Motion Resonance Research Articles

Analysis and Control on a Specific Electromagnetic Micromirror

In this paper, 10 resonant modes were divided based on the structure of a specific two-dimensional electromagnetic micromirror from Professor Shen’s team and Finite Element Method (FEM), and using as many as 10 resonant modes to do such analysis was the first time according to the best of our knowledge. The results showed that the slow axis can participate in several resonant motions under the signals of resonant frequencies. In particular, participating in Mode 1 for slow-scan axis was the key reason to the instability of Vertical Refreshing Scanning (VRS) in raster scanning. In addition, a piecewise PID control based on filters design for this electromagnetic micromirror was proposed to suppress the unexpected resonant oscillation and to improve the angular positioning accuracy in slow-scan axis control. Finally, the proposed method was applied to electromagnetic micromirror stages, and the experimental results showed that the proposed approach was reliable.

On orbital stability of resonant periodic motions originating from hyperboloidal precession of a dynamically symmetric satellite

Periodic motions arising from Hyperboloidal precession of a dynamically symmetric rigid-body satellite on a circular orbit are studied in this work. There exist two types of these motions categorized by frequencies ^ and co2 of the linearized system: short-periodic motions with period close to 2n/co2 and long-periodic ones with period close to 2?!/^ (co2 > co). These motions describe oscillations of the satellite’s principal axis in the neighbourhood Hyperboloidal precession and can be obtained as small-parameter power series of the oscillation amplitude. It has been shown before that in a resonant case there exist more than one family of long-periodic motions. In this work, families of long-periodic motions originating from Hyperboloidal precession in case of fourth order resonance are computed and analysed.

On resonant periodic motions close to conical precession of a dynamically symmetric satellite in a weakly elliptic orbit

The motion of a dynamically symmetric rigid body (satellite) about its centre of mass in an elliptical orbit is considered. It is assumed that the eccentricity of the orbit is small and an external resonance caused by gravitational torque takes place. Periodic motions emanating from conical precession of the satellite are studied. Such periodic motions can be constructed in a form of convergent series of fractional powers of the eccentricity. The first terms of these series expansion have been calculated in an explicit form. The bifurcation phenomenon of the above periodic motions is investigated.

On the free vibrations of locally-resonant structures

This paper addresses the free-vibration response of structures coupled with periodically-distributed resonators, generally referred to as locally-resonant structures. The first step is to show that all exact natural frequencies can be calculated by a proper formulation of the Wittrick-Williams algorithm, involving a condensed dynamic stiffness matrix whose size depends only on the number of degrees of freedom of the structure and is independent of the number of degrees of freedom within every resonator. Indeed, the presence of resonators is accounted for in the condensed dynamic stiffness matrix via a pertinent frequency-dependent stiffness, readily obtainable from the resonator motion equations. Within this framework, a novel procedure is proposed to construct the condensed dynamic stiffness matrix of locally-resonant plates, applicable for any number of resonators. Numerical applications show the exactness of the proposed formulation.

The Effect of Laser Beam Intensity and Microscope Illumination Intensity, on the Response of Electrostatic Resonators

In this work we measure the response of an electrostatic MEMS resonator that is made from single-crystalline silicon. Our setup allows for simultaneous measurement of the resonator motion, using both capacitive sensing and optical sensing with a laser vibrometer. We demonstrate that both vibrometer laser illumination and microscope illumination, can affect the resonance frequency of the resonator. Furthermore, we demonstrate that this thermal effect may be non-monotonic. We demonstrate that for low levels of illumination power, the resonance frequency first increases, but then resonance frequency decreases when the illumination power is further increased. This peculiar response is attributed to the competing effects of prestress, and of thermal stress that is induced by illumination. We demonstrate that the measurement of device resistance is a good indicator of thermal heating.

Proposal of a Three-Degree-of-Freedom Linear-Rotational Resonant Actuator and Inverter Topology

The aim of this study is to propose a new three-degree-of-freedom linear-rotational resonant actuator and its controller. To realize all of the resonant motion, four-phase coils and three sets of the permanent magnet are arranged symmetrically. In addition, in order to control the proposed actuator, inverter topology with six-switches is presented. Parameter characteristics obtained through finite-element analysis support the validity of the proposed actuator. Finally, dynamic simulation is performed to verify the effectiveness of the proposed actuator.

Numerical investigations of gap resonance excited by focused transient wave groups

Two or more structures arranged side by side with narrow gaps may be suffered from large-amplitude free-surface oscillations, which could cause green water on the deck and lead to dramatic increase of hydrodynamic loading acting on structures. Here, transient resonant motions of the free surface inside a narrow gap between two fixed boxes triggered by focused transient wave groups with various focused wave amplitudes are simulated using a two-dimensional numerical wave tank. The free-surface amplifications not only inside the gap but in the vicinity of the two-box system, the response time and the damping time of the transient gap resonance, the maximum wave loads on both boxes and the relative importance of the higher-order wave loads to the first-order ones are systematically investigated. It is found that the most vulnerable position to green water closely depends on the incident focused wave amplitude. The damping time decreases gradually with increasing focused wave amplitude, while the response time seems insensitive to the latter. As the focused wave amplitude increases, the normalized maximum wave loads on both boxes are also shown to decline gradually overall, while the relative importance of the higher-order wave loads to the first-order ones becomes more and more remarkable.

Compensation of Wave Solid-State Gyro Drifts Caused by Anisotropy of Elastic Properties of a Single-Crystal Resonator

Abstract—A new mathematical model has been constructed for the motion of a single-crystal resonator of a wave solid-state gyroscope in the form of a thin elastic shell rotating on a moving base, taking into account the influence of an electrostatic system of oscillations excitation. The expression derived for the potential energy of elastic deformation of the resonator takes into account low anisotropy of the cubic crystal type depending on the resonator orientation relative to the crystallographic axes. A discrete model is used to describe the energy of the electrostatic field of control sensors. Using the Lagrange−Maxwell formalism, nonlinear differential equations are obtained that describe, in the single-mode approximation, the oscillations of the elastic shell rotating on a moving base. The forced and free oscillations of the resonator are considered. It is shown that a systematic error caused by anisotropy of the elastic properties of the resonator material can be compensated by the effect of electrostatic forces of the control sensors. Control signals are proposed to compensate these errors.

Chaos analysis and stability control of the MEMS resonator via the type-2 sequential FNN

In this paper, a fuzzy stability control algorithm based on the type-2 sequential fuzzy neural network (T2SFNN) is proposed to suppress the chaotic motion of the MEMS resonator. The dynamical behaviors of the MEMS resonator are revealed by the bifurcation diagram, exponent diagram, phase diagram and corresponding time history. In the process of the controller design for backstepping control, the T2SFNN is used to tackle the unknown external disturbance and eliminate the effect of time delay, along with the cosine function to ensure that the output constraint is not violated. In addition, an absorber is employed to avoid the repeated derivative associated with the backstepping. Finally, the effectiveness of the proposed scheme is verified by numerical simulation.

Resonant Chaotic Dynamics of a Symmetric Cross-Ply Composite Laminated Plate Under Transverse and In-Plane Excitations

The resonant chaotic dynamics of a symmetric cross-ply composite laminated plate are studied using the exponential dichotomies and an averaging procedure for the first time. The partial differential governing equations of motion for the symmetric cross-ply composite laminated plate are derived by using Reddy’s third-order shear deformation plate theory and von Karman type equation. The partial differential governing equations of motion are discretized into two-degree-of-freedom nonlinear systems including the quadratic and cubic nonlinear terms by using Galerkin method. There exists a fixed point of saddle-focus in the linear part for two-degree-of-freedom nonlinear system. The Melnikov method containing the terms of the nonhyperbolic mode is developed to investigate the resonant chaotic motions of the symmetric cross-ply composite laminated plate. The obtained results indicate that the nonhyperbolic mode of the symmetric cross-ply composite laminated plate does not affect the critical conditions in the occurrence of chaotic motions in the resonant case. When the resonant chaotic motion occurs, we can draw a conclusion that the resonant chaotic motions of the hyperbolic subsystem are shadowed for the full nonlinear system of the symmetric cross-ply composite laminated plate.

Retrograde periodic orbits in 1/2, 2/3 and 3/4 mean motion resonances with Neptune

We study planar and three-dimensional retrograde periodic orbits, using the model of the restricted three-body problem (RTBP) with the Sun and Neptune as primaries and focusing on the dynamics of resonant trans-Neptunian objects (TNOs). The position and the stability character of the periodic orbits can provide important piece of information on the stability and long-term evolution of small TNOs in retrograde motion. Using the circular planar model as the basic model, families of retrograde symmetric periodic orbits are computed at the 1/2, 2/3 and 3/4 exterior mean motion resonances with Neptune. The bifurcations for planar families of the elliptic model and families of the circular spatial model are determined and the bifurcated families are computed. In our study of the planar elliptic model, we consider the eccentricity of the primaries in the whole interval $$0<e'<1$$ for dynamical completeness. In the spatial circular model, retrograde periodic orbits are obtained mainly from bifurcations of the retrograde planar orbits. Also, we obtain retrograde periodic motion from continuing direct orbits for inclination values larger than $$90^\circ $$ . The linear stability of orbits is of major importance. Generally, stable periodic orbits are associated with phase space domains of resonant motion where TNOs can be captured. TNOs of retrograde motion are not common, but new discoveries cannot be excluded.

Second-order resonant motions of a deep-draft semi-submersible under extreme irregular wave excitation

Deep-draft semi-submersible platforms may present significant second-order resonant motions in severe sea states. Evaluating the slow-drift motions of such floating systems is important from the initial stages of their designs considering not only the offset requirement and mooring line load but also the air-gap responses beneath the lower deck. Theories and corresponding applications for these second-order resonant motions have been investigated for decades, but the problem has not been solved completely considering the requirements of a model that is sufficiently accurate and expedient. In this study, high-quality numerical simulations and model tests were conducted. Numerical calculations were carried out with the applications of full quadratic transfer function (QTF) matrices by means of commercial boundary element method (BEM) code. Comparisons show perfect agreement between the wave-frequency components obtained from both the model tests and the numerical calculations. Furthermore, the results also indicate that the second-order resonant motions can be to some extent estimated numerically by the second-order potential theory and that deviations can still be observed compared with those motions obtained by the model tests.

Spike-induced ordering: Stochastic neural spikes provide immediate adaptability to the sensorimotor system

Most biological neurons exhibit stochastic and spiking action potentials. However, the benefits of stochastic spikes versus continuous signals other than noise tolerance and energy efficiency remain largely unknown. In this study, we provide an insight into the potential roles of stochastic spikes, which may be beneficial for producing on-site adaptability in biological sensorimotor agents. We developed a platform that enables parametric modulation of the stochastic and discontinuous output of a stochastically spiking neural network (sSNN) to the rate-coded smooth output. This platform was applied to a complex musculoskeletal-neural system of a bipedal walker, and we demonstrated how stochastic spikes may help improve on-site adaptability of a bipedal walker to slippery surfaces or perturbation of random external forces. We further applied our sSNN platform to more general and simple sensorimotor agents and demonstrated four basic functions provided by an sSNN: 1) synchronization to a natural frequency, 2) amplification of the resonant motion in a natural frequency, 3) basin enlargement of the behavioral goal state, and 4) rapid complexity reduction and regular motion pattern formation. We propose that the benefits of sSNNs are not limited to musculoskeletal dynamics. Indeed, a wide range of the stability and adaptability of biological systems may arise from stochastic spiking dynamics.

Analytical solution for nonlinear vibration of a new arch micro resonator model

Based on the nonlocal strain gradient theory, a new nonlinear dynamic model for an arch micro resonator is developed. The governing nonlinear partial differential equations of the doubly clamped Euler–Bernoulli arch micro resonator are derived by employing Hamilton’s principle. Electrostatic actuation and the Casimir force are considered to provide the excitation of the micro resonator. By application of the Galerkin scheme, the nonlinear partial differential equation of dynamic motion of the micro resonator is discretized to the nonlinear ordinary differential equation with quadratic and cubic nonlinearities. Potential energy and bistability are investigated for the electrostatically actuated arch micro resonator. As an analytical approach, the perturbation method is used to examine the nonlinear forced vibration behavior of the resonator. The frequency–response curves are obtained to study the effect of size dependence on the amplitude of forced vibration of the arch micro resonator for the primary resonance.

A numerical study of the effects of bottom and sidewall stiffeners on sloshing behavior considering roll resonant motion

In the present study, aiming to provide practical guidance for the structural design, the effects of the small bottom and sidewall stiffeners on sloshing loads in shallow and intermediate liquid conditions are investigated numerically. The interaction between the highly nonlinear free surface flow and a large number of small stiffeners is modeled based on the Moving Particle Semi-implicit method. 2D models of a rectangular clean tank and tanks with small sidewalls or bottom stiffeners are considered. For filling ratios ranging from 5% to 20%, harmonic angular motions with periods around the analytical sloshing resonant ones are applied. Simulation snapshots and computed pressure time series, pressure variation, wave run-up, maximum fluid velocity, and kinetic energy were provided to clarify the complex interaction between the small baffles and the shallow free surface flow. As a result, except for the tanks with bottom stiffeners in shallow liquid conditions, in which the response under actual resonant frequency should be considered, the response computed using the clean tank excited by its resonant period can be adopted as a conservative estimation for the sloshing loads of actual tanks with small stiffeners.

Analysis of the dynamical evolution of the Quadrantid meteoroid stream

We investigate numerically the dynamical evolution of simulated meteoroid stream of the Quadrantids ejected from the parent body of the asteroid (196256) 2003 EH1. The main goal of this work is to identify mean motion and secular resonances and to study the mutual influence of resonance relations and close encounters with the major planets. Since the dynamics of this asteroid is predictable only on short time intervals, and not only close and/or multiple close encounters with major planets, but also the presence of at least one unstable resonance can lead to chaotic motion of test particles, we studied their resonant dynamics. The dynamical evolution of the test particles expects possible scenario for resonant motion. We conjecture that the reasons of chaos are the overlap of stable secular resonances and unstable mean motions resonances and close and/or multiple close encounters with the major planets. The estimate of the stability of orbits in which the particles in simulations moved was carried out by analyzing the behavior of the parameter MEGNO (Mean Exponential Growth factor of Nearby Orbits). The larger part of the identified resonances is stable. We found a peculiar behavior for this stream. Here, we show that the orbits of some ejected particles are strongly affected by the Lidov–Kozai mechanism that protects them from close encounters with Jupiter. Lack of close encounters with Jupiter leads to a rather smooth growth in the parameter MEGNO and the behavior imply the stable motion of simulation particles of the Quadrantids meteoroid stream.

Fatigue Life Assessment of KC-1 Membrane Considering the Effects of Cryogenic Temperature and Plastic Deformation

In this study, fatigue life assessment was conducted on a KC-1 membrane, considering cryogenic operation temperature, effect of stamping, and very long service period. KC-1 membranes are produced through a process of stamping, and they make direct contact with LNG filled within a containment system at − 162 °C. The high waves that LNG carriers encounter during sailing, and even when at anchor, cause rolling motions of the hull, which result in resonant fluid motions that generate a sloshing phenomenon; such sloshing motions expose containment systems to a high level of repeated stress. To assess the very high cycle fatigue (VHCF) life of the membrane, the effects of plastic deformation and the mechanical properties of STS304L, a membrane material, were examined at cryogenic temperatures. To identify the effects of plastic deformation and cryogenic temperatures on their mechanical properties, tensile and VHCF tests were conducted at cryogenic temperatures on a sheet to which plastic strain was applied through cold-rolling. Through forming analysis, changes in the thickness and plastic strain of a membrane caused during the process of stamping were examined. The results of earlier studies that performed flow analysis and fluid–structure interaction analysis to measure the stress applied to each component of the KC-1 containment system were cited, and the VHCF life of the membrane was assessed based on the surveyed mechanical properties, and the results of forming analysis.

Centrifuge modelling of structures with oil dampers under seismic loading

SummaryExperimental research into the seismic performance of buildings with passive oil dampers has so far been restricted to large‐scale testing of frames erected on laboratory shaking tables that ignore the foundation soil below. This simplification of the problem falls short of replicating dynamic soil‐structure interaction that would occur in the field. This paper presents the first experimental attempt at utilising high gravity dynamic centrifuge testing to replicate the response of a damped building at a reduced model scale. The paper compares the dynamic response of two similar two‐degree‐of‐freedom model sway frames, one control (bare) frame and one frame equipped with miniature oil dampers, both structures founded on shallow raft foundations in dry dense sand. The miniature oil dampers successfully mitigate floor accelerations, drifts, and storey shear forces in the damped frame with minor modification to the frame stiffness. For strong, near resonance motions, global rocking of the undamped frame associated with physical uplifting of the foundation from the soil surface and subsequent yielding of sand beneath has led to floor acceleration levels, which are comparable to those obtained in the damped building fitted with miniature oil dampers. Assessment of the instrumentation installed on the miniature oil dampers reveals a viscoelastic damper behaviour with a dependency on stroke magnitude and on velocity.

Estimation of damping induced by taut mooring lines

A moored floating structure may exhibit resonant motion responses to low-frequency excitations. Similar to the resonant responses of many vibration systems, the motion amplitude of a moored floating structure is significantly affected by the damping of the entire system. In such cases, the damping contributed by the mooring lines sometimes accounts for as much as 80% of the total damping. While the damping induced by catenary mooring lines is well-investigated, few studies have been conducted on the damping induced by taut mooring lines, especially one partly embedded in soil. The present study develops a simple but accurate model for estimating the damping contributed by mooring lines. A typical type of taut mooring line was used as the reference and the hydrodynamic drag force and soil resistance were taken into consideration. The proposed model was validated by comparing its predictions with those of a previously developed model and experimental measurements obtained by a physical model. Case studies and sensitivity studies were also conducted using the validated model. The damping induced by the soil resistance was found to be considerably smaller than the hydrodynamic damping. The superposition of the wave frequency motion on the low-frequency motion was also observed to significantly amplify the damping induced by the mooring lines.

Sub-femtosecond electron transport in a nanoscale gap

The strong fields associated with few-cycle pulses can drive highly nonlinear phenomena, allowing the direct control of electrons in condensed matter systems. In this context, by employing near-infrared single-cycle pulse pairs, we measure interferometric autocorrelations of the ultrafast currents induced by optical field emission at the nanogap of a single plasmonic nanocircuit. The dynamics of this ultrafast electron nanotransport depends on the precise temporal field profile of the optical driving pulse. Current autocorrelations are acquired with sub-femtosecond temporal resolution as a function of both pulse delay and absolute carrier-envelope phase. Quantitative modelling of the experiments enables us to monitor the spatiotemporal evolution of the electron density and currents induced in the system and to elucidate the physics underlying the electron transfer driven by strong optical fields in plasmonic gaps. Specifically, we clarify the interplay between the carrier-envelope phase of the driving pulse, plasmonic resonance and quiver motion. Single-cycle interferometric autocorrelation measurements of electrons tunnelling across the gap of a plasmonic bowtie antenna and quantitative models provide insight into the physical interactions that drive the electron transfer.