Unstable Amplitude Research Articles

Manifold based feedback linearization of a 1-DOF beam with one-sided spring

Vibration reduction in a harmonically excited 1-DOF beam with one-sided spring is realized by control-ling the system state from a stable large amplitude 1/2 subharmonic response towards a coexisting unstable small amplitude harmonic response using feedback linearization. At the unstable harmonic response no control effort is needed because the unstable harmonic response is a long term solution of the uncontrolled system. To reduce control effort when stabilizing the unstable harmonic response, the stable manifold can be used within the control design because at the stable manifold the system state approaches the unstable harmonic response without control effort. Unfortunately, the calculation of this manifold acquires much off-line computational effort while its usage complicates the on-line control design. Therefore, the stable manifold is approximated by the stable eigenvectors of the monodromy matrix. Due to the local validity of the approximation, a two-stage control approach is used. In the first stage, the system state is controlled towards the unstable harmonic response to reach the region where the stable manifold can be approximated accurately by the stable eigenvectors. In the second stage, the system state is controlled towards the stable eigenvectors and approaches the unstable harmonic response with hardly any control effort

Equatorial dynamics observed by rocket, radar, and satellite during the CADRE/MALTED campaign: 2. Mean and wave structures, coherence, and variability

We present an analysis of the wind and temperature measurements made by rocket, radar, and satellite instrumentation in the equatorial and subtropical middle atmosphere accompanying the MALTED/CADRE campaign conducted at Alcantara, Brazil during August 1994. Measured mean winds and temperatures extended from ∼10 to 110 km, exhibited general consistency between instruments, and revealed an oscillatory nature of the mean zonal wind with altitude at equatorial latitudes. MF radar measurements of tidal structures showed these to exhibit variability on ∼8‐ and 16‐day periods, but to be largely uncorrelated in time. Two‐day wave structures displayed the same periodicities, but were well correlated among sites at northern and equatorial latitudes. Rocket and radar measurements at smaller scales of motion revealed inertia‐gravity waves having significant temporal coherence, quadrature correlations between components indicating clear directions of propagation, and momentum flux and mean wind correlations indicative of gravity wave filtering processes. Rocket estimates of diurnal tidal amplitudes suggest that the diurnal tide achieves convectively unstable amplitudes in the upper equatorial mesosphere.

The dynamics of infectious diseases in orchards with roguing and replanting as control strategy

Roguing and replanting is a widely adopted control strategy of infectious diseases in orchards. Little is known about the e⁄ect of this type of management on the dynamics of the infectious disease. In this paper we analyze a structured population model for the dynamics of an S-I-R type epidemic under roguing and replanting management. The model is structured with respect to the total number of infections and the number of post- infectious infections on a tree. Trees are assumed to be rogued, and replaced by uninfected trees, when the total number of infections on the tree reaches a threshold value. Stability analysis and numerical exploration of the model show that for specific parameter combinations the internal equilibrium can become unstable and large amplitude periodic fluctuations arise. Several hypothesis on the mechanism causing the destabilisation of the steady-state are considered. The mechanism leading to the large amplitude fluctuations is identified and biologically interpreted.

Evaluation of the stability and quality of sleep using hjorth's descriptors

Hjorth's descriptors (NSD) (activity, mobility, and complexity) provide a useful tool for evaluating micro- and macrostructural elements of sleep. In rats, the automatic analysis of sleep recordings by means of NSD calculated from SM and Vis derivations allows different sleep stages to be discriminated. Activity distribution over the total recording permits the definition of a global effect on the EEG. Moreover, the quality of sleep can be evaluated by the variations of the SM activity distribution by considering different classes of amplitude. Index and rate of unstable amplitude segments (UAS) constitute useful parameters to analyse the stability and quality of sleep with different models of insomnia and after pharmacological treatment. The UAS in rats can be compared to CAPs in humans. The NSD are also able to define quality and stability of human sleep. EEG analysis using NSD provides a novel perspective for the analysis of the stability and quality of rat and human sleep. This microstructural analysis of sleep appears to be a useful tool for pharmaco-EEG studies.

Modeling issues for predicting sound propagation at moderate frequencies in bottom-limited sound channels

Consider sound propagation in the moderate frequency range (depth to wavelength ratio, H/λ, between 20 and 100) in shallow water environments with bottom roughness. Measurements in the Straits of Florida have shown remarkable phase stability together with rapid (minutes-to-hours) unstable amplitude fluctuations that nevertheless yield stable envelopes when averaged over many hours. What physical effects should be contained in an acoustic model in order to predict the observed behavior? It is suggested that a full-wave model that is capable of multiple rough bottom forward scattering and includes temporally slowly varying range-dependent sound-speed profiles will yield observed results, when used together with coherent signal processing techniques. A broadband PE model will illustrate the assertion, at least qualitatively. Absolute level prediction is quite another matter that requires more extensive environmental inputs.

Simplified Determination of Stability Bounds in Nonlinear Vibration Systems

Even slight nonlinearities in vibrating systems introduce instability frequency bands and unstable amplitudes. In many vibration problems it is desirable to know precisely the bounds of the instability frequencies and the associated amplitude ranges. Using a general nonlinear single degree of freedom system, based on a Coulomb friction augmented Duffing model, simplified graphical/analytical modus operandi was developed for computing singular amplitudes in the frequency domain. The method may be used in lieu of the usual phase plane approach wherein the physical meaning of the different vibration modes is obscured. In previous publications approximate estimation of instability frequency bands of the Duffing system was achieved by assuming variations about the steady state solution. The new method presented herein allows accurate determination of instability frequency ranges in a more general class of vibration systems, while quantifying “Horizontal Tangents Amplitudes,” in addition to the usual “Resonance Amplitudes” and “Vertical Tangents Amplitudes.”

Catastrophe Theory, Curve Veering and the Vibration of Bladed Discs

The problem of vibration in bladed disc assemblies is discussed in terms of catastrophe theory and the ‘curve veering’ phenomenon. A region in the bifurcation diagram of a bladed disc where unstable vibration amplitudes could occur as a result of coupling and mistumng is identified.

A class of reaction-diffusion mechanisms which preferentially select striped patterns

Reaction-diffusion systems which have reaction term satisfying f(– q =− f( q ) tend strongly to form striped patterns. Haken's slaving principle is used to derive differential equations for unstable mode amplitudes close to the Turing instability. This connects a dynamical symmetry to pattern selection, with possible relevance to biological and chemical pattern-forming phenomena.

Resonant interactions between unstable and neutral baroclinic waves in a continuous model of the atmosphere

Resonant interactions between a finite-amplitude marginally unstable wave and two neutral baroclinic waves are investigated in a quasi-geostrophic, continuous, infinite depth model on the beta-plane channel. Since the neutral waves are characterized by total horizontal wavenumbers less than that of the unstable wave, the kinematic resonant conditions can only be satisfied when the meridional scale of the unstable wave is sufficiently small. Employing asymptotic methods, equations are obtained governing the temporal evolution of the amplitudes and phases of the triad. The neutral waves are scaled smaller in magnitude than the unstable wave as a result of an asymptotic imbalance between the advective non-linearity and instability. Numerical solutions of the amplitude equations reveal a separation between the instability and interaction time scales. The neutral wave amplitudes vacillate on the longer interaction time scale. The unstable wave amplitude vacillates locally on the instability time scale while its envelope vacillates on the interaction time scale in direct proportion to the initial neutral wave amplitudes. DOI: 10.1111/j.1600-0870.1984.tb00251.x

Noise generation by a low-Mach-number jet

Using a ‘clean’ jet facility the relationship between the jet flow and its radiation field was studied experimentally in the Mach-number range 0.05 < Mj < 0.20 and a Reynolds-number range 6 × 104 < ReD < 2.3 × 105. The various acoustic source parameters such as strength, frequency and Mach number were varied systematically, and the far-field pressure measured simultaneously. On the basis of these measurements the nature of the sources in the initial shear layer could be characterized. The principal results, equally valid for unexcited and excited jets, are as follows: the acoustic sources are not convected but are located within a confined volume fixed with respect to the nozzle even though they are being generated by moving disturbances in the jet; they are associated with the nonlinear saturation of the unstable wave amplitudes of the shear layer occurring at the vortex-pairing locations; the radiation intensity varies nonlinearly with the source strength and is highly directional, exponential in character.

Stability of a detuned single mode homogeneously broadened ring laser

We study analytically the influence of detuning on the properties of a homogeneously broadened single mode ring laser. In the good cavity domain the stationary output is stable. In the bad cavity domain the stationary output becomes unstable via a Hopf bifurcation. Near line center this Hopf bifurcation is subcritical, leading to unstable small amplitude oscillations. Far from line center this Hopf bifurcation is supercritical and leads to stable small amplitude output.

Critical currents in bulk superfluidHe3-A

The stability of uniform textures in superfluid /sup 3/He-A is studied with the phenomenological equations of orbital dynamics. For a fixed applied magnetic field, the texture becomes dynamically unstable at a critical current that depends both on the field H and on the angle chi between the flow and the field. In addition, the instability signals a deformation with a finite wave vector (not, in general, parallel to l) that also depends on H and chi. Beyond thresholds, the unstable amplitude does not saturate at some nearby small deformation but instead experiences catastrophic nonlinear growth. Comparison with recent observations suggests other possible experiments.

Harmonic analysis of unsteady transonic flow

Introduction T time averaged mean flow past an airfoil oscillating harmonically at transonic speeds differs from the steady flow obtained at rest. This difference depends on oscillation frequency and amplitude and arises because both mean and disturbance flowfields interact nonlinearly. For small oscillation amplitudes a time linearized description usually suffices: the mean flow is conveniently solved without reference to the unsteady flow and the harmonic flow is solved without explicit reference to the unsteady disturbance amplitude. For larger amplitudes, however, the wave backinteraction induced by the primary disturbance on the mean flow cannot be discounted because the modified mean flow in turn affects the evolution of the harmonic flowfield. This effect may be significant because transonic flows are inherently nonlinear. Linear theory, which generally assumes small unsteady disturbance amplitudes in comparison to the overall thickness, expands the unsteady solution about the known transonic flow corresponding to the stationary airfoil. For oscillatory motions the mean flowfield is therefore defined by a simplified solution rendered independent of disturbance frequency and amplitude: the model implicitly assumes high-frequency oscillations where the mean flow and mean shock position effectively freeze in space. However, for low-frequency motions where large shock excursions are anticipated, the mean flow couples more strongly with the unsteady flow and linear theory may not apply. Thus the practical need arises for a rational harmonic formulation adaptable to unsteady transonic flutter and aeroelastic analyses yielding unstable amplitude as well as frequency boundaries. In this Note, a nonlinear harmonic approach to general unsteady oscillations in transonic flow is developed for those engineering applications where explicit amplitude and frequency information is required. The extent to which nonlinear feedback is significant is addressed, in particular, for the symmetric NACA 64A006 airfoil, unpitched, with a quarter chord oscillating flap executing large amplitude deflections in a subsonic freestream mildly to strongly supercritical. Details of the numerical algorithm are also outlined.

Nonradial m-mode changes in the 53 Persei variable 22 Orionis

The paper considers nonradial m-mode changes in the 53 Persei variable 22 Orionis. The Orionis observations reveal periodic profile variations easily modeled in terms of traveling-wave nonradial pulsations; like other members of the 53 Persei class 22 Ori exhibit unstable mode amplitudes. During the 1976-1977 seasons retrograde wave oscillations of period 4.5 and 9.0 hours were observed, but during 1978-1979 larger amplitude, prograde oscillations of period 14.1 and 22.9 hours were observed. It is suggested that this retrograde to prograde change is explained by the nonlinear coupling of two sectorial modes to a third, standing wave mode.

The role of proton injection processes in the nonlinear evolution of “pearls”

Given a constant number of resonant protons in a field tube the unstable wave amplitude reaches a steady value rapidly due to nonlinear effects. Observations show that the pearl amplitudes grow gradually for a long time. Consistency with observations is obtained by taking into account the processes of proton injection.

繰り返し載荷を受ける H 形鋼はりの復元力特性 : その 2・ランダム変位履歴における耐力の低下

In the preceding report, Part I, the following discussion was stated : When H-shaped steel beams are subjected to cyclic and reversed loadings with constant deflection amplitudes, load deflection hysteresis loops are stable within a certain critical deflection amplidute, while they become unstable beyond that deflection. However, the stationary hysteresis loops are again obtained, if the deflection amplitudes are reduced to within the critical one, even after the beams are damaged to deteriorate the strength. If the strength deterioration of the beams subjected to random deflections can be predicted from the results of the constant deflection amplitude tests, it is thought to be one of clues to prediction for failure of beams during an earthquake. Accordingly, in this paper how the strength of beams deteriorates due to various ratios of deflection amplitudes in the unstable deflection amplitude region is examined, and, based on those data, how to evaluate the strength deterioration of the beams subjected to random deflections is shown.

Equilibrium and Stability of Large-Amplitude Magnetic Bernstein-Greene-Kruskal Waves

The stability of transverse magnetic Bernstein-Greene-Kruskal waves to small-amplitude perturbations is analyzed within the framework of the Vlasov-Maxwell equations. The Vlasov-Maxwell equations are linearized about an equilibrium state which supports (self-consistently) a spatially-periodic finite-amplitude transverse electromagnetic wave. An external magnetic field, B0 = B0êz, is included in the analysis, and spatial variations in equilibrium and perturbed quantities are taken to be in the z direction. A matrix dispersion relation is obtained that relates the (complex) oscillation frequency ω and wavenumber k of the perturbation; stability criteria are obtained for a monochromatic circularly polarized equilibrium wave. As an example, a trapped electron distribution is considered which is isotropic and monoenergetic in the plane perpendicular to the propagation direction of the equilibrium wave, and cold parallel to the propagation direction. The ions are assumed to form a cold neutralizing background. The system is found to be stable to transverse electromagnetic perturbations provided the equilibrium wave amplitude exceeds a certain threshold. The condition for stability is ω¯Be≳γκ where ω¯Be is the magnetic bounce frequency for trapped electrons, and γκ is the linear growth rate in the absence of the equilibrium wave. The results of the stability analysis are consistent with recent computer simulation experiments; for a broad class of transverse electromagnetic instabilities in anisotropic plasmas, these experiments (carried out both for B0=0 and B0≠0) show that the linearly unstable field amplitudes saturate once ω¯Be has increased to a value comparable to γκ.

Galloping Oscillations of Prismatic Structures

Galloping oscillations can arise above a certain onset wind velocity with lateral force coefficient A 1 > 0 (unstable cross sections) and also at A 1 ≤ 0 (stable cross sections). In the latter case, an initial disturbance is also necessary to trigger the vibrations. This triggering disturbance must be larger than the unstable amplitude, proportional to structural damping, and in some cases must be able to decrease with increasing wind velocity. The onset velocities are higher with A 1 ≤ 0 and are directly proportional to structural damping in all cases. Turbulence can drastically change the aeroelastic stability of prismatic bodies. With rectangular cross sections of 2/1 the tendency to galloping instability from zero position decreases with increasing turbulence intensity and can vanish at intensities of 8% or so. On the contrary, prisms of 1/2, stable in the smooth flow, can become unstable in the turbulent flow and their tendency to galloping oscillations increases with turbulence intensity.

Dynamic Stabilization of the m = 1 Instability in a Bumpy Theta Pinch

Both theoretically and experimentally a bumpy theta pinch is known to be hydromagnetically unstable. The possibility of dynamic stabilization of this configuration is discussed. The results show that stability can be achieved in this way. The plasma column is assumed to be separated from a vacuum magnetic field by a sharp boundary. The analysis is based on a generalization of the hydromagnetic energy principle. Within the framework of this theory a sufficient condition for stability is obtained for the m = 1 mode. This condition contains the amplitude of the unstable bulge, the frequency and amplitude of the forced oscillations, and the characteristic lengths and speeds in the system. The condition shows that stability is obtained for sufficiently large amplitude in the oscillatory magnetic field. The case of β = 1 and “arbitrary” m numbers is also briefly reviewed.