Much ado about shear correction factors in Timoshenko beam theory

AbstractMany shear correction factors have appeared since the inception of Timoshenko beam theory in 1921. While rational bases for them have been offered, there continues to be some reluctance to their full acceptance because the explanations are not totally convincing and their efficacies have not been comprehensively evaluated over a range of application. Herein, three-dimensional static and dynamic information and results for a beam of general (both symmetric and non-symmetric) cross-section are brought to bear on these issues. Only homogeneous, isotropic beams are considered. Semi-analytical finite element (SAFE) computer codes provide static and dynamic response data for our purposes. Greater clarification of issues relating to the bases for shear correction factors can be seen. Also, comparisons of numerical results with Timoshenko beam data will show the effectiveness of these factors beyond the range of application of elementary (Bernoulli–Euler) theory.An issue concerning principal shear axes arose in the definition of shear correction factors for non-symmetric cross-sections. In this method, expressions for the shear energies of two transverse forces applied on the cross-section by beam and three-dimensional elasticity theories are equated to determine the shear correction factors. This led to the necessity for principal shear axes. We will argue against this concept and show that when two forces are applied simultaneously to a cross-section, it leads to an inconsistency. Only one force should be used at a time, and two sets of calculations are needed to establish the shear correction factors for a non-symmetrical cross-section

End reflections in a layered piezoelectric circular cylinder

AbstractEnd reflection phenomenon in a semi-infinitely long layered piezoelectric circular cylinder is constructed with modal data from a spectral decomposition of the differential operator governing its natural vibrations. These modal data consist of all propagating modes and edge vibrations and they constitute the basis for a wave function expansion of the reflection of waves arriving at the traction-free end of the cylinder. Without any other external stimulus, a passive reflection event occurs. This traction-free end condition is enforced at the Gaussian integration points over the end cross-section on the combination of incoming and reflected wave fields. Reflections due to monochromatic incoming axisymmetric (m=0) and flexural (m=1) waves are studied and two numerical examples are presented.For an incoming axisymmetric wave, there is a particular frequency that induces an end resonance, which is characterized by high (but finite) amplitudes of end displacements vis-a-vis those of neighboring (i.e., slightly different) frequencies. This phenomenon is illustrated in the two cylinder examples.It is possible to modify the passive reflection event by imposing some voltage distribution over the free end. For an oscillating end voltage that is out-of-phase with the incoming wave, it is possible to extract electrical energy from it, i.e., energy harvesting. Examples of such an oscillating voltage with a particular radial distribution are given, that illustrate the amount of extracted energy as a function of the frequency of the incident monochromatic wave

Magnetocapacitive La0.6Sr0.4MnO3 0.7Pb(Mg0.33Nb0.67)O3 0.3PbTiO3 epitaxial heterostructures

Epitaxial heterostructures of La0.6Sr0.4MnO3 0.7Pb(Mg0.33Nb0.67)O3 0.3PbTiO3 were fabricated on LaNiO3 coated LaAlO3 (100) substrates by pulsed laser ablation. Ferromagnetic and ferroelectric hysteresis established their biferroic nature. Dielectric behviour studied under different magnetic fields over a wide range of frequency and temperatures revealed that the capacitance in these heterostructures varies with the applied magnetic field. Appearance of magnetocapacitance and its dependence on magnetic fields, magnetic layer thickness, temperature and frequency indicated a combined contribution of strain mediated magnetoelectric coupling, magnetoresistance of the magnetic layer and Maxwell Wagner effect on the observed properties

Electronic Structure and Optical Properties of the Co-doped Anatase TiO2_{2} Studied from First Principles

The Co-doped anatase TiO$_{2}$, a recently discovered room-temperature ferromagnetic insulator, has been studied by the first-principles calculations in the pseudo-potential plane-wave formalism within the local-spin-density approximation (LSDA), supplemented by the full-potential linear augmented plane wave (FP-LAPW) method. Emphasis is placed on the dependence of its electronic structures and linear optical properties on the Co-doping concentration and oxygen vacancy in the system in order to pursue the origin of its ferromagnetism. In the case of substitutional doping of Co for Ti, our calculated results are well consistent with the experimental data, showing that Co is in its low spin state. Also, it is shown that the oxygen vacancy enhances the ferromagnetism and has larger effect on both the electronic structure and optical properties than the Co-doping concentration only.Comment: 12 pages, 4 figure

Efficient scheme for one-way quantum computing in thermal cavities

We propose a practical scheme for one-way quantum computing based on efficient generation of 2D cluster state in thermal cavities. We achieve a controlled-phase gate that is neither sensitive to cavity decay nor to thermal field by adding a strong classical field to the two-level atoms. We show that a 2D cluster state can be generated directly by making every two atoms collide in an array of cavities, with numerically calculated parameters and appropriate operation sequence that can be easily achieved in practical Cavity QED experiments. Based on a generated cluster state in Box$^{(4)}$ configuration, we then implement Grover's search algorithm for four database elements in a very simple way as an example of one-way quantum computing.Comment: 6 pages, 3 figure

Current and Spin-Torque in Double Tunnel Barrier Ferromagnet - Superconductor - Ferromagnet Systems

We calculate the current and the spin-torque in small symmetric double tunnel barrier ferromagnet - superconductor - ferromagnet (F-S-F) systems. Spin-accumulation on the superconductor governs the transport properties when the spin-flip relaxation time is longer than the transport dwell time. In the elastic transport regime, it is demonstrated that the relative change in the current (spin-torque) for F-S-F systems equals the relative change in the current (spin-torque) for F-N-F systems upon changing the relative magnetization direction of the two ferromagnets. This differs from the results in the inelastic transport regime where spin-accumulation suppresses the superconducting gap and dramatically changes the magnetoresistance [S. Takahashi, H. Imamura, and S. Maekawa, Phys. Rev. Lett. 82, 3911 (1999)]. The experimental relevance of the elastic and inelastic transport regimes, respectively, as well as the reasons for the change in the transport properties are discussed.Comment: 7 page

Magnetism in Dense Quark Matter

We review the mechanisms via which an external magnetic field can affect the ground state of cold and dense quark matter. In the absence of a magnetic field, at asymptotically high densities, cold quark matter is in the Color-Flavor-Locked (CFL) phase of color superconductivity characterized by three scales: the superconducting gap, the gluon Meissner mass, and the baryonic chemical potential. When an applied magnetic field becomes comparable with each of these scales, new phases and/or condensates may emerge. They include the magnetic CFL (MCFL) phase that becomes relevant for fields of the order of the gap scale; the paramagnetic CFL, important when the field is of the order of the Meissner mass, and a spin-one condensate associated to the magnetic moment of the Cooper pairs, significant at fields of the order of the chemical potential. We discuss the equation of state (EoS) of MCFL matter for a large range of field values and consider possible applications of the magnetic effects on dense quark matter to the astrophysics of compact stars.Comment: To appear in Lect. Notes Phys. "Strongly interacting matter in magnetic fields" (Springer), edited by D. Kharzeev, K. Landsteiner, A. Schmitt, H.-U. Ye

Azimuthal anisotropy and correlations in p+p, d+Au and Au+Au collisions at 200 GeV

We present the first measurement of directed flow ($v_1$) at RHIC. $v_1$ is found to be consistent with zero at pseudorapidities $\eta$ from -1.2 to 1.2, then rises to the level of a couple of percent over the range $2.4 < |\eta| < 4$. The latter observation is similar to data from NA49 if the SPS rapidities are shifted by the difference in beam rapidity between RHIC and SPS. Back-to-back jets emitted out-of-plane are found to be suppressed more if compared to those emitted in-plane, which is consistent with {\it jet quenching}. Using the scalar product method, we systematically compared azimuthal correlations from p+p, d+Au and Au+Au collisions. Flow and non-flow from these three different collision systems are discussed.Comment: Quark Matter 2004 proceeding, 4 pages, 3 figure

Azimuthal anisotropy: the higher harmonics

We report the first observations of the fourth harmonic (v_4) in the azimuthal distribution of particles at RHIC. The measurement was done taking advantage of the large elliptic flow generated at RHIC. The integrated v_4 is about a factor of 10 smaller than v_2. For the sixth (v_6) and eighth (v_8) harmonics upper limits on the magnitudes are reported.Comment: 4 pages, 6 figures, contribution to the Quark Matter 2004 proceeding