom-made NIR fluorescence intraoperative confocal microscope with an outer diameter of 5.5 mm at its distal-end. Axial scanning has been achieved by using a piezoelectric actuator-based driving mechanism. We have successfully demonstrated ex vivo 2D imaging on human tissue specimens with up to five frames/s. The 2D resonant MEMS scanner can potentially be utilized for many applications, including multiphoton microendoscopy and wide-field endoscopy.

Transverse motion instability of a submerged moored buoy

Wave energy converters and other offshore structures may exhibit instability, in which one mode of motion is excited parametrically by motion in another. Here, theoretical results for the transverse motion instability (large sway oscillations perpendicular to the incident wave direction) of a submerged wave energy converter buoy are compared to an extensive experimental dataset. The device is axi-symmetric (resembling a truncated vertical cylinder) and is taut-moored via a single tether. The system is approximately a damped elastic pendulum. Assuming linear hydrodynamics, but retaining nonlinear tether geometry, governing equations are derived in six degrees of freedom. The natural frequencies in surge/sway (the pendulum frequency), heave (the springing motion frequency) and pitch/roll are derived from the linearized equations. When terms of second order in the buoy motions are retained, the sway equation can be written as a Mathieu equation. Careful analysis of 80 regular wave tests reveals a good agreement with the predictions of sub-harmonic (period-doubling) sway instability using the Mathieu equation stability diagram. As wave energy converters operate in real seas, a large number of irregular wave runs is also analysed. The measurements broadly agree with a criterion (derived elsewhere) for determining the presence of the instability in irregular waves, which depends on the level of damping and the amount of parametric excitation at twice the natural frequency.

A Study on Parametric Amplification in a Piezoelectric MEMS Device

In various applications, damping from the surrounding fluid severely degrades the performance of micro-electro-mechanical systems (MEMS). In this paper, mechanical amplification through parametric resonance was investigated in a piezoelectrically actuated MEMS to overcome the effects of damping. The device was fabricated using the PiezoMUMPS process, which is based on a Silicon-on-Insulator (SOI) process with an additional aluminum nitride (AlN) layer. Here, a double-clamped cantilever beam with a concentrated mass at the center was excited at its first resonance mode (out-of-plane motion) in air and at atmospheric conditions. A parametric signal modulating the stiffness of the beam was added at twice the frequency of the excitation signal, which was swept through the resonance frequency of the mode. The displacement at the center of the device was detected optically. A four-fold increase in the quality-factor, Q, of the resonator was obtained at the highest values in amplitude used for the parametric excitation. The spring modulation constant was obtained from the effective quality-factor, Q e f f , versus parametric excitation voltage curve. This study demonstrates that through these methods, significant improvements in performance of MEMS in fluids can be obtained, even for devices fabricated using standard commercial processes.

Accurate Simulation of Parametrically Excited Micromirrors via Direct Computation of the Electrostatic Stiffness

Electrostatically actuated torsional micromirrors are key elements in Micro-Opto-Electro- Mechanical-Systems. When forced by means of in-plane comb-fingers, the dynamics of the main torsional response is known to be strongly non-linear and governed by parametric resonance. Here, in order to also trace unstable branches of the mirror response, we implement a simplified continuation method with arc-length control and propose an innovative technique based on Finite Elements and the concepts of material derivative in order to compute the electrostatic stiffness; i.e., the derivative of the torque with respect to the torsional angle, as required by the continuation approach.

Bifurcation Control of an Electrostatically-Actuated MEMS Actuator with Time-Delay Feedback

The parametric excitation system consisting of a flexible beam and shuttle mass widely exists in microelectromechanical systems (MEMS), which can exhibit rich nonlinear dynamic behaviors. This article aims to theoretically investigate the nonlinear jumping phenomena and bifurcation conditions of a class of electrostatically-driven MEMS actuators with a time-delay feedback controller. Considering the comb structure consisting of a flexible beam and shuttle mass, the partial differential governing equation is obtained with both the linear and cubic nonlinear parametric excitation. Then, the method of multiple scales is introduced to obtain a slow flow that is analyzed for stability and bifurcation. Results show that time-delay feedback can improve resonance frequency and stability of the system. What is more, through a detailed mathematical analysis, the discriminant of Hopf bifurcation is theoretically derived, and appropriate time-delay feedback force can make the branch from the Hopf bifurcation point stable under any driving voltage value. Meanwhile, through global bifurcation analysis and saddle node bifurcation analysis, theoretical expressions about the system parameter space and maximum amplitude of monostable vibration are deduced. It is found that the disappearance of the global bifurcation point means the emergence of monostable vibration. Finally, detailed numerical results confirm the analytical prediction.

An electromechanical Ising Hamiltonian

Solving intractable mathematical problems in simulators composed of atoms, ions, photons, or electrons has recently emerged as a subject of intense interest. We extend this concept to phonons that are localized in spectrally pure resonances in an electromechanical system that enables their interactions to be exquisitely fashioned via electrical means. We harness this platform to emulate the Ising Hamiltonian whose spin 1/2 particles are replicated by the phase bistable vibrations from the parametric resonances of multiple modes. The coupling between the mechanical spins is created by generating two-mode squeezed states, which impart correlations between modes that can imitate a random, ferromagnetic state or an antiferromagnetic state on demand. These results suggest that an electromechanical simulator could be built for the Ising Hamiltonian in a nontrivial configuration, namely, for a large number of spins with multiple degrees of coupling.

Modeling and Simulation of a Parametrically Resonant Micromirror With Duty-Cycled Excitation

High frequency large scanning angle electrostatically actuated microelectromechanical systems (MEMS) mirrors are used in a variety of applications involving fast optical scanning. A 1-D parametrically resonant torsional micromirror for use in biomedical imaging is analyzed here with respect to operation by duty-cycled square waves. Duty-cycled square wave excitation can have significant advantages for practical mirror regulation and/or control. The mirror's nonlinear dynamics under such excitation is analyzed in a Hill's equation form. This form is used to predict stability regions (the voltage-frequency relationship) of parametric resonance behavior over large scanning angles using iterative approximations for nonlinear capacitance behavior of the mirror. Numerical simulations are also performed to obtain the mirror's frequency response over several voltages for various duty cycles. Frequency sweeps, stability results, and duty cycle trends from both analytical and simulation methods are compared with experimental results. Both analytical models and simulations show good agreement with experimental results over the range of duty cycled excitations tested. This paper discusses the implications of changing amplitude and phase with duty cycle for robust open-loop operation and future closed-loop operating strategies.

Forward flight of birds revisited. Part 2: short-term dynamic stability and trim

Thrust generation by flapping is accompanied by alternating pitching moment. On the down-stroke, it pitches the bird down when the wings are above its centre of gravity and up when they are below; on the up-stroke, the directions reverse. Because the thrust depends not only on the flapping characteristics but also on the angle of attack of the bird's body, interaction between the flapping and body motions may incite a resonance that is similar to the one that causes the swinging of a swing. In fact, it is shown that the equation governing the motion of the bird's body in flapping flight resembles the equation governing the motion of a pendulum with periodically changing length. Large flapping amplitude, low flapping frequency, and excessive tilt of the flapping plane may incite the resonance; coordinated fore-aft motion, that uses the lift to cancel out the moment generated by the thrust, suppresses it. It is probably incited by the tumbler pigeon in its remarkable display of aerobatics. The fore-aft motion that cancels the pitching moment makes the wing tip draw a figure of eight relative to the bird's body when the wings are un-swept, and a ring when the wings are swept back and fold during the upstroke.