Nonlinear Dynamic Effects Research Articles

Modeling of Flexible Beams for Robotic Manipulators

This work treats the problem of modeling robotic manipulators withstructural flexibility. A mathematical model of a planarmanipulator with a single flexible link is developed. This modelis capable of reproducing nonlinear dynamic effects, such as thebeam stiffening due to the centrifugal forces induced by therotation of the joints, giving it the capability to predictreliable dynamic behaviors for a wide range of applications. Onthe other hand, the model complexity is reduced, in order to keepit amenable for analysis and controller design. The models foundin current literature for control design of flexible manipulatorarms present dynamic limitations for the sake of real timeimplementation in a control scheme. These limitations are theresult of premature linearizations in the formulation of thedynamics equations. In this paper, these common linearizations arepresented and their dynamic limitations uncovered. An alternativereliable model is then presented. The model is founded on twobasic assumptions: inextensibility of the neutral fiber, andmoderate rotations of the cross sections in order to account forthe foreshortening of the beam due to bending. Simulation andexperimental results show that the proposed model has the closestdynamic behavior to the real beam.

Atom-laser dynamics

An ideal atom laser would produce an atomic beam with highly stable flux and energy. In practice the stability is likely to be limited by technical noise and nonlinear dynamical effects. We investigate the dynamics of an atom laser using a comprehensive one dimensional, mean-field numerical model. We fully model the output beam and experimentally important physics such as three-body recombination. We find that at high pump rates the latter plays a role in suppressing the high frequency dynamics, which would otherwise limit the stability of the output beam.

Nonlinear Dynamic Combustion in Solid Rockets: L* Effects

nonlinear combustion phenomena that have been observed experimentally but that are beyond the capability of linearized models are also predicted. These include rapid initial (over-) pressurization, propellant extinction, and dual-frequency and limit-cycle oscillations. The results suggest that some of these combustion phenomena could be due to nonlinear (but still quasi ‐steady) dynamic burning and mass conservation effects within the classical bulk-mode framework rather than more complicated e uid and e ame dynamic effects that have been proposed. In particular, the rapid rate of initial pressurization and the ignition spike commonly attributed to erosive burning may be due to nonlinear dynamic burning at low L ¤ . Even without an overpressurization spike, it appears that

Electromagnetically driven solitons in inhomogeneous overdense plasma

In the framework of nonlinear Schrödinger equation (NSE), the dynamics of soliton excitation by an incident electromagnetic wave in an inhomogeneous overdense plasma is investigated. The periodic and chaotic regimes of the excitation are obtained, the thresholds for periodic and chaotic regimes are found. It is shown that the regimes depend on the unique parameter, which is determined by the scale of plasma inhomogeneity and the amplitude of the incident wave. Dynamic nonlinear effects connected with the soliton excitation: spectrum broadening of the reflected wave and local fields, the expansion of the excitation region deep into the overdense plasma, “super-reflection” and “after-effect” are studied.

Nonlinear dynamic effects at the head-disk interface

The contact dynamics of pico sliders is investigated using a high bandwidth laser Doppler vibrometer (LDV) and a high bandwidth acoustic emission (AE) sensor. Sliding contact of the slider near the glide avalanche point is analyzed for a lubricant thickness of 1.5 nm, 2.5 nm, and 3.5 nm, respectively. Slider airbearing modes as well as torsional and bending mode vibrations are investigated as a function of disk velocity and lubricant thickness. Damping of the airbearing pitch and roll frequency is found to increase with increased lubricant thickness. Nonlinear slider/lubricant interactions are observed leading to additional peaks in the LDV spectrum near the bending mode frequency. Nonlinear effects due to slider/lubricant interactions are modeled using a nonlinear stiffness term in the equation of motion. The numerical and experimental results are found to be in good agreement.

Self-Regulation Phenomena in Bacterial Reaction Centers. I. General Theory

A model for light-induced charge separation in a donor-acceptor system of the reaction center of photosynthetic bacteria is described. This description is predicated on a self-regulation of the flow of photo-activated electrons due to self-consistent, slow structural rearrangements of the macromolecule. Effects of the interaction between the separated charges and the slow structural modes of the biomolecule may accumulate during multiple, sequential charge transfer events. This accumulation produces non-linear dynamic effects on system function, providing a regulation of the charge separation efficiency. For a biomolecule with a finite number of different charge-transfer states, the quasi-stationary populations of these states with a localized electron on different cofactors may deviate from a Lagmuir law dependence with actinic light intensity. Such deviations are predicted by the model to be due to light-induced structural changes. The theory of self-regulation developed here assumes that light-induced changes in the effective adiabatic potential occur along a slow structural coordinate. In this model, a “light-adapted” conformational state appears when bifurcation produces a new minimum in the adiabatic potential. In this state, the lifetime of the charge-separated state may be quite different from that of the “dark-adapted” conformation. The results predicted by this theory agree with previously obtained experimental results on photosynthetic reaction centers.

Modeling of Flexible Manipulators for Control Design

In this paper an extended metogy for modeling of general flexible link robot manipulators is presented. By using the classic theory of mechanics of deformation the dynamic nonlinearities of the flexible robot are derived in a natural way through a consistent formulation. The approach allows to capture the nonlinear dynamic effects without the use of any ad-hoc improvisions, by taking into account both quadratic rotations of the beam cross sections and linear shear deformations. The dynamics equations of a flexible manipulator are systematicaly obtained through the application of the Extended Hamilton Principle. The adoption of the assumed modes method for the spatial discretization of the nonlinear partial differential equations of motion minimizes the overall computational complexity, making it suitable for analysis and control purposes.

Nonlinear effects in two-layer large-amplitude geostrophic dynamics. Part 2. The weak-beta case

This paper is a continuation of our study on nonlinear processes in large-amplitude geostrophic (LAG) dynamics. Here, we examine the so-called weak-β models. These models arise when the intrinsic length scale is large enough so that the dynamics is geostrophic to leading order but not so large that the β-effect enters into the dynamics at leading order (but remains, nevertheless, dynamically non-negligible). In contrast to our previous analysis of strong-β LAG models in Part 1, we show that the weak-β models allow for vigorous linear baroclinic instability.For two-layer weak-β LAG models in which the mean depths of both layers are approximately equal, the linear instability problem can exhibit an ultraviolet catastrophe. We argue that it is not possible to establish conditions for the nonlinear stability in the sense of Liapunov for a steady flow. We also show that the finite-amplitude evolution of a marginally unstable flow possesses explosively unstable modes, i.e. modes for which the amplitude becomes unbounded in finite time. Numerical simulations suggest that the development of large-amplitude meanders, squirts and eddies is correlated with the presence of these explosively unstable modes.For two-layer weak-β LAG models in which one of the two layers is substantially thinner than the other, the linear stability problem does not exhibit an ultraviolet catastrophe and it is possible to establish conditions for the nonlinear stability in the sense of Liapunov for steady flows. A finite-amplitude analysis for a marginally unstable flow suggests that nonlinearities act to stabilize eastward and enhance the instability of westward flows. Numerical simulations are presented to illustrate these processes.

Nonlinear effects in two-layer large-amplitude geostrophic dynamics. Part 1. The strong-beta case

Baroclinic large-amplitude geostrophic (LAG) models, which assume a leading-order geostrophic balance but allow for large-amplitude isopycnal deflections, provide a suitable framework to model the large-amplitude motions exhibited in frontal regions. The qualitative dynamical characterization of LAG models depends critically on the underlying length scale. If the length scale is sufficiently large, the effect of differential rotation, i.e. the β-effect, enters the dynamics at leading order. For smaller length scales, the β-effect, while non-negligible, does not enter the dynamics at leading order. These two dynamical limits are referred to as strong-β and weak-β models, respectively.A comprehensive description of the nonlinear dynamics associated with the strong- β models is given. In addition to establishing two new nonlinear stability theorems, we extend previous linear stability analyses to account for the finite-amplitude development of perturbed fronts. We determine whether the linear solutions are subject to nonlinear secondary instabilities and, in particular, a new long-wave–short-wave (LWSW) resonance, which is a possible source of rapid unstable growth at long length scales, is identified. The theoretical analyses are tested against numerical simulations. The simulations confirm the importance of the LWSW resonance in the development of the flow. Simulations show that instabilities associated with vanishing potential- vorticity gradients can develop into stable meanders, eddies or breaking waves. By examining models with different layer depths, we reveal how the dynamics associated with strong-β models qualitatively changes as the strength of the dynamic coupling between the barotropic and baroclinic motions varies.

A Coherency Function Approach for Model-Free Fault Detection and Isolation

This paper presents a model-free fault detection technique based on the use of a specific spectral analysis tool, namely, the squared coherency functions. The fault-free dynamic behavior of the plant is described by a stochastic linear state equation, where the stochastic part is due to unpredictable external disturbances. The fault is assumed to be a nonlinear dynamic perturbation to the linear plant dynamics. The detection of the fault is achieved by on-line monitoring the estimates of the squared coherency function, which is sensitive to the occurrence of nonlinear effects in the plant dynamics. An algorithm for low-bias estimates of the squared coherency function is used. Finally, results on data from the three tank benchmark problem are outlined.

Dynamical Mechanisms for the South China Sea Seasonal Circulation and Thermohaline Variabilities

Abstract The seasonal ocean circulation and the seasonal thermal structure in the South China Sea (SCS) were studied numerically using the Princeton Ocean Model (POM) with 20-km horizontal resolution and 23 sigma levels conforming to a realistic bottom topography. A 16-month control run was performed using climatological monthly mean wind stresses, restoring-type surface salt and heat, and observational oceanic inflow/outflow at the open boundaries. The seasonally averaged effects of isolated forcing terms are presented and analyzed from the following experiments: 1) nonlinear dynamic effects removed, 2) wind effects removed, and 3) open boundary inflow/outflow set to zero. This procedure allowed analysis of the contribution of individual parameters to the general hydrology and specific features of the SCS: for example, coastal jets, mesoscale topographic gyres, and countercurrents. The results show that the POM model has the capability of simulating seasonal variations of the SCS circulation and thermoha...

Nonlinear dynamics of self-pulsating laser diodes under external drive

A self-pulsating laser diode under external drive shows the nonlinear dynamical effects of two competing frequencies. One can establish a route to chaos by increasing the modulation current. However, when the modulation frequency is varied, the chaotic state is suddenly destroyed at the harmonic frequencies of the self-pulsating frequency. This approach therefore offers a simple chaotic light source for possible optical chaotic communication.

The Power Spectrum of Mass Fluctuations Measured from the Lyα Forest at Redshiftz = 2.5

We measure the linear power spectrum of mass-density fluctuations at redshift z = 2.5 from the Lyα forest absorption in a sample of 19 QSO spectra, using the method introduced by Croft et al. The P(k) measurement covers the range 2π/k ~ 450-2350 km s-1 (2-12 comoving h-1 Mpc for Ω = 1), limited on the upper end by uncertainty in fitting the unabsorbed QSO continuum and on the lower end by finite spectral resolution (0.8-2.3 A FWHM) and by nonlinear dynamical effects. We examine a number of possible sources of systematic error and find none that are significant on these scales. In particular, we show that spatial variations in the UV background caused by the discreteness of the source population should have negligible effect on our P(k) measurement. We estimate statistical errors by dividing the data set into ten subsamples. The statistical uncertainty in the rms mass-fluctuation amplitude, σ [P(k)]1/2, is ~20%, and is dominated by the finite number of spectra in the sample. We obtain consistent P(k) measurements (with larger statistical uncertainties) from the high- and low-redshift halves of the data set, and from an entirely independent sample of nine QSO spectra with mean redshift z = 2.1. A power-law fit to our results yields a logarithmic slope n = -2.25 ± 0.18 and an amplitude Δ2ρ(kp) = 0.57+0.26-0.18, where Δ2ρ is the contribution to the density variance from a unit interval of ln k and kp = 0.008(km s-1)-1. Direct comparison of our mass P(k) to the measured clustering of Lyman break galaxies shows that they are a highly biased population, with a bias factor b ~ 2-5. The slope of the linear P(k), never previously measured on these scales, is close to that predicted by models based on inflation and cold dark matter (CDM). The P(k) amplitude is consistent with some scale-invariant, COBE-normalized CDM models (e.g., an open model with Ω0 = 0.4) and inconsistent with others (e.g., Ω = 1). Even with limited dynamic range and substantial statistical uncertainty, a measurement of P(k) that has no unknown bias factors offers many opportunities for testing theories of structure formation and constraining cosmological parameters.

Tracking control of mechanical systems in the presence of nonlinear dynamic friction effects

In this paper, we design an observer-based exact model knowledge position tracking controller for a second-order mechanical system with nonlinear load dynamics and a nonlinear dynamic friction model. Since the controller requires an estimate of the unmeasurable friction state, we demonstrate how the friction dynamics can be exploited to design three different observers which foster different transient response characteristics for the composite closed-loop system. We then present two adaptive controllers which utilize nonlinear observer/filter structures to provide for asymptotic position tracking while compensating for selected parametric uncertainty. Dynamic simulation and experimental results are utilized to illustrate control performance.

Finite memory non-linear model of a S/H-ADC device

A new model has been proposed for the characterisation of the non-linear dynamic effects of a S/H-ADC device and a new mathematical approach has been introduced to describe its non-ideal dynamic behaviour. The measurement procedure to deduce the parameters of the proposed model is given together with the experimental results on a commercial device.

Nonlinear dynamic effects in a two-wave CO2 laser

Theoretical and experimental investigations were made of nonlinear dynamic regimes of the operation of a two-wave CO2 laser with cw excitation in an electric discharge and loss modulation in one of the channels. Nonlinear amplitude — frequency characteristics of each of the laser channels have two low-frequency resonance spikes, associated with forced linear oscillations of two coupled oscillators, and high-frequency spikes, corresponding to doubling of the period of the output radiation oscillations. At low loss-modulation frequencies the intensity oscillations of the output radiation in the coupled channels are in antiphase, whereas at high modulation frequencies the dynamics is cophasal. Nonlinear dynamic effects, such as doubling of the period and of the repetition frequency of the pulses and chaotic oscillations of the output radiation intensity, are observed for certain system parameters.

A new object-oriented finite element analysis program architecture

This paper presents a new architecture for finite element analysis software, developed using object-oriented design. The resulting system is capable of the modeling and simulation of structural behavior, including the consideration of nonlinear static and dynamic effects. An innovation of the system design is the creation of several classes of objects that separate the analysis tasks from the details of the finite element model. This separation leads to flexible, extensible code. The overall system design and a prototype implementation are presented.

Many-electron dynamics in collisions of slow ions with metal clusters

We present a many-body quantum dynamical treatment of electron capture in ion-metal cluster collisions at low velocities. The model includes nonlinear dynamical effects induced by the projectile. We have evaluated cross sections and energy deposits in ${\mathrm{H}}^{+}+{\mathrm{Na}}_{20}$ collisions and found that, in contrast with atomic collisions, (i) capture-excitation mechanisms contribute significantly to neutralization and (ii) excitation cross sections are comparable to capture cross sections.

Strange attractor in resonant tunneling

We consider the process of resonant electron tunneling through a double-barrier potential, taking into account nonlinear dynamical effects generated by charge accumulation in the interbarrier space. We use the perturbation approach of Davydov and Ermakov, which was developed for investigating intrinsic bistability in resonant tunneling. For incoming electron flow, which is modulated slowly in time, we show that the resulting nonlinear dynamics can become chaotic, with the chaos described (because of the open nature of the system) by a strange attractor. We determine the conditions for the existence of this strange attractor and estimate characteristic experimental parameters for its observation.

Doppler-Shifted Self-Reflection from a Semiconductor

We report the experimental observation of a self-reflected wave inside a dense saturable absorber. A femtosecond pulse saturates the absorption and causes a density front to penetrate into the semiconductor. The dielectric constant change across the boundary between areas of low and high densities results in internal reflection. Due to the front propagation the self-reflected light is shifted by the Doppler effect. The Doppler shift makes it possible to distinguish between surface reflection and self-reflection and is used to experimentally verify the dynamic nonlinear skin effect. The measurements are in agreement with our theory which is within the framework of the reduced semiconductor Maxwell-Bloch equations.