Computation of Thermal Stress Intensity Factors for Bimaterial Interface Cracks Using Domain Integral Method

The concept of domain integral used extensively for J integral has been applied in this work for the formulation of J(2) integral for linear elastic bimaterial body containing a crack at the interface and subjected to thermal loading. It is shown that, in the presence of thermal stresses, the J(k) domain integral over a closed path, which does not enclose singularities, is a function of temperature and body force. A method is proposed to compute the stress intensity factors for bimaterial interface crack subjected to thermal loading by combining this domain integral with the J(k) integral. The proposed method is validated by solving standard problems with known solutions.

Effect of residual stresses and metallographic stability on the over all performance of integral diaphragm material

The integral diaphragm pressure transducer consists of a diaphragm machined from precipitation hardened martensitic (APX4) steel. Its performance is quite significant as it depends upon various factors such as mechanical properties including induced residual stress levels, metallurgical and physical parameters due to different stages of processing involved. Hence, the measurement and analysis of residual stress becomes very important from the point of in-service assessment of a component. In the present work, the stress measurements have been done using the X-ray diffraction (XRD) technique, which is a non-destructive test (NDT). This method is more reliable and widely used compared to the other NDT techniques. The metallurgical aspects have been studied by adopting the conventional metallographic practices including examination of microstructure using light microscope. The dimensional measurements have been carried out using dimensional gauge. The results of the present investigation reveals that the diaphragm material after undergoing series of realization processes has yielded good amount of retained austenite in it. Also, the presence of higher compressive stresses induced in the transducer results in non-linearity, zero shift and dimensional instability. The problem of higher retained austenite content and higher compressive stress have been overcome by adopting a new realization process involving machining and cold and hot stabilization soak which has brought down the retained austenite content to about 5–6% and acceptable level of compressive stress in the range −100 to −150 MPa with fine tempered martensitic phase structure and good dimensional stability. The new realization process seems to be quite effective in terms of controlling retained austenite content, residual stress, metallurgical phase as well as dimensional stability and this may result in minimum zero shift of the diaphragm system.

Block Convolution Using Discrete Trigonometric Transforms and Discrete Fourier Transform

We derive expressions for convolution multiplication properties of discrete cosine transform II (DCT II) starting from equivalent discrete Fourier transform (DFT) representations. Using these expressions, a method for implementing linear filtering through block convolution in the DCT II domain is presented. For the case of nonsymmetric impulse response, additional discrete sine transform II (DST II) is required for implementing the filter in DCT II domain, where as for a symmetric impulse response, the additional transform is not required. Comparison with recently proposed circular convolution technique in DCT II domain shows that the proposed new method is computationally more efficient.

Testing and Modeling of MR Damper and Its Application to SDOF Systems Using Integral Backstepping Technique

Magnetorheological dampers are intrinsically nonlinear devices, which make the modeling and design of a suitable control algorithm an interesting and challenging task. To evaluate the potential of magnetorheological (MR) dampers in control applications and to take full advantages of its unique features, a mathematical model to accurately reproduce its dynamic behavior has to be developed and then a proper control strategy has to be taken that is implementable and can fully utilize their capabilities as a semi-active control device. The present paper focuses on both the aspects. First, the paper reports the testing of a magnetorheological damper with an universal testing machine, for a set of frequency, amplitude, and current. A modified Bouc-Wen model considering the amplitude and input current dependence of the damper parameters has been proposed. It has been shown that the damper response can be satisfactorily predicted with this model. Second, a backstepping based nonlinear current monitoring of magnetorheological dampers for semi-active control of structures under earthquakes has been developed. It provides a stable nonlinear magnetorheological damper current monitoring directly based on system feedback such that current change in magnetorheological damper is gradual. Unlike other MR damper control techniques available in literature, the main advantage of the proposed technique lies in its current input prediction directly based on system feedback and smooth update of input current. Furthermore, while developing the proposed semi-active algorithm, the dynamics of the supplied and commanded current to the damper has been considered. The efficiency of the proposed technique has been shown taking a base isolated three story building under a set of seismic excitation. Comparison with widely used clipped-optimal strategy has also been shown.

Hanle-Zeeman redistribution matrix. I. Classical theory expressions in the laboratory frame

Polarized scattering in spectral lines is governed by a 4; 4 matrix that describes how the Stokes vector is scattered and redistributed in frequency and direction. Here we develop the theory for this redistribution matrix in the presence of magnetic fields of arbitrary strength and direction. This general magnetic field case is called the Hanle- Zeeman regime, since it covers both of the partially overlapping weak- and strong- field regimes in which the Hanle and Zeeman effects dominate the scattering polarization. In this general regime, the angle-frequency correlations that describe the so-called partial frequency redistribution (PRD) are intimately coupled to the polarization properties. We develop the theory for the PRD redistribution matrix in this general case and explore its detailed mathematical properties and symmetries for the case of a J = 0 -> 1 -> 0 scattering transition, which can be treated in terms of time-dependent classical oscillator theory. It is shown how the redistribution matrix can be expressed as a linear superposition of coherent and noncoherent parts, each of which contain the magnetic redistribution functions that resemble the well- known Hummer- type functions. We also show how the classical theory can be extended to treat atomic and molecular scattering transitions for any combinations of quantum numbers.

Existence and approximations of solutions to some fractional order functional integral equations

In this paper we shall study a fractional order functional integral equation. In the first part of the paper, we proved the existence and uniqueness of mile and global solutions in a Banach space. In the second part of the paper, we used the analytic semigroups theory oflinear operators and the fixed point method to establish the existence, uniqueness and convergence of approximate solutions of the given problem in a separable Hilbert space. We also proved the existence and convergence of Faedo-Galerkin approximate solution to the given problem. Finally, we give an example.

On some integral properties of hypergeometric functions

In this note certain integrals involving hypergeometric functions have been evaluated in convenient and elegant forms. © 1971 Indian Academy of Sciences.

A fourier-integral solution for the elastic quarter-plane

The problem of an elastic quarter-plane with arbitrary loadings on the boundaries has been solved using a Fourier-integral approach.

Application of D transforms in the analysis of nonlinear distributed parameter systems

The scope of application of Laplace transforms presently limited to the study of linear partial differential equations, is extended to the nonlinear domain by this study. This has been achieved by modifying the definition of D transforms, put forth recently for the study of classes of nonlinear lumped parameter systems. The appropriate properties of the new D transforms are presented to bring out their applicability in the analysis of nonlinear distributed parameter systems.

Approximation of solutions to fractional integral equation

In this paper we shall study a fractional integral equation in an arbitrary Banach space X. We used the analytic semigroups theory of linear operators and the fixed point method to establish the existence and uniqueness of solutions of the given problem. We also prove the existence of global solution. The existence and convergence of the Faedo–Galerkin solution to the given problem is also proved in a separable Hilbert space with some additional assumptions on the operator A. Finally we give an example to illustrate the applications of the abstract results.

A semi-classical model of the electron containing tachyonic matter

It is shown that the mass of the electron could be conceived as the energy associated with its spinning motion and the angular velocity is such that the linear velocities at the surface exceed the velocity of light; this in fact accounts for its stability against the centrifugal forces in the core region.

Anti-windup Schemes for Proportional Integral and Proportional Resonant Controller

Problems like windup or rollover arise in a PI controller working under saturation. Hence anti-windup schemes are necessary to minimize performance degradation.Similar situation may occur in a Proportional Resonant(PR)controller in the presence of a sustained error input.Several methods can be employed based on existing knowledge on PI controller to counter this problem.In this paper few such schemes are proposed and implemented in FPGA and MATLAB and from the obtained results their possible use and limitations have been studied.

Molecular theory of solvation and solvation dynamics of a classical ion in a dipolar liquid

A microscopic theory of equilibrium solvation and solvation dynamics of a classical, polar, solute molecule in dipolar solvent is presented. Density functional theory is used to explicitly calculate the polarization structure around a solvated ion. The calculated solvent polarization structure is different from the continuum model prediction in several respects. The value of the polarization at the surface of the ion is less than the continuum value. The solvent polarization also exhibits small oscillations in space near the ion. We show that, under certain approximations, our linear equilibrium theory reduces to the nonlocal electrostatic theory, with the dielectric function (c(k)) of the liquid now wave vector (k) dependent. It is further shown that the nonlocal electrostatic estimate of solvation energy, with a microscopic c(k), is close to the estimate of linearized equilibrium theories of polar liquids. The study of solvation dynamics is based on a generalized Smoluchowski equation with a mean-field force term to take into account the effects of intermolecular interactions. This study incorporates the local distortion of the solvent structure near the ion and also the effects of the translational modes of the solvent molecules.The latter contribution, if significant, can considerably accelerate the relaxation of solvent polarization and can even give rise to a long time decay that agrees with the continuum model prediction. The significance of these results is discussed.

A simple classical approach for the melting temperature of inert-gas nanoparticles

Like the metal and semiconductor nanoparticles, the melting temperature of free inert-gas nanoparticles decreases with decreasing size. The variation is linear with the inverse of the particle size for large nanoparticles and deviates from the linearity for small nanoparticles. The decrease in the melting temperature is slower for free nanoparticles with non-wetting surfaces, while the decrease is faster for nanoparticles with wetting surfaces. Though the depression of the melting temperature has been reported for inert-gas nanoparticles in porous glasses, superheating has also been observed when the nanoparticles are embedded in some matrices. By using a simple classical approach, the influence of size, geometry and the matrix on the melting temperature of nanoparticles is understood quantitatively and shown to be applicable for other materials. It is also shown that the classical approach can be applied to understand the size-dependent freezing temperature of nanoparticles.