Nonlinear static and dynamic damped response of a composite rectangular plate resting on a two-parameter elastic foundation

Nonlinear static and dynamic response analyses of a clamped. rectangular composite plate resting on a two-parameter elastic foundation have been studied using von Karman's relations. Incorporating the material damping, the governing coupled, nonlinear partial differential equations are obtained for the plate under step pressure pulse load excitation. These equations have been solved by a one-term solution and by applying Galerkin's technique to the deflection equation. This yields an ordinary nonlinear differential equation in time. The nonlinear static solution is obtained by neglecting the time-dependent variables. Thc nonlinear dynamic damped response is obtained by applying the ultraspherical polynomial approximation (UPA) technique. The influences of foundation modulus, shear modulus, orthotropy, etc. upon the nonlinear static and dynamic responses have been presented.

Graphical method to determine the parameters of the two-parameter fracture model for concrete

To evaluate the parameters in the two-parameter fracture model, i.e. the critical stress intensity factor and critical crack tip opening displacement for the fracture of plain concrete in Mode 1 for the given test configuration and geometry, considerable computational effort is necessary. A simple graphical method has been proposed using normalized fracture parameters for the three-point bend (3PB) notched specimen and the double-edged notched (DEN) specimen. A similar graphical method is proposed to compute the maximum load carrying capacity of a specimen, using the critical fracture parameters both for 3PB and DEN configurations.

Two-Parameter Uniformly Elliptic Sturm–Liouville Problems With Eigenparameter-Dependent Boundary Conditions

We consider the two-parameter Sturm–Liouville system $$ -y_1''+q_1y_1=(\lambda r_{11}+\mu r_{12})y_1\quad\text{on }[0,1], $$ with the boundary conditions $$ \frac{y_1'(0)}{y_1(0)}=\cot\alpha_1\quad\text{and}\quad\frac{y_1'(1)}{y_1(1)}=\frac{a_1\lambda+b_1}{c_1\lambda+d_1}, $$ and $$ -y_2''+q_2y_2=(\lambda r_{21}+\mu r_{22})y_2\quad\text{on }[0,1], $$ with the boundary conditions $$ \frac{y_2'(0)}{y_2(0)} =\cot\alpha_2\quad\text{and}\quad\frac{y_2'(1)}{y_2(1)}=\frac{a_2\mu+b_2}{c_2\mu+d_2}, $$ subject to the uniform-left-definite and uniform-ellipticity conditions; where $q_{i}$ and $r_{ij}$ are continuous real valued functions on $[0,1]$, the angle $\alpha_{i}$ is in $[0,\pi)$ and $a_{i}$, $b_{i}$, $c_{i}$, $d_{i}$ are real numbers with $\delta_{i}=a_{i}d_{i}-b_{i}c_{i}>0$ and $c_{i}\neq0$ for $i,j=1,2$. Results are given on asymptotics, oscillation of eigenfunctions and location of eigenvalues.

A robust layer adapted difference method for singularly perturbed two-parameter parabolic problems

A finite difference method for a time-dependent singularly perturbed convection-diffusion-reaction problem involving two small parameters in one space dimension is considered. We use the classical implicit Euler method for time discretization and upwind scheme on the Shishkin-Bakhvalov mesh for spatial discretization. The method is analysed for convergence and is shown to be uniform with respect to both the perturbation parameters. The use of the Shishkin-Bakhvalov mesh gives first-order convergence unlike the Shishkin mesh where convergence is deteriorated due to the presence of a logarithmic factor. Numerical results are presented to validate the theoretical estimates obtained.

Two-mode quantum systems: Invariant classification of squeezing transformations and squeezed states

A general analysis of squeezing transformations for two-mode systems is given based on the four-dimensional real symplectic group Sp(4, R). Within the framework of the unitary (metaplectic) representation of this group, a distinction between compact photon-number-conserving and noncompact photon-number-nonconserving squeezing transformations is made. We exploit the U(2) invariant squeezing criterion to divide the set of all squeezing transformations into a two-parameter family of distinct equivalence classes with representative elements chosen for each class. Familiar two-mode squeezing transformations in the literature are recognized in our framework and seen to form a set of measure zero. Examples of squeezed coherent and thermal states are worked out. The need to extend the heterodyne detection scheme to encompass all of U(2) is emphasized, and known experimental situations where all U(2) elements can be reproduced are briefly described.

Correlation of thermodynamic properties of chloromethanes

A correlation for entropy and enthalpy based on the two-parameter law of corresponding states and the reference substance concept has been obtained. For 199 points tested, the over-all average absolute deviation and the maximum deviations in the calculated values of entropy with the available data are 0.74 and 7.20%. The corresponding deviations of enthalpy are 1.86 and 15.0%, respectively. A compressibility chart for chloromethanes has been made and shown to be superior to existing charts. For 102 points tested, the average absolute and maximum deviations in the compressibilities were 1.80 and 19.5%, respectively.

On the bursting criterion for laminar separation bubbles

Traditionally, laminar separation bubbles have been characterised as being 'long' or 'short' on the basis of a two parameter 'bursting' criterion involving a pressure gradient parameter and Reynolds Number at separation. In the present work we suggest a refined bursting criterion, which takes into account not just the length of the bubble but also the maximum height of the bubble, thereby shedding some light on the less understood phenomenon of 'bursting' in laminar separation bubbles.

Scaling theory of quantum resistance distributions in disordered systems

We have derived explicitly, the large scale distribution of quantum Ohmic resistance of a disordered one-dimensional conductor. We show that in the thermodynamic limit this distribution is characterized by two independent parameters for strong disorder, leading to a two-parameter scaling theory of localization. Only in the limit of weak disorder we recover single parameter scaling, consistent with existing theoretical treatments.

Physical interpretation of the Poynting-Robertson effect

Although the prevalent mathematical description of the Poynting-Robertson effect is correct, its physical interpretation is sometimes problematic. By means of a two-parameter model, we revisit the effect in order to get a better physical understanding of it. The principal conclusion is that the motion of a dust in circumsolar orbit is governed only by solar radiation absorption and not by the asymmetry of reemission, even when viewed in the rest-frame of the Sun. (C) 1999 Academic Press.

Modeling the solubilities of fatty acids in supercritical carbon dioxide

A thermodynamic model was developed for modeling the solubilities of fatty acids in supercritical carbon dioxide. The model combines the Peng-Robinson equation of state (EOS) with the two parameter van der Waal's mixing rules. The model is applied to predict the solubilities of various fatty acids. The two adjustable interaction parameters in the model are found to vary linearly with the chain length of the fatty acids. Thus this model can be used to predict the solubilities of various fatty acids in supercritical carbon dioxide. (C) 2003 Elsevier Science B.V. All rights reserved.

Comparative statistical aging studies on an oil-pressboard insulation model

Accelerated aging experiments have been conducted on a representative oil-pressboard insulation model to investigate the effect of constant and sequential stresses on the PD behavior using a built-in phase resolved partial discharge analyzer. A cycle of the applied voltage starting from the zero of the positive half cycle was divided into 16 equal phase windows (Φ1 to Φ16) and partial discharge (PD) magnitude distribution in each phase was determined. Based on the experimental results, three stages of aging mechanism were identified. Gumbel's extreme value distribution of the largest element was used to model the first stage of aging process. Second and subsequent stages were modeled using two-parameter Weibull distribution. Spearman's non-parametric rank correlation test statistic and Kolmogrov-Smirnov two sample test were used to relate the aging process of each phase with the corresponding process of the full cycle. To bring out clearly the effect of stress level, its duration and test procedure on the distribution parameters and hence of the aging process, non-parametric ANOVA techniques like Kruskal-Wallis and Fisher's LSD multiple comparison tests were used. Results of the analysis show that two phases (Φ13 and Φ14) near the vicinity of the negative voltage peak were found to contribute significantly to the aging process and their aging mechanism also correlated well with that of the corresponding full cycle mechanism. Attempts have been made to relate these results with the published work of other workers

Remoulded shear strength at plastic and semi-solid states

The undrained shear strength of remoulded soils is of great concern in geotechnical engineering applications. This study aims to develop a reliable approach for determining the undrained shear strength of remoulded fine-grained soils, through the use of index test results, at both the plastic and semi-solid states of consistency. Experimental investigation and subsequent analysis involving a number of fine-grained soils of widely varying plasticity and geological origin have led to a two-parameter linear model of the relationship between logarithm of remoulded undrained shear strength and liquidity index. The numerical values of the parameters are found to be dependent to a lesser extent on the soil group and to a greater extent on the soil state. Based on the values of regression coefficient, ranking index and ranking distance, it seems that the relationship represents the experimental results well. It may be pointed out that the possibility of such a relationship in the semi-solid state of a soil has not been explored in the past. It is also shown that the shear strength at the plastic limit is about 32-34 times that at the liquid limit.

Discussion: Remoulded shear strength at plastic and semi-solid states

The undrained shear strength of remoulded soils is of great concern in geotechnical engineering applications. This study aims to develop a reliable approach for determining the undrained shear strength of remoulded fine-grained soils, through the use of index test results, at both the plastic and semi-solid states of consistency. Experimental investigation and subsequent analysis involving a number of fine-grained soils of widely varying plasticity and geological origin have led to a two-parameter linear model of the relationship between logarithm of remoulded undrained shear strength and liquidity index. The numerical values of the parameters are found to be dependent to a lesser extent on the soil group and to a greater extent on the soil state. Based on the values of regression coefficient, ranking index and ranking distance, it seems that the relationship represents the experimental results well. It may be pointed out that the possibility of such a relationship in the semi-solid state of a soil has not been explored in the past. It is also shown that the shear strength at the plastic limit is about 32–34 times that at the liquid limit.

Parameter estimation of a two-horizon soil profile by combining crop canopy and surface soil moisture observations using GLUE

Estimation of soil parameters by inverse modeling using observations on either surface soil moisture or crop variables has been successfully attempted in many studies, but difficulties to estimate root zone properties arise when heterogeneous layered soils are considered. The objective of this study was to explore the potential of combining observations on surface soil moisture and crop variables - leaf area index (LAI) and above-ground biomass for estimating soil parameters (water holding capacity and soil depth) in a two-layered soil system using inversion of the crop model STICS. This was performed using GLUE method on a synthetic data set on varying soil types and on a data set from a field experiment carried out in two maize plots in South India. The main results were (i) combination of surface soil moisture and above-ground biomass provided consistently good estimates with small uncertainity of soil properties for the two soil layers, for a wide range of soil paramater values, both in the synthetic and the field experiment, (ii) above-ground biomass was found to give relatively better estimates and lower uncertainty than LAI when combined with surface soil moisture, especially for estimation of soil depth, (iii) surface soil moisture data, either alone or combined with crop variables, provided a very good estimate of the water holding capacity of the upper soil layer with very small uncertainty whereas using the surface soil moisture alone gave very poor estimates of the soil properties of the deeper layer, and (iv) using crop variables alone (else above-ground biomass or LAI) provided reasonable estimates of the deeper layer properties depending on the soil type but provided poor estimates of the first layer properties. The robustness of combining observations of the surface soil moisture and the above-ground biomass for estimating two layer soil properties, which was demonstrated using both synthetic and field experiments in this study, needs now to be tested for a broader range of climatic conditions and crop types, to assess its potential for spatial applications. (C) 2012 Elsevier B.V. All rights reserved.