Modal tailoring and closed-form solutions for rotating non-uniform Euler-Bernoulli beams

In this paper, the free vibration of a rotating Euler-Bernoulli beam is studied using an inverse problem approach. We assume a polynomial mode shape function for a particular mode, which satisfies all the four boundary conditions of a rotating beam, along with the internal nodes. Using this assumed mode shape function, we determine the linear mass and fifth order stiffness variations of the beam which are typical of helicopter blades. Thus, it is found that an infinite number of such beams exist whose fourth order governing differential equation possess a closed form solution for certain polynomial variations of the mass and stiffness, for both cantilever and pinned-free boundary conditions corresponding to hingeless and articulated rotors, respectively. A detailed study is conducted for the first, second and third modes of a rotating cantilever beam and the first and second elastic modes of a rotating pinned-free beam, and on how to pre-select the internal nodes such that the closed-form solutions exist for these cases. The derived results can be used as benchmark solutions for the validation of rotating beam numerical methods and may also guide nodal tailoring. (C) 2014 Elsevier Ltd. All rights reserved.

Direct correlation between non-random distribution of cations and ion transport mechanism in soda-lime silicate glasses

We report a direct correlation between dissimilar ion pair formation and alkali ion transport in soda-lime silicate glasses established via broad band conductivity spectroscopy and local structural probe techniques. The combined Raman and Nuclear Magnetic Resonance (NMR) spectroscopy techniques on these glasses reveal the coexistence of different anionic species and the prevalence of Na+-Ca2+ dissimilar pairs as well as their distributions. The spectroscopic results further confirm the formation of dissimilar pairs atomistically, where it increases with increasing alkaline-earth oxide content These results, are the manifestation of local structural changes in the silicate network with composition which give rise to different environments into which the alkali ions hop. The Na+ ion mobility varies inversely with dissimilar pair formation, i.e. it decreases with increase of non-random formation of dissimilar pairs. Remarkably, we found that increased degree of non-randomness leads to temperature dependent variation in number density of sodium ions. Furthermore, the present study provides the strong link between the dynamics of the alkali ions and different sites associated with it in soda-lime silicate glasses. (C) 2014 Elsevier B.V. All rights reserved.

Non-uniform beams and stiff strings isospectral to axially loaded uniform beams and piano strings

In this paper, we derive analytical expressions for mass and stiffness functions of transversely vibrating clamped-clamped non-uniform beams under no axial loads, which are isospectral to a given uniform axially loaded beam. Examples of such axially loaded beams are beam columns (compressive axial load) and piano strings (tensile axial load). The Barcilon-Gottlieb transformation is invoked to transform the non-uniform beam equation into the axially loaded uniform beam equation. The coupled ODEs involved in this transformation are solved for two specific cases (pq (z) = k (0) and q = q (0)), and analytical solutions for mass and stiffness are obtained. Examples of beams having a rectangular cross section are shown as a practical application of the analysis. Some non-uniform beams are found whose frequencies are known exactly since uniform axially loaded beams with clamped ends have closed-form solutions. In addition, we show that the tension required in a stiff piano string with hinged ends can be adjusted by changing the mass and stiffness functions of a stiff string, retaining its natural frequencies.

Two-level Mapping Based Cache Index Selection for Packet Forwarding Engines

Packet forwarding is a memory-intensive application requiring multiple accesses through a trie structure. The efficiency of a cache for this application critically depends on the placement function to reduce conflict misses. Traditional placement functions use a one-level mapping that naively partitions trie-nodes into cache sets. However, as a significant percentage of trie nodes are not useful, these schemes suffer from a non-uniform distribution of useful nodes to sets. This in turn results in increased conflict misses. Newer organizations such as variable associativity caches achieve flexibility in placement at the expense of increased hit-latency. This makes them unsuitable for L1 caches.We propose a novel two-level mapping framework that retains the hit-latency of one-level mapping yet incurs fewer conflict misses. This is achieved by introducing a secondlevel mapping which reorganizes the nodes in the naive initial partitions into refined partitions with near-uniform distribution of nodes. Further as this remapping is accomplished by simply adapting the index bits to a given routing table the hit-latency is not affected. We propose three new schemes which result in up to 16% reduction in the number of misses and 13% speedup in memory access time. In comparison, an XOR-based placement scheme known to perform extremely well for general purpose architectures, can obtain up to 2% speedup in memory access time.

Optical, electrochemical and morphological investigations of poly (3,4-propylenedioxythiophene)-sultone (PProDOT-S) thin films

In this paper, we have carried out thin film characterization of poly(3,4-propylenedioxythiophene)-sultone (PProDOT-S), a derivative of electrochromic poly(3,4-propylenedioxythiophene) (PProDOT). PProDOT-S was deposited onto transparent conducting oxide coated glass substrates by solution casting method. Single wavelength spectrophotometry is used to monitor the switching speed and contrast ratio at maximum wavelength (lambda (max)). The percentage transmittance at the lambda (max) of the neutral polymer is monitored as a function of time when the polymer film is repeatedly switched. This experiment gives a quantitative measure of the speed with which a film is able to switch between the two states i.e. the coloured and the bleached states. PProDOT-S films were switched at a voltage of 1 center dot 9 V with a switching speed of 2 s at lambda (max) of 565 nm and showed a contrast of similar to 37%. Cyclic voltammetry performed at different scan rates have shown the characteristic anodic and cathodic peaks. The structural investigations of PProDOT-S films by IR spectra were in good agreement with previously reported results. Raman spectra of PProDOT-S showed a strong Raman peak at 1509 cm (-aEuro parts per thousand 1) and a weak peak at 1410 cm (-aEuro parts per thousand 1) due to the C = C asymmetric and symmetric stretching vibrations of thiophene rings. The morphological investigations carried out by using scanning electron microscope (SEM) of polymer films have shown that these polymers are found to be arranged in dense packed clusters with non-uniform distribution having an average width and length of 95 nm and 160 nm, respectively.

Study Of Fluid-Flow And Residence-Time Distribution In A Continuous Slab Casting Mold

The fluid-flow pattern and residence-time distribution (r.t.d.) of the fluid in a continuous casting mould have been studied using a water model. The two recirculating zones below the discharge ports have been found to be asymmetric. The effect of casting speed, discharge port diameter, shroud well depth and the immersion depth on r.t.d. have been investigated. The r.t.d. curve has been well represented by a model of two backmix cells of equal volume in series. The exist of the fluid has been found to be non-uniform across the cross-section of the mould. The fluid-flow pattern has been observed to change with time in a random fashion. Dead volume of upto 31.8% has been found with smaller discharge ports.

Field-dependent changeover from current-to voltage-limiting characteristics by non-linear n-type BaTiO3 ceramics

Non-linear resistors having current-limiting capabilities at lower field strengths, and voltage-limiting characteristics (varistors) at higher field strengths, were prepared from sintered polycrystalline ceramics of (Ba0.6Sr0.4)(Ti0.97Zr0.03)O3+0.3 at % La, and reannealed after painting with low-melting mixtures of Bi2O3 + PbO +B2O3. These types of non-linear characteristics were found to depend upon the non-uniform diffusion of lead and the consequent distribution of Curie points (T c) in these perovskites, resulting in diffuse phase transitions. Tunnelling of electrons across the asymmetric barrier at tetragonak-cubic interfaces changes to tunnelling across the symmetric barrier as the cubic phase is fully stabilized through Joule heating at high field strengths. Therefore the current-limiting characteristics switch over to voltage-limiting behaviour because tunnelling to acceptor-type mid-bandgap states gives way to band-to-band tunnelling.

Study of temperature distribution along an artificially polluted insulator string

Insulator becomes wet partially or completely, and the pollution layer on it becomes conductive, when collecting pollutants for an extended period during dew, light rain, mist, fog or snow melting. Heavy rain is a complicated factor that it may wash away the pollution layer without initiating other stages of breakdown or it may bridge the gaps between sheds to promote flashover. The insulator with a conducting pollution layer being energized, can cause a surface leakage current to flow (also temperature-rise). As the surface conductivity is non-uniform, the conducting pollution layer becomes broken by dry bands (at spots of high current density), interrupting the flow of leakage current. Voltage across insulator gets concentrated across dry bands, and causes high electric stress and breakdown (dry band arcing). If the resistance of the insulator surface is sufficiently low, the dry band arcs can be propagated to bridge the terminals causing flashover. The present paper concerns the evaluation of the temperature distribution along the surface of an energized artificially polluted insulator string.

Transient electric field distribution within the working volume of an NEMP simulator

Nuclear electro-magnetic pulse (NEMP) simulators which are used in the simulation of transient electromagnetic fields due to a high altitude nuclear detonation are generally excited with a double exponential high voltage pulse. This results in a current distribution on the wires of the simulator and hence a transient electric field in the working volume of the simulator where the test object is kept. It is found that for the simulator under study, the current distribution is non-uniform and so is the field distribution along the width of the simulator in the working volume. To make the current distribution uniform, several methods have been suggested and the results of these methods are analyzed and suitable conclusions are arrived at from those results.

Some Exact-Solutions Describing Unsteady Plane Gas-Flows With Shocks

A new class of exact solutions of plane gasdynamic equations is found which describes piston-driven shocks into non-uniform media. The governing equations of these flows are taken in the coordinate system used earlier by Ustinov, and their similarity form is determined by the method of infinitesimal transformations. The solutions give shocks with velocities which either decay or grown in a finite or infinite time depending on the density distribution in the ambient medium, although their strength remains constant. The results of the present study are related to earlier investigations describing the propagation of shocks of constant strength into non-uniform media.

Korteweg-De Vries Equation for Non-Linear Ion-Acoustic Waves in a Plasma with Negative Ions

The theoretical analysis, based on the perturbation technique, of ion-acoustic waves in the vicinity of a Korteweg-de Vries (K-dV) equation derived in a plasma with some negative ions has been made. The investigation shows that the negative ions in plasma with isothermal electrons introduced a critical concentration at which the ion-acoustic wave plays an important role of wave-breaking and forming a precursor while the plasma with non-isothermal electrons has no such singular behaviour of the wave. These two distinct features of ion waves lead to an overall different approach of present study of ion-waves. A distinct feature of non-uniform transition from the nonisothermal case to isothermal case has been shown. Few particular plasma models have been chosen to show the characteristics behaviour of the ion-waves existing in different cases

Limit analysis of rectangular R.C. slabs on ground

A method is presented for obtaining lower bound on the carrying capacity of reinforced concrete foundation slab-structures subject to non-uniform contact pressure distributions. Functional approach suggested by Vallance for simply supported square slabs subject to uniform pressure distribution has been extended to simply supported rectangular slabs subject to symmetrical non-uniform pressure distributions. Radial solutions, ideally suited for rotationally symmetric problems, are shown to be adoptable for regular polygonal slabs subject to contact pressure paraboloids with constant edge pressures. The functional approach has been shown to be well suited even when the pressure is varying along the edges.

Phase-shift randomness in one-dimensional disordered conductors in the quasi-metallic domain

An invariant imbedding method yields exact analytical results for the distribution of the phase theta (L) of the reflection amplitude and for low-order resistance moments (pn) for a disordered conductor of length L in the quasi-metallic regime L<distribution of theta is significantly non-uniform only for sufficiently small values (

A Novel Method for the Uniform Incorporation of Grain-Boundary Layer Modifiers in Positive Temperature Coefficient of Resistivity Barium Titanate

The presently developed two-stage process involves diping the prefired porous disks of n-BaTiO3 in nonaqueous solutions containing Al-buty rate, Ti-isopropoxide, and tetraethyl silicate and subsequent sintering. This leads to uniform distribution of the grain-boundary layer (GBL) modifiers (Al2O3+ TiO2+ SiO2) and better control of the grain size as well as the positive temperature coefficient of resistivity characteristics. The technique is particularly suited for GBL modifiers in low concentrations (< 1%).