On the sensitivity of elastic waves due to structural damages:Time-frequency based indexing method

Time-frequency analysis of various simulated and experimental signals due to elastic wave scattering from damage are performed using wavelet transform (WT) and Hilbert-Huang transform (HHT) and their performances are compared in context of quantifying the damages. Spectral finite element method is employed for numerical simulation of wave scattering. An analytical study is carried out to study the effects of higher-order damage parameters on the reflected wave from a damage. Based on this study, error bounds are computed for the signals in the spectral and also on the time-frequency domains. It is shown how such an error bound can provide all estimate of error in the modelling of wave propagation in structure with damage. Measures of damage based on WT and HHT is derived to quantify the damage information hidden in the signal. The aim of this study is to obtain detailed insights into the problem of (1) identifying localised damages (2) dispersion of multifrequency non-stationary signals after they interact with various types of damage and (3) quantifying the damages. Sensitivity analysis of the signal due to scattered wave based on time-frequency representation helps to correlate the variation of damage index measures with respect to the damage parameters like damage size and material degradation factors.

Analytical solution of unsteady three-dimensional MHD boundary layer flow and heat transfer due to impulsively stretched plane surface

The unsteady magnetohydrodynamic viscous flow and heat transfer of Newtonian fluids induced by an impulsively stretched plane surface in two lateral directions are studied by using an analytic technique, namely, the homotopy method. The analytic series solution presented here is highly accurate and uniformly valid for all time in the entire region. The effects of the stretching ratio and the magnetic field on the surface shear stresses and heat transfer are studied. The surface shear stresses in x- and y-directions and the surface heat transfer are enchanced by increasing stretching ratio for a fixed value of the magnetic parameter. For a fixed stretching ratio, the surface shear stresses increase with the magnetic parameter, but the heat transfer decreases. The Nusselt number takes longer time to reach the steady state than the skin friction coefficients. There is a smooth transition from the initial unsteady state to the steady state.

Quantum-Ohmic Resistance Fluctuation In Disordered Conductors - An Invariant Imbedding Approach

It is now well known that in extreme quantum limit, dominated by the elastic impurity scattering and the concomitant quantum interference, the zero-temperature d.c. resistance of a strictly one-dimensional disordered system is non-additive and non-self-averaging. While these statistical fluctuations may persist in the case of a physically thin wire, they are implicitly and questionably ignored in higher dimensions. In this work, we have re-examined this question. Following an invariant imbedding formulation, we first derive a stochastic differential equation for the complex amplitude reflection coefficient and hence obtain a Fokker-Planck equation for the full probability distribution of resistance for a one-dimensional continuum with a Gaussian white-noise random potential. We then employ the Migdal-Kadanoff type bond moving procedure and derive the d-dimensional generalization of the above probability distribution, or rather the associated cumulant function –‘the free energy’. For d=3, our analysis shows that the dispersion dominates the mobilitly edge phenomena in that (i) a one-parameter B-function depending on the mean conductance only does not exist, (ii) an approximate treatment gives a diffusion-correction involving the second cumulant. It is, however, not clear whether the fluctuations can render the transition at the mobility edge ‘first-order’. We also report some analytical results for the case of the one dimensional system in the presence of a finite electric fiekl. We find a cross-over from the exponential to the power-low length dependence of resistance as the field increases from zero. Also, the distribution of resistance saturates asymptotically to a poissonian form. Most of our analytical results are supported by the recent numerical simulation work reported by some authors.

Investigation of Missile-Shaped Body with Forward-Facing Cavity at Mach 8

A blunt-nosed hypersonic missile mounted with a forward-facing cavity is a good alternative to reduce the stagnation heating rates. The effects of a forward-racing cavity on heat transfer and aerodynamic coefficients are addressed in this paper. Tests were carried out in hypersonic shock tunnel HST2, at a hypersonic Mach number of 8 using a 41 deg apex-angle blunt cone. The aerodynamic forces on the test model with and without a forward-facing cavity at various angles of attack are measured by using an internally mountable accelerometer force balance system. Heat flux measurements have been carried out on the test model with and without a forward-facing cavity of the entire surface at zero degree angle of attack with platinum sensors. A numerical simulation was also carried out using the computational fluid dynamics code (CFX-Ansys 5.7). An important result of this study is that the smaller cavity diameter has the highest lift-to-drag ratio, whereas the medium cavity has the highest heat flux reduction. Theshock structure around the test model has also been visualized using the Schlieren flow visualization technique. The visualized shock structure and the measured aerodynamic forces on the missile-shaped body with cavity configurations agree well with the axisymmetric numerical simulations.

Active vibration suppression of non-linear beams using optimal dynamic inversion

Euler–Bernoulli beams are distributed parameter systems that are governed by a non-linear partial differential equation (PDE) of motion. This paper presents a vibration control approach for such beams that directly utilizes the non-linear PDE of motion, and hence, it is free from approximation errors (such as model reduction, linearization etc.). Two state feedback controllers are presented based on a newly developed optimal dynamic inversion technique which leads to closed-form solutions for the control variable. In one formulation a continuous controller structure is assumed in the spatial domain, whereas in the other approach it is assumed that the control force is applied through a finite number of discrete actuators located at predefined discrete locations in the spatial domain. An implicit finite difference technique with unconditional stability has been used to solve the PDE with control actions. Numerical simulation studies show that the beam vibration can effectively be decreased using either of the two formulations.

Extending temporal simulations

Direct numerical simulations (DNS) of spatially growing turbulent shear layers may be performed as temporal simulations by solving the governing equations with some additional terms while imposing streamwise periodicity. These terms are functions of the means whose spatial growth is calculated easily and accurately from statistics of the temporal DNS. Equations for such simulations are derived.

Response of nonlinear systems to narrow-band excitation

The hardening cubic spring oscillator is studied under narrow-band gaussian excitation. Equivalent linearization leads to multiple steady states. The realizability of the solution is discussed through stochastic stability analysis. Theoretical results are supported by numerical simulation.

Denoising signals corrupted by chaotic noise

We consider the problem of signal estimation where the observed time series is modeled as y(i) = x(i) + s(i) with {x(i)} being an orbit of a chaotic self-map on a compact subset of R-d and {s(i)} a sequence in R-d converging to zero. This model is motivated by experimental results in the literature where the ocean ambient noise and the ocean clutter are found to be chaotic. Making use of observations up to time n, we propose an estimate of s(i) for i < n and show that it approaches s(i) as n -> infinity for typical asymptotic behaviors of orbits. (C) 2010 Elsevier B.V. All rights reserved.

Conditional linearization in nonlinear random vibration

In this paper, an improved probabilistic linearization approach is developed to study the response of nonlinear single degree of freedom (SDOF) systems under narrow-band inputs. An integral equation for the probability density function (PDF) of the envelope is derived. This equation is solved using an iterative scheme. The technique is applied to study the hardening type Duffing's oscillator under narrow-band excitation. The results compare favorably with those obtained using numerical simulation. In particular, the bimodal nature of the PDF for the response envelope for certain parameter ranges is brought out.

FIR system identification based on subspaces of a higher order cumulant matrix

A new linear algebraic approach for identification of a nonminimum phase FIR system of known order using only higher order (>2) cumulants of the output process is proposed. It is first shown that a matrix formed from a set of cumulants of arbitrary order can be expressed as a product of structured matrices. The subspaces of this matrix are then used to obtain the parameters of the FIR system using a set of linear equations. Theoretical analysis and numerical simulation studies are presented to characterize the performance of the proposed methods.

Role of elasto-plastic analysis under cyclic loading in fatigue crack growth studies

Linear Elastic Fracture Mechanics (LEFM) has been widely used in the past for fatigue crack growth studies, but this is acceptable only in situations which are within small scale yielding (SSY). In many practical structural components, conditions of SSY could be violated and one has to look for fracture criteria based on elasto-plastic analysis. Crack closure phenomenon, one of the most striking discoveries based on inelastic deformations during crack growth, has significant effect on fatigue crack growth rate. Numerical simulation of this phenomenon is computationally intensive and involved but has been successfully implemented. Stress intensity factors and strain energy release rates lose their meaning, J-integral (or its incremental) values are applicable only in specific situations, whereas alternate path independent integrals have been proposed in the literature for use with elasto-plastic fracture mechanics (EPFM) based criteria. This paper presents certain salient features of two independent finite element (numerical) studies of relevance to fatigue crack growth, where elasto-plastic analysis becomes significant. These problems can only be handled in the current day computational environment, and would have been only a dream just a few years ago.

Process-kinetics in facing targets sputtering of multi-component oxide thin films

The kinetics of the processes in facing targets sputtering of multicomponent oxide films is presented. The novel configuration of the process exhibits an enhanced ionization efficiency. Discharge diagnostics performed using optical emission spectroscopy revealed strong dependence of plasma parameters on process conditions. Numerical simulation based on thermalization and diffusion of sputtered atoms has been performed to estimate the transport efficiency in off-axis mode. Composition, structure and epitaxial quality of YBa2Cu3O7-x films prepared was found to be strongly dependent on atomic flux ratios (of Cu/Y and Ba/Y) arriving at the substrate, resputtering effect and phase stability of YBa2Cu3O7-x These studies have been shown to be useful in understanding the complex processes that occur in sputtering of multicomponent films. (C) 1999 Elsevier Science S.A. All rights reserved.

Incremental-angle and angular velocity estimation using a star sensor

A method is described for estimating the incremental angle and angular velocity of a spacecraft using integrated rate parameters with the help of a star sensor alone. The chief advantage of this method is that the measured stars need not be identified, whereas the identification of the stars is necessary in earlier methods. This proposed estimation can be carried out with all of the available measurements by a simple linear Kalman filter, albeit with a time-varying sensitivity matrix. The residuals of estimated angular velocity by the proposed spacecraft incremental-angle and angular velocity estimation method are as accurate as the earlier methods. This method also enables the spacecraft attitude to be reconstructed for mapping the stars into an imaginary unit sphere in the body reference frame, which will preserve the true angular separation of the stars. This will pave the way for identification of the stars using any angular separation or triangle matching techniques applied to even a narrow field of view sensor that is made to sweep the sky. A numerical simulation for inertial as well as Earth pointing spacecraft is carried out to establish the results.

Rayleigh-Benard convection during solidification of an eutectic solution cooled from the top

The interaction between laminar Rayleigh-Benard convection and directional solidification is studied for the case of an eutectic solution kept in a rectangular cavity cooled from the top. Experiments and numerical simulations are carried out using an NH4Cl-H2O solution as the model fluid. The flow is visualized using a sheet of laser light scattered by neutrally buoyant, hollow-glass spheres seeded in the fluid. The numerical modeling is performed using a pressure-based finite-volume method according to the SIMPLER algorithm. The present configuration enables us to visualize flow vortices in the presence of a continuously evolving solid/liquid interface. Clear visualization of the Rayleigh-Benard convective cells and their interaction with the solidification front are obtained. It is observed that the convective cells are characterized by zones of up-flow and down-flow, resulting in the development of a nonplanar interface. Because of the continuous advancement of the solid/liquid interface, the effective liquid height of the cavity keeps decreasing. Once the height of the fluid layer falls below a critical value, the convective cells become weaker and eventually die out, leading to the growth of a planar solidification front. Results of flow visualization and temperature measurement are compared with those from the numerical simulation, and a good agreement is found.

Scaling analysis of momentum and heat transport in gas tungsten arc weld pools

A systematic procedure is outlined for scaling analysis of momentum and heat transfer in gas tungsten arc weld pools. With suitable selections of non-dimentionalised parameters, the governing equations coupled with appropriate boundary conditions are first scaled, and the relative significance of various terms appearing in them is analysed accordingly. The analysis is then used to predict the orders of magnitude of some important quantities, such as the velocity scene lit the top surface, velocity boundary layer thickness, maximum temperature increase in the pool, and time required for initiation of melting. Some of the quantities predicted from the scaling analysis can also be used for optimised selection of appropriate grid size and time steps for full numerical simulation of the process. The scaling predictions are finally assessed by comparison with numerical results quoted in the literature, and a good qualitative agreement is observed.