Random vibration response statistics for fatigue analysis of nonlinear structures

Statistical analysis methods are developed for determining fatigue time to failure for nonlinear structures when subjected to random loading. The change in the response, as structures progress from a linear regime to a large amplitude nonlinear regime, is studied in both the time and frequency domains. The analyses in the two domains are shown to compliment each other, allowing keen understanding of the physical fundamentals of the problem. Analysis of experimental random vibration data, obtained at Wright Patterson Air Force Base, is included to illustrate the challenge for a real, multi-mode, nonlinear structure. The reverse path frequency response identification method was used with the displacement and strain response to estimate nonlinear frequency response functions. The coherence functions of these estimates provided insight into nonlinear models of the system. Time domain analysis of the nonlinear data showed how the displacement and strain departed from a normal distribution. Inverse distribution function methods were used to develop functions that related the linear to the nonlinear response of the structure. These linear to the nonlinear functions were subsequently used to estimate probability density functions that agreed well with measured histograms. Numerical simulations of a nonlinear single degree of freedom system were produced to study other aspects of the large deflection structural response. Very large sample size data sets of displacement, velocity, acceleration and stress were used to quantify the rate of convergence of several random response statistics. The inverse distribution function method was also applied to the simulation results to estimate normal and peak linear to nonlinear functions. These functions were shown to be useful for probability density function estimates and for estimating rates of response zero crossings. Fatigue analysis was performed on the experimental and simulated linear and nonlinear data. The time to failure estimates for the nonlinear results was shown to increase dramatically when compared to the linear results. The nonlinear stresses have significant positive mean values due to membrane effects, that when used with fatigue equations that account for mean stresses, show reductions in time to failure. Further studies of the nonlinear increase in the frequency of stress response are included in the fatigue analysi

The rheology of solid glass

As the glass transition is approached from the high temperature side, viewed as a liquid, the properties of the ever more viscous supercooled liquid are continuous functions of temperature and pressure. The point at which we decide to classify the fluid as a solid is therefore subjective. This subjective decision does, however, have discontinuous consequences for how we determine the rheological properties of the glass. We apply the recently discovered relaxation theorem to the time independent, nondissipative, nonergodic glassy state to derive an expression for the phase space distribution of an ensemble of glass samples. This distribution is then used to construct a time dependent linear response theory for aged glassysolids. The theory is verified using molecular dynamics simulations of oscillatory shear for a realistic model glass former with excellent agreement being obtained between the response theory calculations and direct nonequilibrium molecular dynamics calculations. Our numerical results confirm that unlike all the fluid states, including supercooled liquids, a solidglass (in common with crystalline states) has a nonzero value for the zero frequency shear modulus. Of all the states of matter, a supercooled fluid approaching the glass transition has the highest value for the limiting zero frequency shear viscosity. Finally, solidglasses like dilute gases and crystals have a positive temperature coefficient for the shear viscosity whereas supercooled and normal liquids have a negative temperature coefficient.We thank the National Computational Infrastructure NCI for computational facilities and the Australian Research Council ARC for funding

Assessing the Influence of Temporal Autocorrelations on the Population Dynamics of a Disturbance Specialist Plant Population in a Random Environment

Biological populations are strongly influenced by random variations in their environment, which are often autocorrelated in time. For disturbance specialist plant populations, the frequency and intensity of environmental stochasticity (via disturbances) can drive the qualitative nature of their population dynamics. In this article, we extended our earlier model to explore the effect of temporally autocorrelated disturbances on population persistence. In our earlier work, we only assumed disturbances were independent and identically distributed in time. We proved that the plant seed bank population converges in distribution, and we showed that the mean and variance in seed bank population size were both increasing functions of the autocorrelation coefficient for all parameter values considered, but the interplay between increasing population size and increasing variability caused interesting relationships between quasi-extinction probability and autocorrelation. For example, for populations with low seed survival, fecundity, and disturbance frequency, increasingly positive autocorrelated disturbances decreased quasi-extinction probability. Higher disturbance frequency coupled with low seed survival and fecundity caused a nonmontone relationship between autocorrelation and quasi-extinction, where increasingly positive autocorrelations eventually caused an increase in quasi-extinction probability. For higher seed survival, fecundity, and/ or disturbance frequency, quasi-extinction probability was generally a monotonically increasing function of the autocorrelation coefficient

Modeling stretched solitary waves along magnetic field lines

International audienceA model is presented for a new type of fast solitary waves which is observed in downward current regions of the auroral zone. The three-dimensional, coherent structures are electrostatic, have a positive potential, and move along the magnetic field lines with speeds on the order of the electron drift. Their parallel potential profile is flattened and cannot fit to the Gaussian shape used in previous work. We develop a detailed BGK model which includes a flattened potential and an assumed cylindrical symmetry around a centric magnetic field line. The model envisions concentric shells of trapped electrons slowly drifting azimuthally while bouncing back and forth in the parallel direction. The electron dynamics is analysed in terms of three basic motions that occur on different time scales characterized by the cyclotron frequency We , the bounce frequency wb , and the azimuthal drift frequency wg. The ordering We >> wb >> wg is required. Self-consistent distribution functions are calculated in terms of approximate constants of motion. Constraints on the parameters characterizing the amplitude and shape of the stretched solitary wave are discussed

General relativistic modelling of the negative reverberation X-ray time delays in AGN

We present the first systematic physical modelling of the time-lag spectra between the soft (0.3-1 keV) and the hard (1.5-4 keV) X-ray energy bands, as a function of Fourier frequency, in a sample of 12 active galactic nuclei which have been observed by XMM-Newton. We concentrate particularly on the negative X-ray time-lags (typically seen above $10^{-4}$ Hz) i.e. soft band variations lag the hard band variations, and we assume that they are produced by reprocessing and reflection by the accretion disc within a lamp-post X-ray source geometry. We also assume that the response of the accretion disc, in the soft X-ray bands, is adequately described by the response in the neutral iron line (Fe k$\alpha$) at 6.4 keV for which we use fully general relativistic ray-tracing simulations to determine its time evolution. These response functions, and thus the corresponding time-lag spectra, yield much more realistic results than the commonly-used, but erroneous, top-hat models. Additionally we parametrize the positive part of the time-lag spectra (typically seen below $10^{-4}$ Hz) by a power-law. We find that the best-fitting BH masses, M, agree quite well with those derived by other methods, thus providing us with a new tool for BH mass determination. We find no evidence for any correlation between M and the BH spin parameter, $\alpha$, the viewing angle, $\theta$, or the height of the X-ray source above the disc, $h$. Also on average, the X-ray source lies only around 3.7 gravitational radii above the accretion disc and the viewing angles are distributed uniformly between 20 and 60 degrees. Finally, there is a tentative indication that the distribution of spin parameters may be bimodal above and below 0.62.Comment: Accepted for publication in MNRAS. The paper is 22 pages long and contains 19 figures and 2 table