Anisotropy in elastic properties of lithium sodium sulphate hexahydrate single crystal—An ultrasonic study

The double sulfate family (ABSO4), where A and B are alkali metal cations, is the object of great interest owing to the complexity and richness of its sequence of phase transition induced by temperature variation. A new sulfate salt characterized by the presence of water molecule in the unit cell with the chemical formula, Li2Na3(SO4)2⋅6H2O (LSSW), was obtained. The ultrasonic velocity measurement was done with pulse echo overlap technique [PEO]. All the six second order elastic stiffness constants, C11 = C22, C33, C44 = C55, C12, C14 and C13 = C23 are reported for the first time. The anisotropy in the elastic properties of the crystal are well explained by the pictorial representation of the polar plots of phase velocity, slowness, Young’s modulus and linear compressibility in a–b and a–c planes.

Elastic constant measurements of super ionic LiKSO4:Na single crystals

Elastic properties of sodium doped Lithium potassium sulphate, LiK0.9Na0.1SO4, crystal has been studied by ultrasonic Pulse Echo Overlap [PEO] technique and are reported for the first time. The controversy regarding the type of crystal found while growth is performed at 35 °C with equimolar fraction of Li2SO4H2O, K2SO4 and Na2SO4 has been resolved by studying the elastic properties. The importance of this crystal is that it exhibits pyroelectric, ferroelectric and electro optic properties. It is simultaneously ferroelastic and superionic. The elastic properties of LiK0.9Na0.1SO4 crystal are well studied by measuring ultrasonic velocity in the crystal in certain specified crystallographic directions and evaluating the elastic stiffness constants, compliance constants and Poisson’s ratios. The anisotropy in the elastic properties of the crystal are well explained by the pictorial representation of the surface plots of phase velocity, slowness and linear compressibility in a-b and a-c planes.

Ultrasonic measurement of the elastic properties of benzoyl glycine single crystals

Certain organic crystals are found to possess high non- linear optical coefficients,often one to two orders of magnitude higher than those of the well known inorganic non-linear optical materials.Benzoyl glycine is one such crystal whose optical second-harmonic generation efficiency is much higher than that of potassium dihydrogen phosphate. Single crystals of benzoyl glycine are grown by solvent evaporation technique using N,N-dimethyl formamide as the solvent.All the nine second-order elastic stiffness constants of this orthorhombic crystal are determined from ultrasonic wave velocity measurements employing the pulse echo overlap technique.The anisotropy of elastic wave propagation in this crystal is demonstrated by plotting the phase velocity, slowness,Young's modulus and linear compressibility surfaces along symmetry planes.The volume compressibility, bulk modulus and relevant Poisson's ratios are also determined. Variation of the diagonal elastic stiffness constants with temperature over a limited range are measured and reported.

Comment on "Reappraisal of experimental values of third-order elastic constants of some cubic semiconductors and metals"

In a recent paper A. S. Johal and D. J. Dunstan [Phys. Rev. B 73, 024106 (2006)] have applied multivariate linear regression analysis to the published data of the change in ultrasonic velocity with applied stress. The aim is to obtain the best estimates for the third-order elastic constants in cubic materials. From such an analysis they conclude that uniaxial stress data on metals turns out to be nearly useless by itself. The purpose of this comment is to point out that by a proper analysis of uniaxial stress data it is possible to obtain reliable values of third-order elastic constants in cubic metals and alloys. Cu-based shape memory alloys are used as an illustrative example.

Linear and nonlinear microrheology of dense colloidal suspensions

The length and time scales accessible to optical tweezers make them an ideal tool for the examination of colloidal systems. Embedded high-refractive-index tracer particles in an index-matched hard sphere suspension provide 'handles' within the system to investigate the mechanical behaviour. Passive observations of the motion of a single probe particle give information about the linear response behaviour of the system, which can be linked to the macroscopic frequency-dependent viscous and elastic moduli of the suspension. Separate 'dragging' experiments allow observation of a sample's nonlinear response to an applied stress on a particle-by particle basis. Optical force measurements have given new data about the dynamics of phase transitions and particle interactions; an example in this study is the transition from liquid-like to solid-like behaviour, and the emergence of a yield stress and other effects attributable to nearest-neighbour caging effects. The forces needed to break such cages and the frequency of these cage breaking events are investigated in detail for systems close to the glass transition.

An elastic net orthogonal forward regression algorithm

In this paper we propose an efficient two-level model identification method for a large class of linear-in-the-parameters models from the observational data. A new elastic net orthogonal forward regression (ENOFR) algorithm is employed at the lower level to carry out simultaneous model selection and elastic net parameter estimation. The two regularization parameters in the elastic net are optimized using a particle swarm optimization (PSO) algorithm at the upper level by minimizing the leave one out (LOO) mean square error (LOOMSE). Illustrative examples are included to demonstrate the effectiveness of the new approaches.

Elastic-net prefiltering for two-class classification

A two-stage linear-in-the-parameter model construction algorithm is proposed aimed at noisy two-class classification problems. The purpose of the first stage is to produce a prefiltered signal that is used as the desired output for the second stage which constructs a sparse linear-in-the-parameter classifier. The prefiltering stage is a two-level process aimed at maximizing a model's generalization capability, in which a new elastic-net model identification algorithm using singular value decomposition is employed at the lower level, and then, two regularization parameters are optimized using a particle-swarm-optimization algorithm at the upper level by minimizing the leave-one-out (LOO) misclassification rate. It is shown that the LOO misclassification rate based on the resultant prefiltered signal can be analytically computed without splitting the data set, and the associated computational cost is minimal due to orthogonality. The second stage of sparse classifier construction is based on orthogonal forward regression with the D-optimality algorithm. Extensive simulations of this approach for noisy data sets illustrate the competitiveness of this approach to classification of noisy data problems.

Particle swarm optimisation assisted classification using elastic net prefiltering

A novel two-stage construction algorithm for linear-in-the-parameters classifier is proposed, aiming at noisy two-class classification problems. The purpose of the first stage is to produce a prefiltered signal that is used as the desired output for the second stage to construct a sparse linear-in-the-parameters classifier. For the first stage learning of generating the prefiltered signal, a two-level algorithm is introduced to maximise the model's generalisation capability, in which an elastic net model identification algorithm using singular value decomposition is employed at the lower level while the two regularisation parameters are selected by maximising the Bayesian evidence using a particle swarm optimization algorithm. Analysis is provided to demonstrate how “Occam's razor” is embodied in this approach. The second stage of sparse classifier construction is based on an orthogonal forward regression with the D-optimality algorithm. Extensive experimental results demonstrate that the proposed approach is effective and yields competitive results for noisy data sets.

Elastic net orthogonal forward regression

An efficient two-level model identification method aiming at maximising a model׳s generalisation capability is proposed for a large class of linear-in-the-parameters models from the observational data. A new elastic net orthogonal forward regression (ENOFR) algorithm is employed at the lower level to carry out simultaneous model selection and elastic net parameter estimation. The two regularisation parameters in the elastic net are optimised using a particle swarm optimisation (PSO) algorithm at the upper level by minimising the leave one out (LOO) mean square error (LOOMSE). There are two elements of original contributions. Firstly an elastic net cost function is defined and applied based on orthogonal decomposition, which facilitates the automatic model structure selection process with no need of using a predetermined error tolerance to terminate the forward selection process. Secondly it is shown that the LOOMSE based on the resultant ENOFR models can be analytically computed without actually splitting the data set, and the associate computation cost is small due to the ENOFR procedure. Consequently a fully automated procedure is achieved without resort to any other validation data set for iterative model evaluation. Illustrative examples are included to demonstrate the effectiveness of the new approaches.

Análise não linear física e geométrica de pórticos espaciais

Apresenta-se uma formulação do tipo incrementaliterativa destinada a análise não linear de pórticos espaciais. Considera-se os efeitos não lineares introduzidos pelas mudanças de configuração geométrica da estrutura e também pela combinação destes efeitos com aqueles inerentes ao comportamento plástico exibido pelo material. As relações cinemáticas empregadas permitem a consideração de deslocamentos arbitrariamente grandes, acompanhadas de pequenas deformações . A modelagem do comportamento plástico do material é efetuada através do conceito de rótula plástica, estabelecido a partir de um critério de plastificação generalizado. Adota-se uma matriz de rigidez geométrica de barra baseada em momentos semitangenciais. Para elementos com extremos plastificados, é deduzida uma matriz de rigidez elasto-plástica. Emprega-se um método numérico do tipo incremental-iterativo, que utiliza como condição básica de controle da análise a constância do trabalho realizado pelos incrementos de cargas, em cada passo incremental (Método de Controle por Trabalho).A formulação permite uma descricão completa do desempenho mecânico da estrutura, inclusive em estágio de deformação pós-crítico em que ocorre regressão do carregamento com aumento de deslocamentos, ou vice-versa. A formulação foi implementada em um programa computacional elaborado em linguagem FORTRAN. Vários exemplos numéricos são apresentados para mostrar a eficiência das procedimentos propostos.

Cubic approximation for the transverse displacement in BEM for elastic plates analysis

This work presents an application for the plate analysis formulation by BEM where 3 boundary equations are used, written for the transverse displacement w and the normal and tangential derivatives partial derivativew/partial derivativen and partial derivativew/partial derivatives. In this extension, the transverse displacement w is approximated by a cubic polynomial and, as a consequence, partial derivativew/partial derivatives has a quadratic approximation. This alternative BEM formulation improves the analysis of thin plates, when compared to the formulation using the linear approximation for the displacements, mainly in the obtaining of the bending moments at the boundary of the plate. The implementation of this proposal to the computational codes is simple. (C) 2004 Published by Elsevier Ltd.

On the nonminimal vector coupling in the Duffin-Kemmer-Petiau theory and the confinement of massive bosons by a linear potential

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On a regular convex solver potential for an elastic-damage constitutive model: a theoretical analysis

This work is related with the proposition of a so-called regular or convex solver potential to be used in numerical simulations involving a certain class of constitutive elastic-damage models. All the mathematical aspects involved are based on convex analysis, which is employed aiming a consistent variational formulation of the potential and its conjugate one. It is shown that the constitutive relations for the class of damage models here considered can be derived from the solver potentials by means of sub-differentials sets. The optimality conditions of the resulting minimisation problem represent in particular a linear complementarity problem. Finally, a simple example is present in order to illustrate the possible integration errors that can be generated when finite step analysis is performed. (C) 2003 Elsevier Ltd. All rights reserved.

On non-ideal and non-linear portal frame dynamics analysis using Bogoliubov averaging method

We apply the Bogoliubov Averaging Method to the study of the vibrations of an elastic foundation, forced by a Non-ideal energy source. The considered model consists of a portal plane frame with quadratic nonlinearities, with internal resonance 1:2, supporting a direct current motor with limited power. The non-ideal excitation is in primary resonance in the order of one-half with the second mode frequency. The results of the averaging method, plotted in time evolution curve and phase diagrams are compared to those obtained by numerically integrating of the original differential equations. The presence of the saturation phenomenon is verified by analytical procedures.

Active flutter suppression in a 2-D airfoil using linear matrix inequalities techniques

Flutter is an in-flight vibration of flexible structures caused by energy in the airstream absorbed by the lifting surface. This aeroelastic phenomenon is a problem of considerable interest in the aeronautic industry, because flutter is a potentially destructive instability resulting from an interaction between aerodynamic, inertial, and elastic forces. To overcome this effect, it is possible to use passive or active methodologies, but passive control adds mass to the structure and it is, therefore, undesirable. Thus, in this paper, the goal is to use linear matrix inequalities (LMIs) techniques to design an active state-feedback control to suppress flutter. Due to unmeasurable aerodynamic-lag states, one needs to use a dynamic observer. So, LMIs also were applied to design a state-estimator. The simulated model, consists of a classical flat plate in a two-dimensional flow. Two regulators were designed, the first one is a non-robust design for parametric variation and the second one is a robust control design, both designed by using LMIs. The parametric uncertainties are modeled through polytopic uncertainties. The paper concludes with numerical simulations for each controller. The open-loop and closed-loop responses are also compared and the results show the flutter suppression. The perfomance for both controllers are compared and discussed. Copyright © 2006 by ABCM.