Hard Excitation Research Articles

Reduced B0/B1 + sensitivity in velocity-selective inversion arterial spin labeling using adiabatic refocusing pulses.

To mitigate the B0/B1 + sensitivity of velocity-selective inversion (VSI) pulse trains for velocity-selective arterial spin labeling (VSASL) by implementing adiabatic refocusing. This approach aims to achieve artifact-free VSI-based perfusion imaging through single-pair label-control subtractions, reducing the need for the currently required four-pair dynamic phase-cycling (DPC) technique when using a velocity-insensitive control. We introduce a Fourier-transform VSI (FT-VSI) train that incorporates sinc-modulated hard excitation pulses with MLEV-8-modulated adiabatic hyperbolic secant refocusing pairs. We compare performance between this train and the standard composite refocusing train, including with and without DPC, for dual-module VSI VSASL. We evaluate (1) simulated velocity-selective profiles and subtraction fidelity across a broad B0/B1 + range, (2) subtraction fidelity in phantoms, and (3) image quality, artifact presence, and gray-matter perfusion heterogeneity (as measured by the spatial coefficient of variation) in healthy human subjects. Adiabatic refocusing significantly improves FT-VSI robustness to B0/B1 + inhomogeneity for a single label-control subtraction. Subtraction fidelity is dramatically improved in both simulation and phantoms compared with composite refocusing without DPC, and is similar compared with DPC methods. In humans, marked artifacts seen with the non-DPC composite refocusing approach are eliminated, corroborated by significantly reduced gray-matter heterogeneity (via lower spatial coefficient of variation values). A novel VSASL labeling train using adiabatic refocusing pulses for VSI was found to reduce artifacts related to B0/B1 + inhomogeneity, thereby providing an alternative to DPC and its associated limitations, which include increased vulnerability to physiological noise and motion, reduced functional MRI applicability, and suboptimal data censoring.

Hard excitation mode of a system with optomechanical instability.

Systems with strong photon-phonon interaction and optomechanical instability are perspective for the generation of coherent phonons and photons. We predict the existence of a hard mode of excitation in such systems when a jump-like increase in the photon intensity takes place at the generation threshold. We derive an analytical expression that defines conditions for such an increase. We demonstrate that the hard excitation mode in systems with optomechanical instability arises due to an additional phase condition for the existence of a nonzero solution. We propose to use systems with optomechanical instability operating in the hard excitation mode to create highly sensitive sensors.

Magneto-thermoelastic coupled resonance characteristics of a rotating functionally graded ferromagnetic cylindrical shell under double harmonic line loads

The magneto-thermoelastic coupled resonance of a rotating functionally graded (FG) ferromagnetic cylindrical shell subjected to double harmonic line loads in magnetic and temperature fields is investigated. In accordance with Donnell's thin shell theory on the physical neutral surface, the nonlinear geometric equations are determined. Utilizing the thermoelastic constitutive relationships, combining with the gradient characteristics and temperature dependence of physical parameters, the governing equations of kinetic energy and strain energy are given. Based on the magnetoelasticity theory, and considering the nonlinear magnetization of ferromagnetic metal, the calculation formulas of Lorentz force and magnetizing force acting on the shell are deduced. The magneto-thermoelastic coupled dynamic equations are derived by applying Hamilton principle and discretized by Galerkin method. Subsequently, considering the different resonance forms, the multiple scales method and Lyapunov stability theory are employed to obtain the theoretical solutions and stability discriminants. Numerical examples are carried out to plot the characteristic diagrams with different parameters, which are used to analyze the characteristics of nonlinear coupled resonance. Furthermore, the primary resonance and combination resonance are selected to analyze the bifurcation and chaotic behavior. Results show that the variation of different parameters affects obviously the resonance amplitude and stability. The changes of amplitude and position of hard excitation can lead to resonance region drift. Amplitude, frequency, and position of excitation have significant effects on bifurcation and chaos. The motion state of cylindrical shell is transmitted from periodic response to chaotic response through the accumulation of period-doubling bifurcation.

Synchronization of oscillators with hard excitation coupled with delay Part 1. Phase approximation

Aim of this work is to develop the theory of mutual synchronization of two oscillators with hard excitation associated with a delay. Taking into account the delay of a coupling signal is necessary, in particular, when analyzing synchronization at microwave frequencies, when the distance between the oscillators is large compared to the wavelength. Methods. Theoretical analysis is carried out under the assumption that the delay time is small compared to the characteristic time for the oscillations. The phase approximation is used when the frequency mismatch and the coupling parameter are considered small. Results. Taking into account the change in oscillation amplitudes up to first-order terms in the coupling parameter, a generalized Adler equation for the phase difference of the oscillators is obtained, which takes into account the combined type of the coupling (dissipative and conservative coupling) and non-isochronism. The conditions for saddle-node bifurcations are found and the stability of various fixed points of the system is analyzed. The boundaries of the domains of in-phase and anti-phase synchronization are plotted on the plane of the parameters “frequency mismatch – coupling parameter”. Conclusion. It is shown that, depending on the control parameters (non-isochronism parameter, excitation parameter, phase advance of the coupling signal), the system exhibits behavior typical of either dissipative or conservative coupling. The obtained formulas allow for trace the transition from one type of coupling to another when varying the control parameters.

Temporal Dynamics of an Asymmetrical Dielectric Nanodimer Wrapped with Graphene

We theoretically and numerically investigate the temporal dynamics of a nanodimer system consisting of a pair of graphene-wrapped dielectric nanospheres with tunable radii. Considering that symmetry breaks on resonant frequencies, we derive the temporal kinetic equations in an asymmetric form by utilizing the dispersion relation method in dipole limit. The bifurcation diagrams achieved via the analysis on the linear instability and numerical solutions can quantitatively characterize the complex coexistences of stationary and dynamical behaviors in this dimer system, and the asymmetry apparently can increase the number of regimes with the periodic self-oscillation state or chaos. Furthermore, we find that the indefinite switching not only can be triggered among the stationary steady solutions, but it also universally exists among all the possible solutions in a coexistent regime. The switching can be tuned by applying a hard excitation signal with different durations and saturation values. Our results may provide new paths to realize a nonlinear nanophotonic device with tunable dynamical responses or even multi-functionalities.

Parametrically Excited Nonlinear Pneumatic Artificial Muscle Under Hard Excitation: A Theoretical and Experimental Investigation

In this work, a single degree of freedom system consisting of a mass and a Pneumatic Artificial Muscle subjected to time-varying pressure inside the muscle is considered. The system is subjected to hard excitation and the governing equation of motion is found to be that of a nonlinear forced and parametrically excited system under super- and sub-harmonic resonance conditions. The solution of the nonlinear governing equation of motion is obtained using the method of multiple scales. The time and frequency response, phase portraits, and basin of attraction are plotted to study the system response along with the stability and bifurcations. Further, the different muscle parameters are evaluated by performing experiments which are further used for numerically evaluating the system response using the theoretically obtained closed form equations. The responses obtained from the experiments are found to be in good agreement with those obtained from the method of multiple scales. With the help of examples, the procedure to obtain the safe operating range of different system parameters is illustrated.

Responses of a Strongly Forced Mathieu Equation—Part 1: Cyclic Loading

AbstractThis work concerns the response of a damped Mathieu equation with hard cyclic excitation at the same frequency as the parametric excitation. A second-order perturbation analysis using the method of multiple scales unfolds resonances and stability. Superharmonic and subharmonic resonances are analyzed and the effect of different parameters on the responses are examined. While superharmonic resonances of order two have been captured by a first-order analysis, the second-order analysis improves the prediction of the peak frequency. Superharmonic resonances of order three are captured only by the second-order analysis. The order-two superharmonic resonance amplitude is of order ε0, and the order-three superharmonic amplitude is of order ε. As the parametric excitation level increases, the superharmonic resonance amplitudes increase. An nth-order multiple-scales analysis will indicate conditions of superharmonic resonances of order n + 1. At the subharmonic of order one-half, there is no steady-state resonance, but known subharmonic instability is unfolded consistently. Analytical expressions for resonant responses are presented and compared with numerical results for specific system parameters. The behavior of this system could be relevant to applications such as large wind-turbine blades and parametric resonators.

Traditional and non-traditional active nonlinear vibration absorber with time delay combination feedback for hard excitation

In this work, vibration suppression of a base excited nonlinear spring–mass primary system subjected to simultaneous external hard harmonic and parametric excitations is carried out by using a modified traditional and non-traditional active nonlinear vibration absorber (ANVA). The ANVA consists of a mass, time delayed damper and a PZT stack actuator in series with a linear and nonlinear spring. The ANVA utilizes various combinations of time delayed displacement, velocity and acceleration feedback gains of the primary system for vibration reduction. The governing coupled nonlinear equations of motion for the system with weighted modal matrix approach have been derived and solved by the method of multiple scales (MMS) for simultaneous superharmonic, principal parametric and primary resonance with 1:1 internal resonance conditions. The reduced equations obtained from MMS are solved using Newton’s method, which is then compared with the numerical methods, showing good agreement. The trivial state instability regions are also analyzed for various feedback gains. The parametric analyses are carried out for various system parameters, viz., variation in the nonlinear stiffness, time delay in the damper, changes in the amplitude of excitations, time delay in the feedbacks, stiffness of the absorber and various combinations of feedback gains through different feedbacks. From these parametric analyses, stable and unstable regions of operating frequencies are obtained at which the system response amplitude is minimum for a wide range of operating frequencies. Further, it is shown that 100% vibration reduction of the system can be achieved for a certain range of operating frequencies.

Analysis of the track system in bumpy unstructured hard road environment by vibration test

The complex terrain environment in the hilly land directly affects the operational reliability of agricultural robots. In order to study the impact of road irregularity on walking chassis vibration, the 3SYLZ-750 remote-controlled weeding machine which is applied to orchards was taken as the object of study, and the rear roller was selected as the object of observation to reveal the rules under which the vibration of the track chassis changes as there is a sudden change in road surface elevation. A column-type test-to-pass method based on unit excitation was proposed in this study. The excitation behavior and action process were analyzed by category. A critical acceleration prediction model was built and verified by virtual simulation and hard road surface excitation testing. The results showed that at the forward velocity of 0-2.5 km/h and exciter height of 20-100 mm, the vertical vibration acceleration of the target roller was significantly affected by Track Contact Point Centrifugal Acceleration (TCPCA). As TCPCA increased, the change rate of vertical vibration acceleration decreased, reaching a minimum of [−13.8, 28.8]; as TCPCA decreased, the vertical vibration acceleration tended to increase positively at a maximum variation range of [−13.3, 42.2]. The measured and simulated macroscopic change rules were consistent with the theoretical analysis, further verifying the correctness of variable extraction, and providing a research basis for the accurate modification and improvement of the model. The research conclusions can lay a theoretical foundation for analyzing the walking reliability of the track chassis, and provide a design basis and technical support for the development of a tracked agricultural robot chassis for the hilly land in the future. Keywords: track system, unstructured road, vibration test, simulation analysis, hilly land, agricultural robot DOI: 10.25165/j.ijabe.20221504.7249 Citation: Li M T, Li J L, He L, He J, Hu L, Lyu C X. Analysis of the track system in bumpy unstructured hard road environment by vibration test. Int J Agric & Biol Eng, 2022; 15(4): 163–171.

Study of gyrotron synchronization by an external harmonic signal based on a modified quasi-linear theory

Topic. The paper is devoted to the study of synchronization of a gyrotron by an external harmonic signal. A theoretical study of gyrotron synchronization processes by means of a computational experiment based on certain traditional models of microwave electronics does not provide a complete description of the synchronization pattern. Therefore, the goal of the paper is to develop a modified quasi-linear model based on an approximation of the electron susceptibility by rational functions. Methods. The developed model allows for bifurcation analysis of synchronization processes. On its basis, stationary states are determined and their stability analysis is carried out. The results are in good agreement with numerical simulation based on the non-stationary theory of a gyrotron with a fixed Gaussian high-frequency field structure. Results and discussion. Resonance curves and synchronization bounds are built on the plane of parameters “amplitude – frequency of external signal”. The case where the gyrotron is in the hard excitation mode is considered, since the maximum efficiency is usually achieved in the hard excitation mode. In general, the results are in qualitative agreement with the picture described earlier for a simpler quasi-linear model of a oscillator with hard excitation, in the case of a sufficiently strong phase nonlinearity.

General perturbation correction: full-decomposition and physics-based elimination of non-secular terms

Discretized perturbation analysis based upon a structure's single (finite) mode Galerkin-truncated model may lead to erroneous results in comparison with full-basis discretization (or, equivalently, direct perturbation method). This error is due to the two involved analytical steps, i.e., multi-scale expansion and mode truncation, being non-commutative with each other. However, the key underlying physical origin for this error (or non-commutativity) is still unclear. The novelty of the current work is to propose a new physics-based error source interpretation and, accordingly, a general perturbation correction procedure. Explicitly, a general physics-based interpretation for the error source is referred to the incomplete characterization of low-order non-secular effects due to both spectrum mixture and single (finite) mode truncation. Three typical dynamical scenarios, i.e., hard external excitation, quadratic nonlinearity, and hard boundary motion, are addressed in the same unified framework. By introducing a full spectrum decomposition and a complete elimination of the non-secular term in a physically equivalent manner, a general correction procedure of the finite mode truncation often used in perturbation analysis is proposed and then validated through numerical examples.

Optimization of shaped pulses for radio frequency excitation in NMR logging.

The radio frequency (RF) excitation pulse of the nuclear magnetic resonance (NMR) logging tool can realize slice measurement by designing shaped pulses. In the case of a certain main magnetic field, the accuracy of the shaped pulse designhas a very important impact on the signal-to-noise ratio (SNR) of the NMR signal and the measurement of the short relaxation signal. Hard pulse excitation will produce an undesirable infinite number of side lobes that may perturb the spins in unwanted regions. Soft pulse can achieve selective excitation and has a better slice profile and shorter energy release time while it is not conducive to the measurement of short relaxation signals. This article focuses on the designof shaped pulses in extreme downhole environments and analyzes the characteristics of the three shaped pulses in the two cases of equivalent bandwidth and equivalent pulse duration. At the same time, a kind of RF-shaped pulse transmitting circuit with phase difference control is realized. According to the pulse type optimization strategy, the appropriate shaped pulse is selected. When echo spacing (TE) >0.6ms, the SNR can be increased to more than 12%. When TE is small, it will automatically switch to the hard pulse mode, which is good for short relaxation measurement.

Subcritical Andronov-Hopf scenario for systems with a line of equilibria.

Using numerical simulation methods and analytical approaches, we demonstrate hard self-oscillation excitation in systems with infinitely many equilibrium points forming a line of equilibria in the phase space. The studied bifurcation phenomena are equivalent to the excitation scenario via the subcritical Andronov-Hopf bifurcation observed in classical self-oscillators with isolated equilibrium points. The hysteresis and bistability accompanying the discussed processes are shown and explained. The research is carried out on an example of a nonlinear memristor-based self-oscillator model. First, a simpler model including Chua's memristor with a piecewise-smooth characteristic is explored. Then, the memristor characteristic is changed to a function being smooth everywhere. Finally, the action of the memristor forgetting effect is taken into consideration.

Математичне моделювання жорстких режимів збудження кавітаційних ав-токоливань у системі живлення рідинних ракетних двигунів

Hard self-oscillation excitation differs from soft excitation in that self-oscillations are set up only if the initial departure of an oscillating system from equilibrium is strong enough. Experimental studies of cavitation oscillations in hydraulic systems with cavitating pumps of liquid-propellant rocket engines ((LPREs) include works that describe hard excitation of cavitation oscillations. By mow, hard excitation regimes have not been explained theoretically, to let alone their mathematical simulation. This paper presents a mathematical model of hard excitation of cavitation oscillations in a LPRE feed system, which comprises a mathematical model of cavitation self-oscillations in a LPRE feed system that accounts for pump choking and an external disturbance model. A mechanism of hard excitation of cavitation oscillations in a LPRE feed system is proposed. It is well known that hard excitation of cavitation self-oscillations may take place in cases where the pump feed system is near the boundary of the cavitation self-oscillation region. In this case, the self-oscillation amplitudes are small, and they are limited only by one nonlinearity (cavity volume vs. pump inlet pressure and flow relationship). Under excitation of sufficient intensity, the pump inlet pressure and flow find themselves in the choking characteristic; this may be responsible for choking and developed cavitation self-oscillations, which remain of interrupted type and do not go into the initial small-amplitude oscillations even after excitation removal. A mathematical simulation of hard excitation of cavitation self-oscillations was conducted to determine the parameters of cavitation self-oscillations in a bench feed system of a test pump. The simulation results show that without an external disturbance the pump system exhibits small-amplitude self-oscillations. On an external disturbance, developed (interrupted) cavitation oscillations are set up in the system, which is in agreement with experimental data. The proposed mathematical model of hard excitation of cavitation self-oscillations in a LPRE feed system allows one to simulate a case observed in an experiment in which it was possible to eliminate cavitation self-oscillations by an external disturbance.

Active Vibration Absorber for Superharmonic Resonance Condition

The present paper, analyses vibration suppression of a nonlinear single degree of freedom (SDOF) spring-mass-damper system under hard harmonic excitation by attaching a piezoelectric based active dynamic vibration absorber (ADVA). The host structure consists of spring with cubic nonlinear stiffness and negligible damping. The acceleration feedback is used to provide the actuating force through ADVA on the vibrating host structure. The hard harmonic excitation on the host structure induces superharmonic resonance condition i.e. when excitation frequency nearly matches one-third of the natural frequency of the host structure. The optimal tuning ratio and damping ratio of the vibration absorber are considered to depend upon the actuating force so that one can actively tune the operating frequency of the ADVA. The method of multiple scales (MMS) is used to obtain the reduced equations to study the frequency response of the system. The analysis is carried out by studying the effect of active force and cubic nonlinear stiffness on the responses of the host structure. The results obtained by MMS are compared numerically showing good agreement.

Имитационное моделирование эпилептиформной активности сетью нейроподобных радиотехнических осцилляторов

We developed a radioengineering circuit modeling a hierarchically organized thalamo-cortical network of the brain with an external input. We investigated the resulting model and found various regimes of forced and self-oscillations, including regimes with hard excitation. We established at what parameters the circuit demonstrates activity similar to spike-wave discharges at absence epilepsy, implementing the hypothesis that a spike-wave discharge is a long transient process near the bifurcation of the cycle birth from the condensation of phase trajectories.

Design and Efficiency Enhancement of a Ka-Band Industrial Gyrotron

The key subsystems of a high efficiency material processing gyrotron are designed at an operating frequency of 27.885 GHz. A triode-type electron gun is designed to launch hollow spiraling electron beam. The outer diameter of the gun is kept at 50 mm to lower inside diameter of the magnet. Start oscillation current for TE02 operating as well as competing modes is plotted. The output power and efficiency are predicted to be 18.4 kW and 46%, respectively, based on single mode time-dependent analytical equation. Beam-wave interaction is studied by employing particle-in-cell (PIC) simulation. Electronic efficiency and output power are increased by operating the tube in hard excitation region. An axially slotted cavity is adopted to abridge mode competitions. The output power and electronic efficiency are obtained to be 20.08 kW and 50.2%, respectively, without considering any velocity spread of the electron beam. However, the efficiency is reduced to 45%, when a moderate transverse velocity spread of 5% is considered. The power efficiency is enhanced to 67.07% by introducing a 3-staged depressed collector.

Energy harvesting from the secondary resonances of a nonlinear piezoelectric beam under hard harmonic excitation

This paper investigates the dynamical response of a nonlinear piezoelectric energy harvester under a hard harmonic excitation and assesses its output power. The system is composed of a unimorph cantilever beam with a tip mass and exposed to an harmonic tip excitation with a hard forcing amplitude. First, the governing dimensionless nonlinear electromechanical ordinary differential equations (ODEs) are obtained. Next, the multiple scales method (MSM) is exploited to provide an approximate-analytical solution for the ODEs in hard and soft forcing scenarios. It is observed that, the hard force results in sub- and super-harmonic resonances. The MSM-based solutions are then validated by a numerical integration method and a good agreement is observed between the approximate-analytical and numerical results. Furthermore, utilizing the MSM-based solutions for the subharmonic, superharmonic, and soft primary resonances cases, the associated frequency and force response curves are constructed. It is revealed that the hard excitation leads to a remarkable voltage generation in the secondary resonances; this leads to a broadband energy harvesting. In addition, the time-domain electrical responses of the secondary resonances are also obtained and compared with each other. Finally, the three-dimensional graphs of the electrical power versus detuning parameter and time constant ratio in the cases of the secondary resonances are plotted. The results show that the optimum output power of the superharmonic resonance is considerably larger than the maximum power of the subharmonic resonance case.

Nonlinear conditions for instability of the free surface of a conducting liquid in an external electric field in a confined axisymmetric geometry

The behavior of the free surface of a perfectly conducting liquid in an external uniform electric field is considered in the framework of the Hamiltonian formalism for the case of bounded axisymmetric geometry of the system (the fluid is bounded by a cylindrical rigid wall). Taking into account the influence of quadratic nonlinearities, we derive an amplitude equation which describes the evolution of the boundary. Using this equation, we find the condition for the hard excitation of boundary instability that leads to an explosive growth of surface perturbations. The differences in the description of the dynamics of axisymmetric perturbations of the boundary from the cases of plane, square, and hexagonal symmetries of the problem are discussed.

Numerical Investigation of Nonlinear Dynamics of a Pneumatic Artificial Muscle With Hard Excitation

Abstract In this work, a numerical analysis has been carried out to study the nonlinear dynamics of a system with pneumatic artificial muscle (PAM). The system is modeled as a single degree-of-freedom system and the governing nonlinear equation of motion has been derived to study the various responses of the system. The system is subjected to hard excitation and hence the subharmonic and superharmonic resonance conditions have been studied. The second-order method of multiple scales (MMS) has been used to find the response, stability, and bifurcations of the system. The effect of various system parameters on the system response has been studied using time response, phase portraits, and basin of attraction. In these responses, while the saddle node bifurcation is found in both super and subharmonic resonance conditions, the Hopf bifurcation is found only in superharmonic resonance condition. By changing different system parameters, it has been shown that the response with three periods leads to chaotic response for superharmonic resonance condition. This study will find applications in the design of PAM actuators.