A Nonlinear System Under Combined Periodic and Random Excitation

The anharmonic oscillator under combined sinusoidal and white noise excitation is studied using the Gaussian closure approximation. The mean response and the steady-state variance of the system is obtained by the WKBJ approximation and also by the Fokker Planck equation. The multiple steadystate solutions are obtained and their stability analysis is presented. Numerical results are obtained for a particular set of system parameters. The theoretical results are compared with a digital simulation study to bring out the usefulness of the present approximate theory.

Tipping points: Teachers' reported reasons for referring primary school children for excessive anxiety

The current study explored the reasons that primary school teachers reported were tipping points for them in deciding whether or not and when to refer a child to the school student support team for excessive anxiety. Twenty teachers in two Queensland primary schools were interviewed. Content analysis of interview transcripts revealed six themes reflecting teachers' perceived reasons for deciding to refer anxious children: 1)impact on learning; 2)atypical child behavior; 3)repeated difficulties that do not improve over time; 4)poor response to strategies; 5)teachers' need for support; and 6)information from parents/carers. Teachers considered different combinations of reasons, and had many different tipping points for making a referral. Both teacher-and system-level influences impacted referral decisions. Implications and future research are discussed.

Some mechanisms of excitation of a railway wheel

Railway wheel vibrations are caused by a number of mechanisms. Two of these are considered: (a) gravitational load reaction acting on different points of the wheel rim, as the wheel rolls on, and (b) random fluctuating forces generated at the contact patch by roughness on the mating surfaces of the wheel and rail. The wheel is idealized as a thin ring, and the analysis is limited to a single wheel rolling on a rail. It is shown that the first mechanism results in a stationary pattern of vibration, which would not radiate any sound. The acceleration caused by roughness-excited forces is much higher at higher frequencies, but is of the same order as that caused by load reaction at lower frequencies. The computed acceleration level (and hence the radiated SPL) caused by roughness is comparable with the observed values, and is seen to increase by about 10 dB for a doubling of the wagon speed. The driving point impedance of the periodic rail-sleeper system at the contact patch, which is used in the analysis, is derived in a companion paper.

Continuation of limit cycles near saddle homoclinic points using splines in phase space

We present a new algorithm for continuation of limit cycles of autonomous systems as a system parameter is varied. The algorithm works in phase space with an ordered set of points on the limit cycle, along with spline interpolation. Currently popular algorithms in bifurcation analysis packages compute time-domain approximations of limit cycles using either shooting or collocation. The present approach seems useful for continuation near saddle homoclinic points, where it encounters a corner while time-domain methods essentially encounter a discontinuity (a relatively short period of rapid variation). Other phase space-based algorithms use rescaled arclength in place of time, but subsequently resemble the time-domain methods. Compared to these, we introduce additional freedom through a variable stretching of arclength based on local curvature, through the use of an auxiliary index-based variable. Several numerical examples are presented. Comparisons with results from the popular package, MATCONT, are favorable close to saddle homoclinic points.

Sustaining productivity of tropical red snappers using new monitoring and reference points

OBJECTIVES: 1. Analyse current monitoring and logbook data sets, as well as survey and other information,to establish whether these data provide sufficient power to develop critical indicators of fishery performance. 2. Provide a risk analysis that examines the use of age structure and catch rate information for development of critical indicators, and response rules for those criteria, in the absence of other fishery information. 3. Develop a monitoring program that uses commercial vessels from the fishery to provide independent data.

Periodic Rayleigh waves of finite amplitude on an isotropic solid

Existence of a periodic progressive wave solution to the nonlinear boundary value problem for Rayleigh surface waves of finite amplitude is demonstrated using an extension of the method of strained coordinates. The solution, obtained as a second-order perturbation of the linearized monochromatic Rayleigh wave solution, contains harmonics of all orders of the fundamental frequency. It is shown that the higher harmonic content of the wave increases with amplitude, but the slope of the waveform remains finite so long as the amplitude is less than a critical value.

A new method for generation of quasi-periodic structures withn fold axes: Application to five and seven folds

A new geometrical method for generating aperiodic lattices forn-fold non-crystallographic axes is described. The method is based on the self-similarity principle. It makes use of the principles of gnomons to divide the basic triangle of a regular polygon of 2n sides to appropriate isosceles triangles and to generate a minimum set of rhombi required to fill that polygon. The method is applicable to anyn-fold noncrystallographic axis. It is first shown how these regular polygons can be obtained and how these can be used to generate aperiodic structures. In particular, the application of this method to the cases of five-fold and seven-fold axes is discussed. The present method indicates that the recursion rule used by others earlier is a restricted one and that several aperiodic lattices with five fold symmetry could be generated. It is also shown how a limited array of approximately square cells with large dimensions could be detected in a quasi lattice and these are compared with the unit cell dimensions of MnAl6 suggested by Pauling. In addition, the recursion rule for sub-dividing the three basic rhombi of seven-fold structure was obtained and the aperiodic lattice thus generated is also shown.

Sequence generator for periodic sampling of transient phenomena

A simple instrument that can provide a sequence of timed pulses for first initiating a transient process and then enabling sampling and recording periodically during the course of the transient event is described. The time delay between the first of these sampling pulses and the start of the transient event is adjustable. This sequence generator has additional features that make it ideal for use in acquiring the waveforms when a storage oscilloscope is used as the recording device. For avoiding the clutter caused by many waveforms being recorded at the same place on an oscilloscope screen such features as displacements of waveforms in the X and Y directions and trace blanking at places where the waveform is not required, have been incorporated. This sequence generator has been employed to acquire a sequence of Raman scattered radiation signals from an adiabatically expanding saturated vapour probed by a flashlamp-pumped dye laser.

Principles and guidelines for managing cattle grazing in the grazing lands of northern Australia: stocking rates, pasture resting, prescribed fire, paddock size and water points - a review

Beef cattle grazing is the dominant land use in the extensive tropical and sub-tropical rangelands of northern Australia. Despite the considerable knowledge on land and herd management gained from both research and practical experience, the adoption of improved management is limited by an inability to predict how changes in practices and combinations of practices will affect cattle production, economic returns and resource condition. To address these issues, past Australian and international research relating to four management factors that affect productivity and resource condition was reviewed in order to identify key management principles. The four management factors considered were stocking rates, pasture resting, prescribed fire, and fencing and water point development for managing grazing distribution. Four management principles for sound grazing management in northern Australia were formulated as follows: (1) manage stocking rates to meet goals for livestock production and land condition; (2) rest pastures to maintain them in good condition or to restore them from poor condition to increase pasture productivity; (3) devise and apply fire regimes that enhance the condition of grazing land and livestock productivity while minimising undesirable impacts; and (4) use fencing and water points to manipulate grazing distribution. Each principle is supported by several more specific guidelines. These principles and guidelines, and the supporting research on which they are based, are presented.

Sustainable grazing management for temporal and spatial variability in north Australian rangelands – a synthesis of the latest evidence and recommendations

Rainfall variability is a major challenge to sustainable grazing management in northern Australia, with management often complicated further by large, spatially-heterogeneous paddocks. This paper presents the latest grazing research and associated bio-economic modelling from northern Australia and assesses the extent to which current recommendations to manage for these issues are supported. Overall, stocking around the safe long-term carrying capacity will maintain land condition and maximise long-term profitability. However, stocking rates should be varied in a risk-averse manner as pasture availability varies between years. Periodic wet-season spelling is also essential to maintain pasture condition and allow recovery of overgrazed areas. Uneven grazing distributions can be partially managed through fencing, providing additional water-points and in some cases patch-burning, although the economics of infrastructure development are extremely context-dependent. Overall, complex multi-paddock grazing systems do not appear justified in northern Australia. Provided the key management principles outlined above are applied in an active, adaptive manner, acceptable economic and environmental outcomes will be achieved irrespective of the grazing system applied.

Vibrations of a periodic rail-sleeper system excited by an oscillating stationary transverse force

The rail-sleeper system is idealized as an infinite, periodic beam-mass system. Use is made of the periodicity principle for the semi-infinite halves on either side of the forcing point for evaluation of the wave propagation constants and the corresponding modal vectors. It is shown that the spread of acceleration away from the forcing point depends primarily upon one of the wave propagation constants. However, all the four modal vectors (two for the left-hand side and two for the right-hand side) determine the driving point impedance of the rail-sleeper system, which in combination with the driving point impedance of the wheel (which is adopted from the preceding companion paper) determines the forces generated by combined surface roughness and the resultant accelerations. The compound one-third octave acceleration levels generated by typical roughness spectra are generally of the same order as the observed levels.

Periodic oscillations in feedback systems with combined pulse modulation

This paper presents a systematic method of investigating the existence of limit cycle oscillations in feedback systems with combined integral pulse frequency-pulse width (IPF-P/V) modulation. The method is based on the non-linear discrete equivalence of the continuous feedback system containing the IPF-PW modulator.

On the stability of a nonlinear system with periodic coefficients

A quasi-geometric stability criterion for feedback systems with a linear time invariant forward block and a periodically time varying nonlinear gain in the feedback loop is developed.