Higher Excitation Amplitudes Research Articles

Fractional derivative operators for modeling the dynamic polarization behavior as a function of frequency and electric field amplitude

Polarization phenomena in ferroelectric materials are frequency-dependent, and the present article describes the use of a fractional derivative for the understanding of these phenomena as well as modeling them as functions of frequency and electric field amplitude. The focus was first directed toward the definition and validation of the proposed model through comparisons between simulations and measurements for high electrical field excitation amplitudes on a large frequency bandwidth (major hysteresis loops, measured over 4 decades). Subsequently, the same comparisons were made under ultra-weak as well as weak electric fields. Large frequency bandwidths were tested in each case, and it was shown that the fractional term provided a very accurate modeling of the dynamic behavior of the ferroelectrics. The dielectric permittivity coefficient along the polarization direction epsilon(33)is a major parameter in ferroelectrics, and the frequency dependence of epsilon(33) is correctly reproduced by the model. The time-dependence of the polarization reversal/variation was accurately simulated by a fractional derivation (a 0.5 order derivative), however, the use of a first-order derivation term (i.e., viscous losses) was in poor agreement with experimental results. It was found that the model was valid for large excitation field amplitudes as well as for large frequency bandwidths.

Rabi-like oscillations of an anharmonic oscillator: Classical versus quantum interpretation

We have observed Rabi-like oscillations in a current-biased dc superconducting quantum interference device presenting enhanced coherence times compared to our previous realization [J. Claudon et al., Phys. Rev. Lett. 93, 187003 (2004)]. This Josephson device behaves as an anharmonic oscillator which can be driven into a coherent superposition of quantum states by resonant microwave flux pulses. Increasing the microwave amplitude, we study the evolution of the Rabi frequency from the two-level regime to the regime of multilevel dynamics. When up to three levels are involved, the Rabi frequency is a clear signature of a quantum behavior. At higher excitation amplitude, classical and quantum predictions for the Rabi frequency converge. This result is discussed in the light of a calculation of the Wigner function. In particular, our analysis shows that pronounced quantum interferences always appear in the course of the Rabi-like oscillations.

Prediction of Self Excitation Frequencies and Amplitudes for a Model Gas Turbine Burner

Forced excitation of a swirl stabilised methane/air flame by acoustic waves at atmospheric pressure has been characterised in order to show that the frequencies and amplitudes where self-excitation occurs, but the natural limit cycle takes effect, can be predicted from these data. Chemiluminescent emission was therefore recorded to measure the Flame Transfer Function (FTF), as the flame was acoustically excited by two loud speakers. The experiments covered a wide range of frequencies and amplitudes with particular emphasis on the FTF at high amplitudes of excitation, where a non-linear response is often reported. The system was modelled by the 1D thermo-acoustic element method, in which each acoustic element, such as a duct or a contraction, is described by a four-pole matrix. The flame is incorporated as another four-pole matrix that describes the measured flame transfer function. The solution of this set of equations without forcing predicts self-excitation frequencies and amplitudes that can be compared with the experimental data. The minimum magnitudes of the FTF for excitation may also be calculated. When proven at this small scale, the procedure will be applied to predict the limit cycling of actual installations from rig tests.

Noise-free stochastic resonance at an interior crisis

We report on the observation of noise-free stochastic resonance in an externally driven diode resonator close to an interior crisis. At sufficiently high excitation amplitudes the diode resonator shows a strange attractor which after the collision with an unstable period-three orbit exhibits crisis-induced intermittency. In the intermittency regime the system jumps between the previously stable chaotic attractor and the phase space region which has been made accessible by the crisis. This random process can be used to amplify a weak periodic signal through the mechanism of stochastic resonance. In contrast to conventional stochastic resonance no external noise is needed. The chaotic intrinsic dynamics plays the role of the stochastic forcing. Our data obtained from the diode resonator are compared with numerical simulations of the logistic map where a similar crisis-induced intermittency is observed.

Nonlinear deformation waves in solids and dispersion

In contemporary technology, high-speed loading, high frequencies and high-amplitude excitations are widely used. For proper analysis, the microstructure of solids must then be taken into account. Together with nonlinear effects, the dispersive effects due to the microstructure are of importance. In this paper, the Mindlin-type model based on the theory of continua is used for describing the microstructure. On the other hand, it is shown how straight-forward numerical methods, like the finite-volume methods, permit to describe the material properties for every discrete element used in numerical simulation. Several phenomena like the existence of solitary waves, the emergence of solitary wave trains, and waves in piece-wise nonlinear laminated materials are briefly discussed and further problems indicated.

Control of pull-in dynamics in a nonlinear thermoelastic electrically actuated microbeam

This work deals with the problem of controlling the nonlinear dynamics, in general, and the dynamic pull-in, in particular, of an electrically actuated microbeam. A single-well softening model recently proposed by Gottlieb and Champneys [1] is considered, and a control method previously proposed by the authors is applied. Homoclinic bifurcation, which triggers the safe basin erosion eventually leading to pull-in, is considered as the undesired event, and it is shown how appropriate controlling superharmonics added to a reference harmonic excitation succeed in shifting it towards higher excitation amplitudes. An optimization problem is formulated, and the optimal excitation shape is obtained. Extensive numerical simulations aimed at checking the effectiveness of the control method in shifting the erosion of the safe basin are reported. They highlight good performances of the control method beyond theoretical expectations.

An Efficient Technique for Design of Hydraulic Engine Mount via Design Variable-Embedded Damping Modeling

For an efficient design of hydraulic mounts, it is most important to have a good mathematical model available, which must be simple yet capable of representing dynamic characteristics of the hydraulic mounts accurately. Under high amplitude excitations in the low-frequency range, the hydraulic mounts show strongly frequency-dependent stiffness and damping characteristics, which are related with so-called inertia track dynamics. Since nonlinear damping models based on fluid mechanics are typically used to predict the dynamic characteristics of the hydraulic mounts, relations between various design variables, such as geometry of the inertia track, and resultant stiffness and damping characteristics are understood only by tedious numerical computations. In this paper, the use of an equivalent viscous damping model—derived from a nonlinear model and represented in terms of design variables in an explicit manner—is proposed and, based on the equivalent linear model, are presented simple as well as very useful formulas for an efficient design of the hydraulic mounts.

Influence of Hysteretic Heating on Asphalt Fatigue Characterization

Abstract This paper presents a study focusing on the influence of hysteretic heating on asphalt samples during laboratory fatigue testing. The experimental test setup for material characterization and temperature measurements, including its effect on fatigue test results, as well as theoretical aspects on hysteretic heating, are described. The experimental part of the investigation concerns linear viscoelastic and cyclic fatigue characterization of six asphalt concrete mixtures using uniaxial testing. All the mixtures show nominally identical volumetric properties (aggregate size distribution, binder and air void content) but different binder properties. Three base bitumens and three polymer modified binders were used. The cyclic fatigue tests were carried out at 0, 10, and 20°C using controlled strain and stress modes and different excitation amplitudes. In order to acquire knowledge regarding temperature changes during fatigue testing, several experimental techniques were used. The main thermal study was performed using thermocouples attached to the midheight envelope surface of each sample. The sample surface temperature distribution and its evolution during fatigue testing were investigated using an infrared thermal camera. Furthermore, a limited study of the magnitude of difference between surface and maximum temperature inside the sample was carried out using thermocouples embedded during gyratory compaction. When compared, each method shows advantages and disadvantages regarding simplicity and reliability. In principle, the three methods provide similar results, but the type of information obtained differs among the methods. The use of thermocouples attached to the envelope surface during fatigue testing provides accurate and consistent results of global temperature that can be used to investigate the influence of heating on asphalt fatigue characteristics. By use of thermal measurements and a continuum damage model, it was possible to show a pronounced effect of heating on fatigue behavior. The influence of heating was especially obvious at high excitation amplitudes and elevated temperatures, i.e., conditions where the material produces high amounts of viscoelastic dissipated energy as well as temperature sensitive material behavior.

Intermittent movement of localized excitations of a nonlinear lattice.

The mobility of localized high-amplitude excitations of the discrete nonlinear Schrödinger equation is studied. The excitations can either be pinned at the lattice or they can propagate depending on their energy and particle number. Such localized excitation can emit or absorb waves with a low amplitude which changes the amount of these quantities in the excitation. For statistical reasons, the excitations absorb a high amount of energy per particle through their interaction with low-amplitude waves. They can only move if their energy decreases temporarily either by a random fluctuation or by an external force.

Resonant bar simulations in media with localized damage

As a rule, problems of wave propagation in finite media with non-uniform spatial distribution of material properties can only be tackled by numerical models. In addition, the modeling of damage features in a material requires the introduction of locally non-linear and––more important––non-unique equations of state. Using a multiscale approach, we have implemented a non-linear hysteretic stress–strain relation based on the Preisach–Mayergoyz (PM) model, into a numerical elastodynamic finite integration technique program, which has originally been developed for linearly elastic wave propagation in inhomogeneous media. The simulation results show qualitatively good agreement with data of non-linear resonant bar experiments in homogeneously non-linear and hysteretic media. When the PM density distribution of hysteretic units at the mesoscopic level is not uniform and/or confined to a finite area in stress–stress space, the response at high amplitude excitation tend to deviate from the quasi-analytical results obtained in the case of a uniform PM-space density. Localized microdamage features in an intact medium can be modeled by conceiving finite zones with pronounced hysteretic stress–strain relations within a “linear” surrounding. Forward calculations reveal a significant influence of the amplitude dependent resonance behavior on the location (edge versus center of a bar), the extend (width of the zone) and the degree (density of hysteretic units) of damage.

Low Field Second Harmonic Response and AC Susceptibility of (Bi,Pb)-2223 Pellet in a Generalized Critical State Model

The AC susceptibility and second harmonic response of bulk high Tc superconductor (Bi,Pb) -2223 is measured in presence of small AC field excitation and DC magnetic field superimposed on it. This response increases with the increase in DC field whereas decreases at a higher excitation amplitude. Critical state models are used to explain the nonlinear magnetic response in HTSCs. With a generalized field dependence of critical current Jc : Jc(B) = J0/(1 + B/B0)n, the fundamental AC susceptibility and low field second harmonics response are calculated for different n values. It is found that the theoretical consideration adopted here explains the observed AC susceptibility and low field second harmonic response qualitatively reasonably well within the Anderson–Kim regime (n = 1).

Effect of Leading-Edge Curvature on Airfoil Separation Control

Separation control on NACA 0012 and NACA 0015 airfoils was compared under incompressible conditions, using leading-edgeperiodicexcitation, in orderto assess the effect of leading-edgecurvature. Both lift and moment coefe cients were considered to compare and analyse control effectiveness. In contrast to the relatively mild NACA 0015 trailing-edge stall, NACA 0012 stall was dominated by a leading-edge bubble-bursting mechanism that gave rise to alternating intervals of partial attachment and separation, but with no regular frequency. Low-amplitude excitation downstream of the bubble enhanced poststall lift and signie cantly attenuated the associated unsteadiness. In general, larger momentum coefe cients were required for NACA 0012 separation control due to the large centrifugal acceleration of the e ow around the leading edge. Because of the different stalling characteristics, relatively high- and low-excitation frequencies were effectivefor the NACA 0012 and NACA 0015 airfoils, respectively. However, the combination of high-excitation amplitudes with relatively low frequencieswas effective on the NACA 0012, and this was believed to be associated with the large harmonic content of the evolving perturbations.

Combustion and stabilization characteristics of a branched flame under Helmholtz-type excitations

The combustion and pollution characteristics of the newly rediscovered “branched flame” are experimentally investigated using a Helmholtz-type excitation. Under specific excitation conditions, high-amplitude Helmholtz excitation induces side jet ejection, which leads to a branched flame. Intense combustion and enhanced heat transfer due to strong oscillation of the flame and hot gases of the branched flame increase the heating effectiveness and fuel saving. Strong velocity oscillation results in accumulation of jet fluid ahead of the ring structure for generation of the side jet. In the side-jet evolution, the strong entrainment of the ring vortex in the initial stages followed by the early growth of the streamwise vortical structures greatly shortens the route to mixing transition of fuel and air in the upstream region of the flame. This enhanced premixing process of the side jet leading to high F probability, which is defined as the probability of the presence of a premixture of fuel and air with concentration within the flammability limits, and low strain rate has significant implications for the stabilization of the branched flame. NOx emission indices for the branched flames can be 30% higher and CO emission indices 50% lower than the unexcited case.

Resonant accelerometer with self-test

A new resonant accelerometer is presented consisting of a doubly clamped beam coupled to a seismic mass. The beam is thermally excited by an implanted resistor and its vibration is sensed piezoresistively. An acceleration which deflects the seismic mass leads to characteristic strains inside the resonator, shifting its resonance frequency. We studied the oscillation characteristics of the resonant beam. The non-linearity at high excitation amplitudes is treated theoretically and experimentally. Further, it is shown that the electrical and thermal cross-talk can be eliminated. The resonant sensing principle ensures a quasi-digital output signal, high sensitivity and a mechanical integrity test. Advanced automotive safety systems and x-by wire applications require a high reliability of the employed sensors. The sensor presented here allows an on-going self-test without any constructive changes of the sensor element. The self-test concept, we developed also finds applications in other sensors with resonant structures.

FREE-VIBRATION BEHAVIOUR OF A CRACKED CANTILEVER BEAM AND CRACK DETECTION

This study is based on cracks that occurred in metal beams obtained under controlled fatigue-crack propagation. The beams were clamped in a heavy vise and struck in order to obtain a clean impulse modal response. Spectrograms of the free-decay responses showed a time drift of the frequency and damping: the usual hypothesis of constant modal parameters is no longer appropriate, since the latter are revealed to be a function of the amplitude. Signal processing such as the worm transform and phase spectrogram methods have been developed with enough accuracy to display the behaviour of an uncracked beam where a slight non-linear stiffness is generated by the clamping. Moreover, extracted worms show that the second mode of a beam with a deep crack is modulated in frequency by the first mode. In fact, the dominant mode opens and closes the crack, thereby modulating the beam stiffness, which affects higher modal frequencies. With deep cracks, three vibration states are observed: one where the crack is alternately fully open and fully closed, a second with a crack partially opened, and a third with an alternating force acting on a closed crack. In the latter case, the peak force is smaller than the intrinsic closure load of the crack. The first state is difficult for a small crack to reach since high-amplitude excitation is required to fully open the crack. For crack detection purposes, the damping criterion, harmonic distortion criterion and bispectrum appear less sensitive to small cracks than the phase spectrogram and coherent-modulated power.

Strong acoustic forcing on conical premixed flames

Premixed conical flames deform to a quasi-hemispherical shape in the presence of an intense acoustic field. Visualizations show different behaviors of the flame that may be stable or unstable, according to the acoustic power. Effects of the burner geometry are analyzed, and emphasis is put on the influence of the burner exit on the flame shape. Comparisons are made with the acoustic equipotential surfaces at the exit, for two different burners, and mechanisms leading to the modifications of the flame are studied. Using one of the configurations, it was possible to observe strong cells on the flame surface for very high excitation amplitudes. These cells are characteristic of the secondary parametric instability. The instability threshold is given, and the results are compared with studies concerning flames propagating in tubes. In the conditions leading to a stable behavior, where the flame is smooth and quasi-hemispherical, the area of the flame surface is measured. A slight decrease of this area is observed, when the acoustic amplitude is high enough. The displacement speed of the flame front, deduced from measurements of the unburnt gas velocity extrapolated at the flame position, indicates that the flame structure does not seem to be perturbed by the acoustic excitation.

Numerical Model of Impact-Damped Continuous Systems

In earlier studies of multiple-degree-of-freedom (MDOF) systems, an impact had always been assumed to affect the velocity of the lumped mass at the point of impact. Experiments show that the velocities of all points in a continuous system are influenced by the impact of the damper. In this study, the stead7-state behavior of an impact-damped beam is modeled by applying conservation of momentum between .the tmpact damper and the modal masses of the beam. Friction and gravity are considered for the case of honzontal and vertical motions, respectively. The impact damper exhibits a wide range of impact patterns and its optimum behavior occurs at two impacts per cycle. Three types of impact are identified for the case of two impacts per cycle, one of which expands the limit cycle of the system and therefore is detrimental.. Within limi~s, the effectiveness of the impact damper improves with an increase in its mass, with a decrease In the coeffictent of restitution, and when it is at a point of large amplitude. An optimum gap exists for each of the first three modes of vibrations. The damper expands the limit cycle of the system at higher excitation amplitudes. The phenomena of bouncedown and stuck impacts are shown to exist in continuous systems. as previously suggested (Masri 1973b). Therefore, there is a need to understand the particle's motion, at varying parame­ ters, as it travels between the container's boundaries to explore the potential of the impact damper fully. Studies mentioned above were very crucial in the develop­ ment of the theory presented in this paper, though limited in their scope. This study employs the consistent mass matrix to develop a finite-element model of a continuous beam, thus considering rotational and translational inertia at the nodes. The response of the system between impacts is obtained through the mode-superposition method. It is assumed, as had been suggested by Masri (1970), that the impact occurs during an infinitesimal period and that the displacement of the system does not change immediately before and after the impact. Pre­ vious experimental work shows that the duration of impact is indeed infinitesimal (Akl and Butt 1994). Momentum and res­ titution equations in terms of the principal coordinates are used to model the behavior of the impacting mass and the oscillat­ ing system. By using principal coordinates, we can determine the velocity of the system at all the nodes simultaneously after each impact without oversimplifying the model. The exact time of impact is determined by employing an optimization algorithm. Eventually, frequency response functions are ob­ tained by transforming the time domain data to the frequency domain by performing fast Fourier transforms (Weaver 1989).

Role of large coherent structures in turbulent compressible mixing

Turbulent compressible shear layers of round supersonic jets were excited by placing an open cavity near the nozzle exit, which produced pressure oscillations due to flow-induced cavity resonance. As a result of the excitation, large coherent structures were created in the highly compressible shear layers, making it possible to study the effect of such structures on turbulent compressible mixing. For this study, pressure-matched Mach 2 jets were used under both nonreacting and afterburning conditions. By varying the cavity dimensions, we could apply excitation over a wide range of frequencies and manipulate the coherent structure dynamics in the near field of the jets. Mie-scattering flow visualization images revealed that large coherent structures were generated when high-amplitude excitation occurred at frequencies close to the jet preferred mode, which was near the Strouhal number of about one-half. Growth rate of nonreacting shear layers was quantified as a function of excitation frequency; and, for afterburning jets, the change in global flame luminosity due to excitation was measured. It was observed that the growth rate was drastically increased in the near field when the coherent structures were organized. The afterburning characteristics were also modified by coherent structures and their dynamics. Under these conditions, afterburning intensity increased when the excitation frequency was higher than the preferred mode frequency and decreased at lower frequencies. The results suggest that the initial size of the coherent structures not only determined the rate of large-scale entrainment, but also modified molecular-level mixing by affecting the timing of large-structure breakdown.

Selective parent ion axialization for improved efficiency of collision-induced dissociation in laser desorption-ionization Fourier transform ion cyclotron resonance mass spectrometry

We have systematically established the excitation frequency, amplitude, duration, and buffer gas pressure for optimal axialization efficiency and mass selectivity of quadrupolar excitation-collisional cooling for isolation of parent ions for collision-induced dissociation in Fourier transform ion cyclotron resonance mass spectrometry. For example, at high quadrupolar excitation amplitude, ion axialization efficiency and selectivity are optimal when the applied quadrupolar excitation frequency is lower than the unperturbed ion cyclotron frequency by up to several hundred hertz. Moreover, at high buffer gas pressure (10 −6 Torr), quadrupolar excitation duration can be quite short because of efficient collisional cooling of the cyclotron motion produced by magnetron-to-cyclotron conversion. Efficiency, detected signal magnitude, and mass resolving power for collision-induced dissociation (CID) product ions are significantly enhanced by prior parent ion axilization. With this method, we use argon CID to show that C + 94 ( m/z 1128) formed by Nd:YAG laser desorption-ionization behaves as a closed-cage structure.

Stability and Hopf bifurcations in an inverted pendulum

The inverted state of a simple pendulum is a configuration of unstable equilibrium. This instability may be removed if the pivot is harmonically displaced up and down with appropriate frequency and amplitude. Numerical simulations are employed to investigate the stable domains of the system. The associated basins of attraction, extracted by interpolated cell mapping, are seen to be fractal. Loss of stability at high excitation amplitudes is observed to follow a Hopf bifurcation.