Approximation of the vibration modes of a Timoshenko curved rod of arbitrary geometry

Rodolfo Rodríguez ^{The aim of this paper is to analyse a mixed finite-element methodfor computing the vibration modes of a Timoshenko curved rodwith arbitrary geometry. Optimal order error estimates are provedfor displacements, rotations and shear stresses of the vibrationmodes, as well as a double order of convergence for the vibrationfrequencies. These estimates are essentially independent ofthe thickness of the rod, which leads to the conclusion thatthe method is locking-free. Numerical tests are reported inorder to assess the performance of the method.}     

Chiral effects in uniformly loaded rods

Examples of chiral materials include some auxetic materials, bones, some honeycomb structures, as well as composites with inclusions. The chiral effects cannot be described within classical elasticity. In the context of the linear theory of Cosserat elastic solids, we investigate the deformation of a chiral rod subjected to tractions on the lateral surface, to body loads, and to resultant forces and moments on the ends. The work is motivated by the recent interest in the using of the Cosserat elastic solid as model for auxetic composites, carbon nanotubes and bones. The three-dimensional problem is reduced to the study of some generalized plane strain problems. New chiral effects are presented. In the case of cylinders of arbitrary cross-section, the flexure produced by a transversal force, in contrast with the case of achiral materials, is accompanied by extension and bending by terminal couples. The body loads and the tractions on the lateral surface produce extension, flexure, torsion, bending by terminal couples and a plane strain. It is shown that a uniform pressure acting on the lateral surface of a chiral circular cylinder does not produce bending effects.     

Compression of a suspension of helical Yukawa rods

ABSTRACT

We present a Monte Carlo simulation study of the compression of helical Yukawa rods under isobaric conditions. The model is a chiral liquid crystal mesogen, which mimics, for instance, cellulose nanocrystals. It has several parameters (e.g. surface charge and internal pitch), which influence the compression route and the final structure. The strongest dependence of the structure of the condensed phase is found for the internal pitch of the charge helix: decreasing the internal pitch reduces the maximum density under otherwise equal conditions.     

Controlling growth of ZnO rods by polyvinylpyrrolidone (PVP) and their optical properties

ZnO rods with different morphologies were synthesized through a wet chemical method by addition of polyvinylpyrrolidone (PVP). By adjusting the concentration of the additive in the growth solution, we can control the diameter, ratio of length to diameter and density of ZnO rods. FESEM images showed that the rods in nanoscale could be obtained at the polyvinylpyrrolidone concentration of 1.0 mM. Meanwhile, the resonant Raman scattering and photoluminescence spectra showed that the crystalline quality and the optical property of ZnO rods were improved through moderate addition of polyvinylpyrrolidone (concentration of 1.0 mM) in the growth solution. In addition, the possible mechanism of the PVP effect on the growth of ZnO rods was discussed based on the FT-IR spectra.     

二维三角柱光子晶体的传输特性

利用时域有限差分方法对二维三角介质柱光子晶体的传输特性进行了研究,计算了不同晶格、同一晶格柱体截面面积不同、放置方位角不同、入射波入射方向不同时光子晶体的传输特性。结果表明:光子禁带的宽度与中心频率和晶格结构有很大关系,三角晶格更易形成平坦光子禁带,柱体截面面积大,则形成的禁带较宽,在其他因素相同的条件下柱体放置的方位角在一定范围内对光子禁带有重要影响;对不同入射方向时光子晶体的传输特性的研究结果表明,在低频范围内,入射角对禁带宽度和中心频率没有任何影响,在高频段,透射率随入射角变大而降低。研究结果为实验上制作三角柱光子晶体器件提供了重要的理论依据。     

Equilibrium state of a classical fluid of hard rods in an external field

The external field required to produce a given density pattern is obtained explicitly for a classical fluid of hard rods. All direct correlation functions are shown to be of finite range in all pairs of variables. The one-sided factors of the pair direct correlation are also found to be of finite range.Supported in part by U.S. ERDA, Contract No. E(11-1)-3077.     

Limiting polytope geometry for rigid rods,disks, and spheres

The available configuration space for finite systems of rigid particles separates into equivalent disconnected regions if those systems are highly compressed. This paper presents a study of the geometric properties of the limiting high-compression regions (polytopes) for rods, disks, and spheres. The molecular distribution functions represent cross sections through the convex polytopes, and for that reason they are obliged to exhibit single-peak behavior by the Brünn-Minkowski inequality. We demonstrate that increasing system dimensionality implies tendency toward nearest-neighbor particle-pair localization away from contact. The relation between the generalized Euler theorem for the limiting polytopes and cooperative jamming of groups of particles is explored. A connection is obtained between the moments of inertia of the polytopes (regarded as solid homogeneous bodies) and crystal elastic properties. Finally, we provide a list of unsolved problems in this geometrical many-body theory.     

Fractional Calculus via Functional Calculus: Theory and Applications

This paper demonstrates the power of the functional-calculus definition oflinear fractional (pseudo-)differential operators via generalised Fouriertransforms.Firstly, we describe in detail how to get global causal solutions of linearfractional differential equations via this calculus. The solutions arerepresented as convolutions of the input functions with the related impulseresponses. The suggested method via residue calculus separates an impulseresponse automatically into an exponentially damped (possibly oscillatory)part and a `slow' relaxation. If an impulse response is stable it becomesautomatically causal, otherwise one has to add a homogeneous solution to getcausality.Secondly, we present examples and, moreover, verify the approach alongexperiments on viscolelastic rods. The quality of the method as an effectivefew-parameter model is impressively demonstrated: the chosen referenceexample PTFE (Teflon) shows that in contrast to standard classical modelsour model describes the behaviour in a wide frequency range within theaccuracy of the measurement. Even dispersion effects are included.Thirdly, we conclude the paper with a survey of the required theory. Therethe attention is directed to the extension from the L ₂-approachon the space of distributions .     

Elastica hypoarealis

We examine the equilibria of a rigid loop in the plane, characterized by an energy functional quadratic in the curvature, subject to the constraints of fixed length and fixed enclosed area. Whereas the only non self-intersecting equilibrium corresponding to the fixed length constraint is the circle, the area constraint gives rise to distinct equilibria labeled by an integer. These configurations exhibit self-intersections and bifurcations as the area is reduced. In addition, not only can the Euler-Lagrange equation be integrated to provide a quadrature for the curvature but the embedding itself can be expressed as a local function of the curvature. Perturbations connecting equilibria are shown to satisfy a first order ODE which is readily solved. Analytical expressions for the energy as a function of the area are obtained in the limiting regimes. Received 18 October 2001 / Received in final form 31 May 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: capo@fis.cinvestav.mx RID="b" ID="b"e-mail: chryss@nuclecu.unam.mx RID="c" ID="c"e-mail: jemal@nuclecu.unam.mx