Violin string shape functions for finite element analysis of rotating Timoshenko beams

Violin strings are relatively short and stiff and are well modeled by Timoshenko beam theory. We use the static part of the homogeneous differential equation of violin strings to obtain new shape functions for the finite element analysis of rotating Timoshenko beams. For deriving the shape functions, the rotating beam is considered as a sequence of violin strings. The violin string shape functions depend on rotation speed and element position along the beam length and account for centrifugal stiffening effects as well as rotary inertia and shear deformation on dynamic characteristics of rotating Timoshenko beams. Numerical results show that the violin string basis functions perform much better than the conventional polynomials at high rotation speeds and are thus useful for turbo machine applications. (C) 2011 Elsevier B.V. All rights reserved.

Rotating anisotropic disc of uniform strength

A procedure to design a constant thickness composite disc of uniform strength by radially tailoring the anisotropic elastic constants is proposed. A special case of an isotropic disc with radially varying modulus is also examined. Analytical results are also compared with FEM calculations for two cases of radially varying anisotropy and for an isotropic disc with variable modulus. (C) 1999 Elsevier Science Ltd. All rights reserved.

Physics based basis function for vibration analysis of high speed rotating beams

The natural frequencies of continuous systems depend on the governing partial differential equation and can be numerically estimated using the finite element method. The accuracy and convergence of the finite element method depends on the choice of basis functions. A basis function will generally perform better if it is closely linked to the problem physics. The stiffness matrix is the same for either static or dynamic loading, hence the basis function can be chosen such that it satisfies the static part of the governing differential equation. However, in the case of a rotating beam, an exact closed form solution for the static part of the governing differential equation is not known. In this paper, we try to find an approximate solution for the static part of the governing differential equation for an uniform rotating beam. The error resulting from the approximation is minimized to generate relations between the constants assumed in the solution. This new function is used as a basis function which gives rise to shape functions which depend on position of the element in the beam, material, geometric properties and rotational speed of the beam. The results of finite element analysis with the new basis functions are verified with published literature for uniform and tapered rotating beams under different boundary conditions. Numerical results clearly show the advantage of the current approach at high rotation speeds with a reduction of 10 to 33% in the degrees of freedom required for convergence of the first five modes to four decimal places for an uniform rotating cantilever beam.

Zinc-substituted alpha-nickel hydroxide as an electrode material for alkaline secondary cells

Double hydroxides of the formula, Ni1-xZn2x (OH)(2) (CO3)(x). nH(2)O (x = 0.1 to 0.25) having the same structure as that of alpha-nickel hydroxide have been synthesized by partial substitution of zinc for nickel. The hydroxide having the composition x = 0.25 exhibits prolonged stability in 6 M KOH. Pasted electrodes comprising this material are rechargeable with a stabilized reversible discharge capacity of 410 +/- 15 mAh g(-1) of nickel even under suboptimal conditions of electrode fabrication. This compares favorably with the capacity values achieved for beta-nickel hydroxide (221 mAh g(-1)', This work; 297 mAh g(-1), Delahaye-Vidal and Figlarz;(1) 456 mAh g(-1), theoretical). (C) 1999 The Electrochemical Society. S0013-4651(98)01-071-4. All rights reserved.

MHD flow over a moving plate in a rotating fluid with magnetic field, Hall currents and free stream velocity

The non-similar boundary layer flow of a viscous incompressible electrically conducting fluid over a moving surface in a rotating fluid, in the presence of a magnetic field, Hall currents and the free stream velocity has been studied. The parabolic partial differential equations governing the flow are solved numerically using an implicit finite-difference scheme. The Coriolis force induces overshoot in the velocity profile of the primary flow and the magnetic field reduces/removes the velocity overshoot. The local skin friction coefficient for the primary flow increases with the magnetic field, but the skin friction coefficient for the secondary flow reduces it. Also the local skin friction coefficients for the primary and secondary flows are reduced due to the Hall currents. The effects of the magnetic field, Hall currents and the wall velocity, on the skin friction coefficients for the primary and secondary flows increase with the Coriolis force. The wall velocity strongly affects the flow field. When the wall velocity is equal to the free stream velocity, the skin friction coefficients for the primary and secondary flows vanish, but this does not imply separation. (C) 2002 Published by Elsevier Science Ltd.

Temperature profiles of accretion discs around rapidly rotating strange stars in general relativity: A comparison with neutron stars

We compute the temperature profiles of accretion discs around rapidly rotating strange stars, using constant gravitational mass equilibrium sequences of these objects, considering the full effect of general relativity. Beyond a certain critical value of stellar angular momentum (J), we observe the radius ( $r_{\rm orb}$) of the innermost stable circular orbit (ISCO) to increase with J (a property seen neither in rotating black holes nor in rotating neutron stars). The reason for this is traced to the crucial dependence of ${\rm d}r_{\rm orb}/{\rm d}J$ on the rate of change of the radial gradient of the Keplerian angular velocity at $r_{\rm orb}$ with respect to J. The structure parameters and temperature profiles obtained are compared with those of neutron stars, as an attempt to provide signatures for distinguishing between the two. We show that when the full gamut of strange star equation of state models, with varying degrees of stiffness are considered, there exists a substantial overlap in properties of both neutron stars and strange stars. However, applying accretion disc model constraints to rule out stiff strange star equation of state models, we notice that neutron stars and strange stars exclusively occupy certain parameter spaces. This result implies the possibility of distinguishing these objects from each other by sensitive observations through future X-ray detectors.

A study of shock wave interaction with a rotating cylinder

Shock wave reflection over a rotating circular cylinder is numerically and experimentally investigated. It is shown that the transition from the regular reflection to the Mach reflection is promoted on the cylinder surface which rotates in the same direction of the incident shock motion, whereas it is retarded on the surface that rotates to the reverse direction. Numerical calculations solving the Navier-Stokes equations using extremely fine grids also reveal that the reflected shock transition from RRdouble right arrowMR is either advanced or retarded depending on whether or not the surface motion favors the incident shock wave. The interpretation of viscous effects on the reflected shock transition is given by the dimensional analysis and from the viewpoint of signal propagation.

Asymmetric Warps in Disk Galaxies: Dependence on Dark Matter Halo

Recent observations have shown that most of the warps in the disk galaxies are asymmetric. However there exists no generic mechanism to generate these asymmetries in warps. We have shown that a rich variety of possible asymmetries in the z-distribution of the spiral galaxies can naturally arise due to a dynamical wave interference between the first two bending modes i.e. bowl-shaped mode(m=0) and S-shaped warping mode(m = 1) in the galactic disk embedded in a dark matter halo. We show that the asymmetric warps are more pronounced when the dark matter content within the optical disk is lower as in early-type galaxies.

On an oscillatory point force in a rotating stratified fluid

The forced oscillations due to a point forcing effect in an infinite or contained, inviscid, incompressible, rotating, stratified fluid are investigated taking into account the density variation in the inertia terms in the linearized equations of motion. The solutions are obtained in closed form using generalized Fourier transforms. Solutions are presented for a medium bounded by a finite cylinder when the oscillatory forcing effect is acting at a point on the axis of the cylinder. In both the unbounded and bounded case, there exist characteristic cones emanating from the point of application of the force on which either the pressure or its derivatives are discontinuous. The perfect resonance existing at certain frequencies in an unbounded or bounded homogeneous fluid is avoided in the case of a confined stratified fluid.

Lubricant Degradation and Related Wear of a Steel Pin in Lubricated Sliding Against a Steel Disc

In lubricated sliding contacts, components wear out and the lubricating oil ages with time. The present work explores the interactive influence between lubricant aging and component wear. The flat face of a steel pin is slid against a rotating steel disk under near isothermal conditions while the contact is immersed in a reservoir of lubricant (hexadecane). The chemical changes in the oil with time are measured by vibrational spectroscopy and gas chromatography. The corresponding chemistry of the pin surface is recorded using X-ray photoelectron spectroscopy while the morphology of the worn pins; surface and subsurface, are observed using a combination of focused ion beam milling and scanning electron 5 microscopy. When compared to thermal auto-oxidation of the lubricant alone, steel on steel friction and wear are found to accentuate the decomposition of oil and to reduce the beneficial impact of antioxidants. The catalytic action of nascent iron, an outcome of pin wear and disk wear, is shown to contribute to this detrimental effect. Over long periods of sliding, the decomposition products of lubricant aging on their own, as well as in conjunction with their products of reaction with iron, generate a thick tribofilm that is highly protective in terms of friction and wear.

Synthesis of cnt-metal oxide nano-composite electrode materials for supercapacitator by low-pressure mocvd

Homogeneous composite thin films of Fe2O3-carbon nanotube were synthesized in a novel, single-step process by metalorganic chemical vapor deposition (MOCVD) using ferric acetyl acetonate as precursor. The deposition of composite takes place in a narrow range of CVD conditions, beyond which the deposition either multiwall carbon nanotubes (MWNTs) only or hematite (α-Fe2O3) only takes place. The composite film formed on stainless steel substrates were tested for their supercapacitive properties in various aqueous electrolytes.

Unsteady mixed convection flow from a rotating vertical cone with a magnetic field

An analysis is developed to study the unsteady mixed convection flow over a vertical cone rotating in an ambient fluid with a time-dependent angular velocity in the presence of a magnetic field. The coupled nonlinear partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. The local skin friction coefficients in the tangential and azimuthal directions and the local Nusselt number increase with the time when the angular velocity of the-cone increases, but the reverse trend is observed for decreasing angular velocity. However, these are not mirror reflection of each other. The magnetic field reduces the skin friction coefficient in the tangential direction and also the Nusselt number, but it increases the skin friction coefficient in the azimuthal direction. The skin friction coefficients and the Nusselt number increase with the buoyancy force.

Unsteady MUD rotating flow over a rotating sphere near the equator

The unsteady rotating flow of a laminar incompressible viscous electrically conducting fluid over a rotating sphere in the vicinity of the equator has been studied. The fluid and the body rotate either in the same direction or in opposite directions. The effects of surface suction and magnetic field have been included in the analysis. There is an initial steady state that is perturbed by a sudden change in the rotational velocity of the sphere, and this causes unsteadiness in the flow field. The nonlinear coupled parabolic partial differential equations governing the boundary-layer flow have been solved numerically by using an implicit finite-difference scheme. For large suction or magnetic field, analytical solutions have also been obtained. The magnitude of the radial, meridional and rotational velocity components is found to be higher when the fluid and the body rotate in opposite directions than when they rotate in the same direction. The surface shear stresses in the meridional and rotational directions change sign when the ratio of the angular velocities of the sphere and the fluid lambda greater than or equal to lambda(0). The final (new) steady state is reached rather quickly which implies that the spin-up time is small. The magnetic field and surface suction reduce the meridional shear stress, but increase the surface shear stress in the rotational direction.