Stability analysis of stochastically parametered nonconservative columns

Nonconservatively loaded columns. which have stochastically distributed material property values and stochastic loadings in space are considered. Young's modulus and mass density are treated to constitute random fields. The support stiffness coefficient and tip follower load are considered to be random variables. The fluctuations of external and distributed loadings are considered to constitute a random field. The variational formulation is adopted to get the differential equation and boundary conditions. The non self-adjoint operators are used at the boundary of the regularity domain. The statistics of vibration frequencies and modes are obtained using the standard perturbation method, by treating the fluctuations to be stochastic perturbations. Linear dependence of vibration and stability parameters over property value fluctuations and loading fluctuations are assumed. Bounds for the statistics of vibration frequencies are obtained. The critical load is first evaluated for the averaged problem and the corresponding eigenvalue statistics are sought. Then, the frequency equation is employed to transform the eigenvalue statistics to critical load statistics. Specialization of the general procedure to Beck, Leipholz and Pfluger columns is carried out. For Pfluger column, nonlinear transformations are avoided by directly expressing the critical load statistics in terms of input variable statistics.

Appraisal of Bishop's method of slope stability analysis

The stability of slopes is a major problem in geotechnical engineering. Of the methods available for the analysis of soil slopes such as limit equilibrium methods, limit analysis and numerical methods such as FEM and FDM, limit equilibrium methods are popular and generally used, owing to their simplicity in formulation and in evaluating the overall factor of safety of slope. However limit equilibrium methods possess certain disadvantages. They do not consider whether the slope is an embankment or natural slope or an excavation and ignore the effect of incremental construction, initial stress, stress strain behavior etc. In the work reported in this paper, a comparative study of actual state of stress and actual factor of safety and Bishop's factor of safety is performed. The actual factor of safety is obtained by consideration of contours of mobilised shear strains. Using Bishop's method of slices, the critical slip surfaces of a number of soil slopes with different geometries are determined and both the factors of safety are obtained. The actual normal stresses and shear stresses are determined from finite difference formulation using FLAG (Fast Lagrangian Analysis of Continuaa) with Mohr-Coulomb model. The comparative study is performed in terms of parameter lambda(c phi) (= gamma H tan phi/c). I is shown that actual factor of safety is higher than Bishop's factor of safety depending on slope angle and lambda(c phi).

Pseudo-Static and Pseudo-Dynamic Stability Analysis of Tailings Dam Under Seismic Conditions

In this paper the seismic slope stability analyses are performed for a typical section of 44 m high water retention type tailings earthen dam located in the eastern part of India, using both the conventional pseudo-static and recent pseudo-dynamic methods. The tailings earthen dam is analyzed for different upstream conditions of reservoir like filled up with compacted and non-compacted dumped waste materials with different water levels of the pond tailings portion. Phreatic surface is generated using seepage analysis in geotechnical software SEEP/W and that same is used in the pseudo-static and pseudo-dynamic analyses to make the approach more realistic. The minimum values of factor of safety using pseudo-static and pseudo-dynamic method are obtained as 1.18 and 1.09 respectively for the chosen seismic zone in India. These values of factor of safety show clearly the demerits of conventional pseudo-static analysis compared to recent pseudo-dynamic analysis, where in addition to the seismic accelerations, duration, frequency of earthquake, body waves traveling during earthquake and amplification effects are considered.

Stability analysis of aperiodic messages scheduled in the dynamic segment of flex ray protocol

In a cyber physical system like vehicles number of signals to be communicated in a network system has an increasing trend. More and more mechanical and hydraulic parts are replaced by electronic control units and infotainment and multimedia applications has increased in vehicles. Safety critical hard real time messages and aperiodic messages communicated between electronic control units have been increased in recent times. Flexray is a high bandwidth protocol consisting of static segment for supporting hard real time messages and a dynamic segment for transmitting soft and non real time messages. In this paper, a method to obtain the stability region for the random arrival of messages in each electronic control units which is scheduled in the dynamic segment of Flexray protocol is presented. Number of mini slots available in the dynamic segment of Flexray restricts the arrival rate of tasks to the micro controllers or the number of micro controllers connected to the Flexray bus. Stability region of mathematical model of the system is compared with the Flexray protocol simulation results.

Exponential compact higher order scheme and their stability analysis for unsteady convection-diffusion equations

Exponential compact higher-order schemes have been developed for unsteady convection-diffusion equation (CDE). One of the developed scheme is sixth-order accurate which is conditionally stable for the Peclet number 0 <= Pe <= 2.8 and the other is fourth-order accurate which is unconditionally stable. Schemes for two-dimensional (2D) problems are made to use alternate direction implicit (ADI) algorithm. Example problems are solved and the numerical solutions are compared with the analytical solutions for each case.

Noncoherent Integration for Signal Detection: Analysis Under Model Uncertainties

The performance of postdetection integration (PDI) techniques for the detection of Global Navigation Satellite Systems (GNSS) signals in the presence of uncertainties in frequency offsets, noise variance, and unknown data-bits is studied. It is shown that the conventional PDI techniques are generally not robust to uncertainty in the data-bits and/or the noise variance. Two new modified PDI techniques are proposed, and they are shown to be robust to these uncertainties. The receiver operating characteristics (ROC) and sample complexity performance of the PDI techniques in the presence of model uncertainties are analytically derived. It is shown that the proposed methods significantly outperform existing methods, and hence they could become increasingly important as the GNSS receivers attempt to push the envelope on the minimum signal-to-noise ratio (SNR) for reliable detection.

Design and development of Fiber Bragg Grating sensing plate for plantar strain measurement and postural stability analysis

This paper describes an ab initio design and development of a novel Fiber Bragg Grating (FBG) sensor based strain sensing plate for the measurement of plantar strain distribution in human foot. The primary aim of this work is to study the feasibility of usage of FBG sensors in the measurement of plantar strain in the foot; in particular, to spatially resolve the strain distribution in the foot at different regions such as fore-foot, mid-foot and hind-foot. This study also provides a method to quantify and compare relative postural stability of different subjects under test; in addition, traditional accelerometers have been used to record the movements of center of gravity (second lumbar vertebra) of the subject and the results obtained have been compared against the outcome of the postural stability studies undertaken using the developed FBG plantar strain sensing plate. (C) 2013 Elsevier Ltd. All rights reserved.

Small signal Nonquasi-Static Model for Common Double-Gate MOSFETs Adapted to Gate Oxide Thickness Asymmetry

We present a physics-based closed form small signal Nonquasi-static (NQS) model for a long channel Common Double Gate MOSFET (CDG) by taking into account the asymmetry that may prevail between the gate oxide thickness. We use the unique quasi-linear relationship between the surface potentials along the channel to solve the governing continuity equation (CE) in order to develop the analytical expressions for the Y parameters. The Bessel function based solution of the CE is simplified in form of polynomials so that it could be easily implemented in any circuit simulator. The model shows good agreement with the TCAD simulation at-least till 4 times of the cut-off frequency for different device geometries and bias conditions.

Stability analysis of thick piezoelectric metal based FGM plate using first order and higher order shear deformation theory

This paper presents the stability analysis of functionally graded plate integrated with piezoelectric actuator and sensor at the top and bottom face, subjected to electrical and mechanical loading. The finite element formulation is based on first order and higher order shear deformation theory, degenerated shell element, von-Karman hypothesis and piezoelectric effect. The equation for static analysis is derived by using the minimum energy principle and solutions for critical buckling load is obtained by solving eigenvalue problem. The material properties of the functionally graded plate are assumed to be graded along the thickness direction according to simple power law function. Two types of boundary conditions are used, such as SSSS (simply supported) and CSCS (simply supported along two opposite side perpendicular to the direction of compression and clamped along the other two sides). Sensor voltage is calculated using present analysis for various power law indices and FG (functionally graded) material gradations. The stability analysis of piezoelectric FG plate is carried out to present the effects of power law index, material variations, applied mechanical pressure and piezo effect on buckling and stability characteristics of FG plate.

Cold gas in cluster cores: global stability analysis and non-linear simulations of thermal instability

We perform global linear stability analysis and idealized numerical simulations in global thermal balance to understand the condensation of cold gas from hot/virial atmospheres (coronae), in particular the intracluster medium (ICM). We pay particular attention to geometry (e.g. spherical versus plane-parallel) and the nature of the gravitational potential. Global linear analysis gives a similar value for the fastest growing thermal instability modes in spherical and Cartesian geometries. Simulations and observations suggest that cooling in haloes critically depends on the ratio of the cooling time to the free-fall time (t(cool)/t(ff)). Extended cold gas condenses out of the ICM only if this ratio is smaller than a threshold value close to 10. Previous works highlighted the difference between the nature of cold gas condensation in spherical and plane-parallel atmospheres; namely, cold gas condensation appeared easier in spherical atmospheres. This apparent difference due to geometry arises because the previous plane-parallel simulations focused on in situ condensation of multiphase gas but spherical simulations studied condensation anywhere in the box. Unlike previous claims, our non-linear simulations show that there are only minor differences in cold gas condensation, either in situ or anywhere, for different geometries. The amount of cold gas depends on the shape of tcool/tff; gas has more time to condense if gravitational acceleration decreases towards the centre. In our idealized plane-parallel simulations with heating balancing cooling in each layer, there can be significant mass/energy/momentum transfer across layers that can trigger condensation and drive tcool/tff far beyond the critical value close to 10.

Single network adaptive critic design for power system stabilisers

The recently developed single network adaptive critic (SNAC) design has been used in this study to design a power system stabiliser (PSS) for enhancing the small-signal stability of power systems over a wide range of operating conditions. PSS design is formulated as a discrete non-linear quadratic regulator problem. SNAC is then used to solve the resulting discrete-time optimal control problem. SNAC uses only a single critic neural network instead of the action-critic dual network architecture of typical adaptive critic designs. SNAC eliminates the iterative training loops between the action and critic networks and greatly simplifies the training procedure. The performance of the proposed PSS has been tested on a single machine infinite bus test system for various system and loading conditions. The proposed stabiliser, which is relatively easier to synthesise, consistently outperformed stabilisers based on conventional lead-lag and linear quadratic regulator designs.

Time-dependent analysis of an N2O gasdynamic laser

A simplified two-temperature model is presented for the vibrational energy levels of the N2O and N2 molecules of an N2O-N2-He gasdynamic laser (GDL), and the governing equations for the unsteady flow of the gas mixture in a convergent-divergent contour nozzle are solved using a time-dependent numerical technique. Final steady-state distributions are obtained for vibrational temperatures, population inversion, and the small-signal laser gain along the nozzle. It is demonstrated that, for plenum temperatures lower than 1200 K, an N2O GDL such as the present is more efficient than a CO2 GDL in identical operating conditions

Dynamic analysis of voltage instability in AC-DC systems

This paper presents the analysis and study of voltage collapse at any converter bus in A C-DC systems considering the dynamics of DC system. The problem of voltage instability is acute when HVDC links are connected to weak AC systems, the strength determined by short circuit ratio (SCR) at the converter bus. The converter control strategies are important in determining voltage instability. Small signal analysis is used to identify critical modes and evaluate the effect of AC system strength and control parameters. A sample two-terminal DC system is studied and the results compared with those obtained from static analysis. Also, the results obtained from small signal analysis are validated with nonlinear simulation.