Closed-form solutions for axially functionally graded Timoshenko beams having uniform cross-section and fixed-fixed boundary condition

In this paper, we study the free vibration of axially functionally graded (AFG) Timoshenko beams, with uniform cross-section and having fixed-fixed boundary condition. For certain polynomial variations of the material mass density, elastic modulus and shear modulus, along the length of the beam, there exists a fundamental closed form solution to the coupled second order governing differential equations with variable coefficients. It is found that there are an infinite number of non-homogeneous Timoshenko beams, with various material mass density, elastic modulus and shear modulus distributions having simple polynomial variations, which share the same fundamental frequency. The derived results can be used as benchmark solutions for testing approximate or numerical methods used for the vibration analysis of non-homogeneous Timoshenko beams. They can also be useful for designing fixed-fixed non-homogeneous Timoshenko beams which may be required to vibrate with a particular frequency. (C) 2013 Elsevier Ltd. All rights reserved.

A Constitutive Equation for Grain Boundary Sliding: An Experimental Approach

Although grain boundary sliding (GBS) has been recognized as an important process during high-temperature deformation in crystalline materials, there is paucity in experimental data for characterizing a constitutive equation for GBS. High-temperature tensile creep experiments were conducted, together with measurements of GBS at different strains, stresses, grain sizes, and temperatures. Experimental data obtained on a Mg AZ31 alloy demonstrate that, for the first time, dynamic recrystallization during creep does not alter the contribution of GBS to creep during high-temperature deformation. The experimentally observed invariance of the sliding contribution with strain was used together with the creep data for developing a constitutive equation for GBS in a manner similar to the standard creep equation. Using this new approach, it is demonstrated that the stress, grain size, and temperature dependence for creep and GBS are identical. This is rationalized by a model based on GBS controlled by dislocations, within grains or near-grain boundaries. (C) The Minerals, Metals & Materials Society and ASM International 2013

Nearly Constant Switching Frequency Hysteresis Current Controller with Fast Online Computation of Boundary for a 2-Level Induction Motor Drive

A nearly constant switching frequency current hysteresis controller for a 2-level inverter fed induction motor drive is proposed in this paper: The salient features of this controller are fast dynamics for the current, inherent protection against overloads and less switching frequency variation. The large variation of switching frequency as in the conventional hysteresis controller is avoided by defining a current-error boundary which is obtained from the current-error trajectory of the standard space vector PWM. The current-error boundary is computed at every sampling interval based on the induction machine parameters and from the estimated fundamental stator voltage. The stator currents are always monitored and when the current-error exceeds the boundary, voltage space vector is switched to reduce the current-error. The proposed boundary computation algorithm is applicable in linear and over-modulation region and it is simple to implement in any standard digital signal processor: Detailed experimental verification is done using a 7.5 kW induction motor and the results are given to show the performance of the drive at various operating conditions and validate the proposed advantages.

Transmission of elastic waves through a frictional boundary

Incident energy gets transmitted, reflected and absorbed across an interface in jointed rock mass leading to energy dissipation and alteration of waves. Wave velocities get attenuated during their propagation across joints and this behavior is studied using bender/extender element tests. The velocity attenuation and modulus reduction observed in experimental tests are modeled with three dimensional distinct element code and results are validated. Normal propagation of an incident shear wave through a jointed rock mass cause slip of the rock blocks if shear stress of wave exceeds the shear strength of the joint. As the properties of joint determine the transmission of energy across an interface, a parametric study is then conducted with the validated numerical model by varying the parameters that may determine the energy transmission across a joint using modified Miller's method. Results of the parametric study are analyzed and presented in the paper. (C) 2014 Elsevier Ltd. All rights reserved.

Enhancing the high temperature plasticity of a Cu-containing austenitic stainless steel through grain boundary strengthening

The addition of 3 wt% Cu to heat-resistant SUS 304H austenitic steel enhances its high temperature mechanical properties. To further improve the properties, particularly the creep resistance and ductility at high temperatures, a post-solutionizing heat-treatment method that involves an intermediated annealing either at 700 or 800 degrees C after solutionizing for durations up to 180 min was employed. The purpose this heat-treatment is to precipitate planar Cr23C6 at the grain boundaries, which results in the boundaries getting serrated. Detailed microstructural analyses of these `grain boundary engineered' alloys was conducted and their mechanical performance, both at room temperature and at 750 degrees C, was evaluated. While the grain size and texture are unaffected due to the high temperature hold, the volume fraction of Sigma 3 twin boundaries was found to increase significantly. While the strength enhancement was only marginal, the ductility was found to increase significantly, especially at high temperature. A marked increase in the creep resistance was also noted, which is attributed to the reduction of the grain boundary sliding by the grain boundary serrations and the suppression of grain boundary cavitation through the optimization of the volume fraction and spacing of the Cr23C6 precipitates. The special heat-treatment performed with holding time of 3 h at 700 degrees C resulted in the optimum combination of strength, ductility and creep resistance at high temperature. (C) 2014 Elsevier B.V. All rights reserved.

SODAR observations of inertia- gravity waves in the atmospheric boundary layer during the passage of tropical cyclone

This study reports characteristics of inertia-gravity waves (IGWs) in the atmospheric boundary layer during the passage of Tropical Cylone-03B, using the Doppler Sound Detection and Ranging (SODAR) observations at the Indian tropical station of Gadanki (13.45 degrees N, 79.2 degrees E; near the east coast of India). Wavelet analysis of horizontal winds indicates significant wave motion (60h) near the characteristic inertial period. The hodograph analysis of the filtered winds shows an anti-cyclonic turning of horizontal wind with height and time, indicating the presence of IGW. This study finds important implications in boundary layer dynamics during the passage of tropical cyclones.

Hysteresis current controller for a general n-level inverter fed drive with online current error boundary computation and nearly constant switching frequency

A space vector-based hysteresis current controller for any general n-level three phase inverter fed induction motor drive is proposed in this study. It offers fast dynamics, inherent overload protection and low harmonic distortion for the phase voltages and currents. The controller performs online current error boundary calculations and a nearly constant switching frequency is obtained throughout the linear modulation range. The proposed scheme uses only the adjacent voltage vectors of the present sector, similar to space vector pulse-width modulation and exhibits fast dynamic behaviour under different transient conditions. The steps involved in the boundary calculation include the estimation of phase voltages from the current ripple, computation of switching time and voltage error vectors. Experimental results are given to show the performance of the drive at various speeds, effect of sudden change of the load, acceleration, speed reversal and validate the proposed advantages.

Scaling of pressure spectrum in turbulent boundary layers

Scaling of pressure spectrum in zero-pressure-gradient turbulent boundary layers is discussed. Spatial DNS data of boundary layer at one time instant (Re-theta = 4500) are used for the analysis. It is observed that in the outer regions the pressure spectra tends towards the -7/3 law predicted by Kolmogorov's theory of small-scale turbulence. The slope in the pressure spectra varies from -1 close to the wall to a value close to -7/3 in the outer region. The streamwise velocity spectra also show a -5/3 trend in the outer region of the flow. The exercise carried out to study the amplitude modulation effect of the large scales on the smaller ones in the near-wall region reveals a strong modulation effect for the streamwise velocity, but not for the pressure fluctuations. The skewness of the pressure follows the same trend as the amplitude modulation coefficient, as is the case for the velocity. In the inner region, pressure spectra were seen to collapse better when normalized with the local Reynolds stress (-(u'v') over bar) than when scaled with the local turbulent kinetic energy (q(2) = (u'(2)) over bar + (v'(2)) over bar + (w'(2)) over bar)

Suppression of grain boundary relaxation in Zr-doped BiFeO3 thin films

Here, we present the results of temperature dependent dielectric studies on chemical solution processed Zr-doped BiFeO3 (BFO) thin films deposited on Pt/Si substrates. We find that in contrast to the undoped BFO films, Zr doping at Fe-site suppresses the low frequency dielectric relaxation originating from the grain boundaries, attributed to the increased dipolar rigidity due to stronger Zr-O bonds. Temperature dependent dc conductivity obtained from impedance and modulus analyses shows two distinct conduction processes occurring inside the grains. At temperature below similar to 423K, conductivity is nearly temperature independent, while in the high temperature regime (above similar to 423K), conduction is governed by the long range movement of oxygen vacancies with an activation energy of similar to 1eV. (C) 2014 AIP Publishing LLC.

Shock tunnel experiments on control of shock induced large separation bubble using boundary layer bleed

Shock-Boundary Layer Interaction (SBLI) often occurs in supersonic/hypersonic flow fields. Especially when accompanied by separation (termed strong interaction), the SBLI phenomena largely affect the performance of the systems where they occur, such as scramjet intakes, thus often demanding the control of the interaction. Experiments on the strong interaction between impinging shock wave and boundary layer on a flat plate at Mach 5.96 are carried out in IISc hypersonic shock tunnel HST-2. The experiments are performed at moderate flow total enthalpy of 1.3 MJ/kg and freestream Reynolds number of 4 million/m. The strong shock generated by a wedge (or shock generator) of large angle 30.96 degrees to the freestream is made to impinge on the flat plate at 95 mm (inviscid estimate) from the leading edge, due to which a large separation bubble of length (75 mm) comparable to the distance of shock impingement from the leading edge is generated. The experimental simulation of such large separation bubble with separation occurring close to the leading edge, and its control using boundary layer bleed (suction and tangential blowing) at the location of separation, are demonstrated within the short test time of the shock tunnel (similar to 600 mu s) from time resolved schlieren flow visualizations and surface pressure measurements. By means of suction - with mass flow rate one order less than the mass flow defect in boundary layer - a reduction in separation length by 13.33% was observed. By the injection of an array of (nearly) tangential jets in the direction of mainstream (from the bottom of the plate) at the location of separation - with momentum flow rate one order less than the boundary layer momentum flow defect - 20% reduction in separation length was observed, although the flow field was apparently unsteady. (C) 2014 Elsevier Masson SAS. All rights reserved.

Studies and Evaluation of EIT Image Reconstruction in EIDORS with Simulated Boundary Data

Simulated boundary potential data for Electrical Impedance Tomography (EIT) are generated by a MATLAB based EIT data generator and the resistivity reconstruction is evaluated with Electrical Impedance Tomography and Diffuse Optical Tomography Reconstruction Software (EIDORS). Circular domains containing subdomains as inhomogeneity are defined in MATLAB-based EIT data generator and the boundary data are calculated by a constant current simulation with opposite current injection (OCI) method. The resistivity images reconstructed for different boundary data sets and images are analyzed with image parameters to evaluate the reconstruction.

Boundary perturbations and the Helmholtz equation in three dimensions

We propose an analytic perturbative scheme in the spirit of Lord Rayleigh's work for determining the eigenvalues of the Helmholtz equation in three dimensions inside an arbitrary boundary where the eigenfunction satisfies either the Dirichlet boundary condition or the Neumann boundary condition. Although numerous works are available in the literature for arbitrary boundaries in two dimensions, to the best of our knowledge the formulation in three dimensions is proposed for the first time. In this novel prescription, we have expanded the arbitrary boundary in terms of spherical harmonics about an equivalent sphere and obtained perturbative closed-form solutions at each order for the problem in terms of corrections to the equivalent spherical boundary for both the boundary conditions. This formulation is in parallel with the standard time-independent Rayleigh-Schrodinger perturbation theory. The efficacy of the method is tested by comparing the perturbative values against the numerically calculated eigenvalues for spheroidal, superegg and superquadric shaped boundaries. It is shown that this perturbation works quite well even for wide departure from spherical shape and for higher excited states too. We believe this formulation would find applications in the field of quantum dots and acoustical cavities.

Optimal error estimate using mesh equidistribution technique for singularly perturbed system of reaction-diffusion boundary-value problems

In this article, we study the problem of determining an appropriate grading of meshes for a system of coupled singularly perturbed reaction-diffusion problems having diffusion parameters with different magnitudes. The central difference scheme is used to discretize the problem on adaptively generated mesh where the mesh equation is derived using an equidistribution principle. An a priori monitor function is obtained from the error estimate. A suitable a posteriori analogue of this monitor function is also derived for the mesh construction which will lead to an optimal second-order parameter uniform convergence. We present the results of numerical experiments for linear and semilinear reaction-diffusion systems to support the effectiveness of our preferred monitor function obtained from theoretical analysis. (C) 2014 Elsevier Inc. All rights reserved.

Analogous stress and electric field driven structural transformation and decrease in polarization coherence on poling around the morphotropic phase boundary in BiScO3-PbTiO3

The nature of the stress and electric field driven structural and microstructural transformations in the morphotropic phase boundary (MPB) compositions of the high Curie point piezoelectric system BiScO3-PbTiO3 has been examined by ex situ based techniques. Using a powder poling technique, which is based on the concept of exploiting the irreversible structural change that occurs after the application of a strong electric field and stress independently, it was possible to ascertain that both moderate stress and electric field induce identical structural transformation-a fraction of the monoclinic phase transforms irreversibly to the tetragonal phase. Moreover, analysis of the dielectric response before and after poling revealed a counterintuitive phenomenon of poling induced decrease in the spatial coherence of polarization for compositions around the MPB and not so for compositions far away from the MPB range. Exploiting the greater sensitivity of this technique, we demonstrate that the criticality associated with the interferroelectric transition spans a wider composition range than what is conventionally reported in the literature based on bulk x-ray/neutron powder diffraction techniques.

Investigation of the separated region ahead of three-dimensional protuberances on plates and cones in hypersonic flows with laminar boundary layers

Heat transfer rate and pressure measurements were made upstream of surface pro-tuberances on a flat plate and a sharp cone subjected to hypersonic flow in a conventional shock tunnel. Heat flux was measured using platinum thin-film sensors deposited on macor substrate and the pressure measurements were made using fast acting piezoelectric sensors. A distinctive hot spot with highest heat flux was obtained near the foot of the protuberance due to heavy vortex activity in the recirculating region. Schlieren flow visualization was used to capture the shock structures and the separation distance ahead of the protrusions was quantitatively measured for varying protuberance heights. A computational analysis was conducted on the flat plate model using commercial computational fluid dynamics software and the obtained trends of heat flux and pressure were compared with the experimental observation. Experiments were also conducted by physically disturbing the laminar boundary layer to check its effect on the magnitude of the hot spot heat flux. In addition to air, argon was also used as test gas so that the Reynolds number can be varied. (C) 2014 AIP Publishing LLC.