Study of the random vibration of nonlinear systems by the Gaussian closure technique

A technique is developed to study random vibration of nonlinear systems. The method is based on the assumption that the joint probability density function of the response variables and input variables is Gaussian. It is shown that this method is more general than the statistical linearization technique in that it can handle non-Gaussian excitations and amplitude-limited responses. As an example a bilinear hysteretic system under white noise excitation is analyzed. The prediction of various response statistics by this technique is in good agreement with other available results.

Superharmonic vibrations of order 3 in stretched strings

Superharmonic vibrations of order 3 in stretched strings driven by a single-mode planar simple-harmonic force are investigated. It is shown that planar as well as nonplanar superharmonic resonances can occur. After giving a few analytical results, the problem is thoroughly investigated numerically. The stability analysis shows that the region of stable nonplanar oscillations is much smaller than that of stable planar oscillation. It is observed in the case of nonplanar oscillations that the amplitude of the superharmonic in the plane normal to the plane of excitation is larger than that in the plane of excitation.

On methods of calculating successive positions of a shock front

In this paper we have discussed limits of the validity of Whitham's characteristic rule for finding successive positions of a shock in one space dimension. We start with an example for which the exact solution is known and show that the characteristic rule gives correct result only if the state behind the shock is uniform. Then we take the gas dynamic equations in two cases: one of a shock propagating through a stratified layer and other down a nonuniform tube and derive exact equations for the evolution of the shock amplitude along a shock path. These exact results are then compared with the results obtained by the characteristic rule. The characteristic rule not only incorrectly accounts for the deviation of the state behind the shock from a uniform state but also gives a coefficient in the equation which differ significantly from the exact coefficients for a wide range of values of the shock strength.

Phase-shift randomness in one-dimensional disordered conductors in the quasi-metallic domain

An invariant imbedding method yields exact analytical results for the distribution of the phase theta (L) of the reflection amplitude and for low-order resistance moments (pn) for a disordered conductor of length L in the quasi-metallic regime L<

Parametrized tests of post-Newtonian theory using Advanced LIGO and Einstein Telescope

General relativity has very specific predictions for the gravitational waveforms from inspiralling compact binaries obtained using the post-Newtonian (PN) approximation. We investigate the extent to which the measurement of the PN coefficients, possible with the second generation gravitational-wave detectors such as the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) and the third generation gravitational-wave detectors such as the Einstein Telescope (ET), could be used to test post-Newtonian theory and to put bounds on a subclass of parametrized-post-Einstein theories which differ from general relativity in a parametrized sense. We demonstrate this possibility by employing the best inspiralling waveform model for nonspinning compact binaries which is 3.5PN accurate in phase and 3PN in amplitude. Within the class of theories considered, Advanced LIGO can test the theory at 1.5PN and thus the leading tail term. Future observations of stellar mass black hole binaries by ET can test the consistency between the various PN coefficients in the gravitational-wave phasing over the mass range of 11-44M(circle dot). The choice of the lower frequency cutoff is important for testing post-Newtonian theory using the ET. The bias in the test arising from the assumption of nonspinning binaries is indicated.

Resistance fluctuations, phase randomness and noise in one-dimensional conductors with a long-range correlated potential

When the size (L) of a one-dimensional metallic conductor is less than the correlation length λ-1 of the Gaussian random potential, one expects transport properties to show ballistic behaviour. Using an invariant imbedding method, we study the exact distribution of the resistance, of the phase θ of the reflection amplitude of an incident electron of wave number k0, and of dθ/dk0, for λL ll 1. The resistance is non-self-averaging and the n-th resistance moment varies periodically as (1 - cos 2k0L)n. The charge fluctuation noise, determined by the distribution of dθ/dk0, is constant at low frequencies.

Total risk rating and stability analysis of embankment dams in the Kachchh Region, Gujarat, India

A method for total risk analysis of embankment dams under earthquake conditions is discussed and applied to the selected embankment dams, i.e., Chang, Tapar, Rudramata, and Kaswati located in the Kachchh region of Gujarat, India, to obtain the seismic hazard rating of the dam site and the risk rating of the structures. Based on the results of the total risk analysis of the dams, coupled non-linear dynamic numerical analyses of the dam sections are performed using acceleration time history record of the Bhuj (India) earthquake as well as five other major earthquakes recorded worldwide. The objective of doing so is to perform the numerical analysis of the dams for the range of amplitude, frequency content and time duration of input motions. The deformations calculated from the numerical analyses are also compared with other approaches available in literature, viz, Makdisi and Seed (1978) approach, Jansen's approach (1990), Swaisgood's method (1995), Bureau's method (1997). Singh et al. approach (2007), and Saygili and Rathje approach (2008) and the results are utilized to foresee the stability of dams in future earthquake scenario. (C) 2010 Elsevier B.V. All rights reserved.

Occupational chronic solvent encephalopathy in Finland 1995 - 2007 : incidence and diagnostic methods

The occurrence of occupational chronic solvent encephalopathy (CSE) seems to decrease, but still every year reveals new cases. To prevent CSE and early retirement of solvent-exposed workers, actions should focus on early CSE detection and diagnosis. Identifying the work tasks and solvent exposure associated with high risk for CSE is crucial. Clinical and exposure data of all the 128 cases diagnosed with CSE as an occupational disease in Finland during 1995-2007 was collected from the patient records at the Finnish Institute of Occupational Health (FIOH) in Helsinki. The data on the number of exposed workers in Finland were gathered from the Finnish Job-exposure Matrix (FINJEM) and the number of employed from the national workforce survey. We analyzed the work tasks and solvent exposure of CSE patients and the findings in brain magnetic resonance imaging (MRI), quantitative electroencephalography (QEEG), and event-related potentials (ERP). The annual number of new cases diminished from 18 to 3, and the incidence of CSE decreased from 8.6 to 1.2 / million employed per year. The highest incidence of CSE was in workers with their main exposure to aromatic hydrocarbons; during 1995-2006 the incidence decreased from 1.2 to 0.3 / 1 000 exposed workers per year. The work tasks with the highest incidence of CSE were floor layers and lacquerers, wooden surface finishers, and industrial, metal, or car painters. Among 71 CSE patients, brain MRI revealed atrophy or white matter hyperintensities or both in 38% of the cases. Atrophy which was associated with duration of exposure was most frequently located in the cerebellum and in the frontal or parietal brain areas. QEEG in a group of 47 patients revealed increased power of the theta band in the frontal brain area. In a group of 86 patients, the P300 amplitude of auditory ERP was decreased, but at individual level, all the amplitude values were classified as normal. In 11 CSE patients and 13 age-matched controls, ERP elicited by a multimodal paradigm including an auditory, a visual detection, and a recognition memory task under single and dual-task conditions corroborated the decrease of auditory P300 amplitude in CSE patients in single-task condition. In dual-task conditions, the auditory P300 component was, more often in patients than in controls, unrecognizable. Due to the paucity and non-specificity of the findings, brain MRI serves mainly for differential diagnostics in CSE. QEEG and auditory P300 are insensitive at individual level and not useful in the clinical diagnostics of CSE. A multimodal ERP paradigm may, however, provide a more sensitive method to diagnose slight cognitive disturbances such as CSE.

The behaviour of excited plane jets

A plane subsonic jet can be excited to entrain more fluid from its surroundings by subjecting it to antisymmetric periodic disturbances. The essential feature in this phenomenon is the rolling-up motion of an initially flapping jet to form large vortices which are responsible for greater entrainment. Several methods developed to impart oscillations to the flow at the nozzle, such as the acoustic pressure oscillator, the vibration of a single vane in the potential core region, the reciprocating lip system and the twin vane exciter, are described in this article. A minimum threshold in amplitude is necessary for exciting the flow. However, the frequency of oscillation is much less than that predicted by stability considerations.

Analysis of EXAFS data of complex systems

Analysis of EXAFS data of complex systems containing more than one phase and one type of coordination, has been discussed. It is shown that a modified treatment of EXAFS function as well as the amplitude ratio plots provide useful means of obtaining valuable structural information. The systems investigated are: biphasic Ni+NiO mixture, NiAl2O4 with two coordinations for Ni, NiO+NiAl2O4 mixture, CoS+CoO system and Ni dispersed on Al2O3. The results obtained with these systems have been most satisfactory and serve to illustrate the utility and the applicability of the innovations described in this paper.

Nonadiabatic charge pumping by oscillating potentials in one dimension: Results for infinite system and finite ring

We study charge pumping when a combination of static potentials and potentials oscillating with a time period T is applied in a one-dimensional system of noninteracting electrons. We consider both an infinite system using the Dirac equation in the continuum approximation and a periodic ring with a finite number of sites using the tight-binding model. The infinite system is taken to be coupled to reservoirs on the two sides which are at the same chemical potential and temperature. We consider a model in which oscillating potentials help the electrons to access a transmission resonance produced by the static potentials and show that nonadiabatic pumping violates the simple sin phi rule which is obeyed by adiabatic two-site pumping. For the ring, we do not introduce any reservoirs, and we present a method for calculating the current averaged over an infinite time using the time evolution operator U(T) assuming a purely Hamiltonian evolution. We analytically show that the averaged current is zero if the Hamiltonian is real and time-reversal invariant. Numerical studies indicate another interesting result, namely, that the integrated current is zero for any time dependence of the potential if it is applied to only one site. Finally we study the effects of pumping at two sites on a ring at resonant and nonresonant frequencies, and show that the pumped current has different dependences on the pumping amplitude in the two cases.

ADC Static Characterization Using Nonlinear Ramp Signal

Static characteristics of an analog-to-digital converter (ADC) can be directly determined from the histogram-based quasi-static approach by measuring the ADC output when excited by an ideal ramp/triangular signal of sufficiently low frequency. This approach requires only a fraction of time compared to the conventional dc voltage test, is straightforward, is easy to implement, and, in principle, is an accepted method as per the revised IEEE 1057. However, the only drawback is that ramp signal sources are not ideal. Thus, the nonlinearity present in the ramp signal gets superimposed on the measured ADC characteristics, which renders them, as such, unusable. In recent years, some solutions have been proposed to alleviate this problem by devising means to eliminate the contribution of signal source nonlinearity. Alternatively, a straightforward step would be to get rid of the ramp signal nonlinearity before it is applied to the ADC. Driven by this logic, this paper describes a simple method about using a nonlinear ramp signal, but yet causing little influence on the measured ADC static characteristics. Such a thing is possible because even in a nonideal ramp, there exist regions or segments that are nearly linear. Therefore, the task, essentially, is to identify these near-linear regions in a given source and employ them to test the ADC, with a suitable amplitude to match the ADC full-scale voltage range. Implementation of this method reveals that a significant reduction in the influence of source nonlinearity can be achieved. Simulation and experimental results on 8- and 10-bit ADCs are presented to demonstrate its applicability.

Effect of soil preparation of boreal spruce forest on air and soil temperature conditions in forest regeneration areas.

The effect of scarification, ploughing and cross-directional plouhing on temperature conditions in the soil and adjacent air layer have been studied during 11 consecutive growth periods by using an unprepared clear-cut area as a control site. The maximum and minimum temperatures were measured daily in the summer months, and other temperature observations were made at four-hour intervals by means of a Grant measuring instrument. The development of the seedling stand was also followed in order to determine its shading effect on the soil surface. Soil preparation decreased the daily temperature amplitude of the air at the height of 10 cm. The maximum temperatures on sunny days were lower in the tilts of the ploughed and in the humps of the cross-directional ploughed sites compared with the unprepared area. Correspondingly, the night temperatures were higher and so the soil preparation considerably reduced the risk of night frost. In the soil at the depth of 5 cm, soil preparation increased daytime temperatures and reduced night temperatures compared with unprepared area. The maximum increase in monthly mean temperatures was almost 5 °C, and the daily variation in the surface parts of the tilts and humps increased so that excessively high temperatures for the optimal growth of the root system were measured from time to time. The temperature also rose at the depths of 50 and 100 cm. Soil preparation also increased the cumulative temperature sum. The highest sums accumulated during the summer months were recorded at the depth of 5 cm in the humps of cross-directional ploughed area (1127 dd.) and in the tilts of the ploughed area (1106 dd.), while the corresponding figure in the unprepared soil was 718 dd. At the height of 10 cm the highest temperature sum was 1020 dd. in the hump, the corresponding figure in the unprepared area being 925 dd. The incidence of high temperature amplitudes and percentage of high temperatures at the depth of 5 cm decreased most rapidly in the humps of cross-directional ploughed area and in the ploughing tilts towards the end of the measurement period. The decrease was attributed principally to the compressing of tilts, the ground vegetation succession and the growth of seedlings. The mean summer temperature in the unprepared area was lower than in the prepared area and the difference did not diminish during the period studied. The increase in temperature brought about by soil preparation thus lasts at least more than 10 years.

The Skill of ECMWF Medium-Range Forecasts during the Year of Tropical Convection 2008

This study uses the European Centre for Medium-Range Weather Forecasts (ECMWF) model-generated high-resolution 10-day-long predictions for the Year of Tropical Convection (YOTC) 2008. Precipitation forecast skills of the model over the tropics are evaluated against the Tropical Rainfall Measuring Mission (TRMM) estimates. It has been shown that the model was able to capture the monthly to seasonal mean features of tropical convection reasonably. Northward propagation of convective bands over the Bay of Bengal was also forecasted realistically up to 5 days in advance, including the onset phase of the monsoon during the first half of June 2008. However, large errors exist in the daily datasets especially for longer lead times over smaller domains. For shorter lead times (less than 4-5 days), forecast errors are much smaller over the oceans than over land. Moreover, the rate of increase of errors with lead time is rapid over the oceans and is confined to the regions where observed precipitation shows large day-to-day variability. It has been shown that this rapid growth of errors over the oceans is related to the spatial pattern of near-surface air temperature. This is probably due to the one-way air-sea interaction in the atmosphere-only model used for forecasting. While the prescribed surface temperature over the oceans remain realistic at shorter lead times, the pattern and hence the gradient of the surface temperature is not altered with change in atmospheric parameters at longer lead times. It has also been shown that the ECMWF model had considerable difficulties in forecasting very low and very heavy intensity of precipitation over South Asia. The model has too few grids with ``zero'' precipitation and heavy (>40 mm day(-1)) precipitation. On the other hand, drizzle-like precipitation is too frequent in the model compared to that in the TRMM datasets. Further analysis shows that a major source of error in the ECMWF precipitation forecasts is the diurnal cycle over the South Asian monsoon region. The peak intensity of precipitation in the model forecasts over land (ocean) appear about 6 (9) h earlier than that in the observations. Moreover, the amplitude of the diurnal cycle is much higher in the model forecasts compared to that in the TRMM estimates. It has been seen that the phase error of the diurnal cycle increases with forecast lead time. The error in monthly mean 3-hourly precipitation forecasts is about 2-4 times of the error in the daily mean datasets. Thus, effort should be given to improve the phase and amplitude forecast of the diurnal cycle of precipitation from the model.

Modelling, Design and Analysis of Low Frequency Platform for Attenuating Micro-Vibration in Spacecraft

One of the most important factors that affect the pointing of precision payloads and devices in space platforms is the vibration generated due to static and dynamic unbalanced forces of rotary equipments placed in the neighborhood of payload. Generally, such disturbances are of low amplitude, less than 1 kHz, and are termed as ‘micro-vibrations’. Due to low damping in the space structure, these vibrations have long decay time and they degrade the performance of payload. This paper addresses the design, modeling and analysis of a low frequency space frame platform for passive and active attenuation of micro-vibrations. This flexible platform has been designed to act as a mount for devices like reaction wheels, and consists of four folded continuous beams arranged in three dimensions. Frequency and response analysis have been carried out by varying the number of folds, and thickness of vertical beam. Results show that lower frequencies can be achieved by increasing the number of folds and by decreasing the thickness of the blade. In addition, active vibration control is studied by incorporating piezoelectric actuators and sensors in the dynamic model. It is shown using simulation that a control strategy using optimal control is effective for vibration suppression under a wide variety of loading conditions.