Small Transverse Displacements Research Articles

Flow-induced vibration suppression of elastic square cylinder using windward-suction-leeward-blowing approach

This article covers the application of the windward-suction-leeward-blowing concept in the reduction of flow-induced vibration of an elastically-mounted square-section cylinder in the active open-loop control framework. Certain slots with equal length are devised on the front and rear surfaces of the cylinder to perform flow suction and flow blowing. These slots have the same actuation velocity. To study the effectiveness of the present flow control approach, fluid-structure interaction simulations for both the lock-in (85 < Reynolds Number < 95) and galloping (Reynolds Number > 170) regions are conducted based on a finite volume code. According to the plots of maximum cylinder cross-flow displacement, planar orbital trajectories and snapshots of vorticity contours, the success of this control approach in complete suppression of vortex shedding and thus the flow-induced oscillations in both mentioned regions is shown. Also, increasing the actuation velocity and slot length improves the performance of windward-suction-leeward-blowing in flow control and vibration attenuation. The minimum actuation velocity required for attenuation of cylinder oscillations in the galloping zone is higher than that of the lock-in region. Moreover, with increasing actuation velocity and slot length, the shear layer is stretched, suppressing the vortex-shedding and changing the mode of wake structure from 2S (for lock-in region) and 2S+2P (for galloping zone) to a vortex-free symmetric wake. Also, the proposed control approach alters the orbital pattern diagrams of the cylinder that are in the form of figure-8-shaped plots and transfers them to a bounded region commensurate to the small transverse and in-line displacements of the cylinder.

Molecular Aggregate Photophysics beyond the Kasha Model: Novel Design Principles for Organic Materials.

The transport and photophysical properties of organic molecular aggregates, films, and crystals continue to receive widespread attention, driven mainly by expanding commercial applications involving display and wearable technologies as well as the promise of efficient, large-area solar cells. The main blueprint for understanding how molecular packing impacts photophysical properties was drafted over five decades ago by Michael Kasha. Kasha showed that the Coulombic coupling between two molecules, as determined by the alignment of their transition dipoles, induces energetic shifts in the main absorption spectral peak and changes in the radiative decay rate when compared to uncoupled molecules. In H-aggregates, the transition dipole moments align "side-by-side" leading to a spectral blue-shift and suppressed radiative decay rate, while in J-aggregates, the transition dipole moments align "head-to-tail" leading to a spectral red-shift and an enhanced radiative decay rate. Although many examples of H- and J-aggregates have been discovered, there are also many "unconventional" aggregates, which are not understood within the confines of Kasha's theory. Examples include nanopillars of 7,8,15,16-tetraazaterrylene, as well as several perylene-based dyes, which exhibit so-called H- to J-aggregate transformations. Such aggregates are typically characterized by significant wave function overlap between neighboring molecular orbitals as a result of small (∼4 Å) intermolecular distances, such as those found in rylene π-stacks and oligoacene herringbone lattices. Wave function overlap facilitates charge-transfer which creates an effective short-range exciton coupling that can also induce J- or H-aggregate behavior, depending on the sign. Unlike Coulomb coupling, short-range coupling is extremely sensitive to small (sub-Å) transverse displacements between neighboring chromophores. For perylene chromophores, the sign of the short-range coupling changes several times as two molecules are "slipped" from a "side-by-side" to "head-to-tail" configuration, in marked contrast to the sign of the Coulomb coupling, which changes only once. Such sensitivity allows J- to H-aggregate interconversions over distances several times smaller than those predicted by Kasha's theory. Moreover, since the total coupling drives exciton transport and photophysical properties, interference between the short- and long-range (Coulomb) couplings, as manifest by their relative signs and magnitudes, gives rise to a host of new aggregate types, referred to as HH, HJ, JH, and JJ aggregates, with distinct photophysical properties. An extreme example is the "null" HJ-aggregate in which total destructive interference leads to absorption line shapes practically identical to uncoupled molecules. Moreover, the severely compromised exciton bandwidth effectively shuts down energy transport. Most importantly, the new aggregates types described herein can be exploited for electronic materials design. For example, the enhanced exciton bandwidth and weakly emissive properties of HH-aggregates make them ideal candidates for solar cell absorbers, while the enhanced charge mobility and strong emissive behavior of JJ-aggregates makes them excellent candidates for light-emitting diodes.

Nonlocal postbuckling analysis of graphene sheets with initial imperfection based on first order shear deformation theory

In this paper, the first order shear deformation theory (FSDT) is used to investigate the postbuckling behavior of orthotropic single-layered graphene sheet (SLGS) under in-plane loadings. Nonlocal elasticity theory and von-Karman nonlinear model in combination with the isogeometric analysis (IGA) have been applied to study the postbuckling characteristics of SLGSs. In contrast to the classical model, the nonlocal continuum model developed in this work considers the size-effects on the postbuckling characteristics of SLGSs. FSDT takes into account effects of shear deformations through-the-thickness of plate. Geometric imperfection which is defined as a very small transverse displacement of the mid-plane is applied on undeformed nanoplate to create initial deviation in graphene sheet from being perfectly flat. Nonlinear governing equations of motion for SLGS are derived from the principle of virtual work and a variational formulation. At the end, the results are presented as the postbuckling equilibrium paths of SLGS. The influence of various parameters such as edge length, nonlocal parameter, compression ratio, boundary conditions and aspect ratio on the postbuckling path is investigated. The results of this work show the high accuracy of nonlocal FSDT-based analysis for postbuckling behavior of graphene sheets.

Interference between Coulombic and CT-mediated couplings in molecular aggregates: H- to J-aggregate transformation in perylene-based π-stacks.

The spectroscopic differences between J and H-aggregates are traditionally attributed to the spatial dependence of the Coulombic coupling, as originally proposed by Kasha. However, in tightly packed molecular aggregates wave functions on neighboring molecules overlap, leading to an additional charge transfer (CT) mediated exciton coupling with a vastly different spatial dependence. The latter is governed by the nodal patterns of the molecular LUMOs and HOMOs from which the electron (te) and hole (th) transfer integrals derive. The sign of the CT-mediated coupling depends on the sign of the product teth and is therefore highly sensitive to small (sub-Angstrom) transverse displacements or slips. Given that Coulombic and CT-mediated couplings exist simultaneously in tightly packed molecular systems, the interference between the two must be considered when defining J and H-aggregates. Generally, such π-stacked aggregates do not abide by the traditional classification scheme of Kasha: for example, even when the Coulomb coupling is strong the presence of a similarly strong but destructively interfering CT-mediated coupling results in "null-aggregates" which spectroscopically resemble uncoupled molecules. Based on a Frenkel/CT Holstein Hamiltonian that takes into account both sources of electronic coupling as well as intramolecular vibrations, vibronic spectral signatures are developed for integrated Frenkel/CT systems in both the perturbative and resonance regimes. In the perturbative regime, the sign of the lowest exciton band curvature, which rigorously defines J and H-aggregation, is directly tracked by the ratio of the first two vibronic peak intensities. Even in the resonance regime, the vibronic ratio remains a useful tool to evaluate the J or H nature of the system. The theory developed is applied to the reversible H to J-aggregate transformations recently observed in several perylene bisimide systems.

Enhanced aeroelastic energy harvesting with a beam stiffener

In this article, we propose an easy but quite effective method to significantly enhance the power generation capability of an aeroelastic energy harvester. The method is to attach a beam stiffener to the substrate of the harvester, which works as an electromechanical coupling magnifier. It is shown to be effective for all three considered types of harvesters based on galloping, vortex-induced vibration and flutter, leading to a superior performance over the conventional designs without the beam stiffener, with dozens of times the increase in power and an almost 100% increase in the power extraction efficiency yet with comparable or even smaller transverse displacement. Choice guidelines of optimal types of energy harvesters are also suggested based on the given wind situations where the electronic device is located.

Immersed finite element methods for 4th order differential equations

We propose three new finite element methods for solving boundary value problems of 4th order differential equations with discontinuous coefficients. Typical differential equations modeling the small transverse displacement of a beam and a thin plate formed by multiple uniform materials are considered. One important feature of these finite element methods is that their meshes can be independent of the interface between different materials. Finite element spaces based on both the conforming and mixed formulations are presented. Numerical examples are given to illustrate capabilities of these methods.

Radiation force on spheres in helicoidal Bessel beams modeled using finite elements.

Analysis of the scattering of sound by spheres centered on ordinary and helicoidal (higher-order) Bessel beams [P. L. Marston, J. Acoust. Soc. Am. 124, 2905–2910 (2008)] makes it possible to evaluate the radiation force on spheres centered on the beam in an ideal inviscid fluid. Potentially surprising results include cases where the radiation force is directed opposite the propagation direction of both types of beams [P. L. Marston (submitted for publication)]. For potential biomedical applications such as drug delivery, it would be necessary to know if a small transverse displacement of the sphere from the beam’s axis causes a radiation force that pushes the sphere toward (or away from) the axis of the beam. Three-dimensional finite elements were applied to that problem. To trust FEM calculations of the radiation force with helicoidal beams, it was first necessary to verify that analytical values for the axial force are recovered in the on-axis helicoidal case since only the zero-order beam had been previously studied [D. B. Thiessen and P. L. Marston, J. Acoust. Soc. Am. 122, 3025 (2007)]. Cases were found where displacement of a sphere from the beam axis causes a transverse restoring force. [Supported by ONR and NASA.]

Analysis of Composite Structures

1R16. Analysis of Composite Structures. - C Decolon (Dept of Mech, Conservatoire Natl des Arts et Metiers, France). Hermes Sci Publ, Paris. Distributed in USA by Taylor &amp; Francis Publ, New York NY. 2002. 336 pp. ISBN 1-56032-982-3. $135.00.Reviewed by E Armanios (Sch of Aerospace Eng, Georgia Inst of Tech, Atlanta GA 30332-0150).This book, comprising three parts and four appendices, provides a mathematical presentation of the governing equations for laminated composite plates and beams. The first part is devoted to the anisotropic constitutive relationships with emphasis on orthotropic materials. Hygrothermal effects are covered. Maximum stress and strain failure criteria are presented as well as Tsai-Hill, Tsai-Wu, and Hoffman polynomial based criteria. The second part treats laminated plates. The governing equations for thin plates based on the Kischhoff-Love assumptions are presented first. Symmetric orthotropic plates are studied for the cases of bending, vibration, and buckling. The stiffness coefficients for asymmetrical cases are presented as well. Bending, vibration, and buckling is presented for thin plates with asymmetric cross-ply as well as asymmetric balanced stacking sequences. Thermo-elastic behavior is considered through the derivation of the 3D and plane stress constitutive relationships for orthotropic off-axes layups. Applications to balanced and symmetric laminates are presented. Moderately thick orthotropic symmetric plates are analyzed using Reissner-Mindlin assumptions. Cylindrical bending of thin and moderately thick laminated plates is presented for the cases of bending, vibration, and buckling. The third part considers symmetrical beams starting with axial loading and followed by bending, including transverse shear strain effects. Applications to bending, vibration, and buckling are provided. Four appendices are devoted to the derivation of the governing equations for laminated plates. In the first two appendices, the governing equations of small and large transverse displacements of plates are derived by integrating the equations of motion. The third and fourth appendices use a variational formulation to obtain the governing equations for laminated plates based on Kirchoff-Love and Reissner-Mindlin assumptions, respectively. The book aims at presenting the basis for the analysis of composites structures. As such, minimum derivation of equations is provided mainly in appendices. The focus is on the mathematical presentation of governing equations and closed-form solutions. The book is suited as a reference for graduate students and practitioners of mechanics of laminated composites. Its appealing feature is the systematic and compact presentation of the governing equations of beams and laminated composite thin and moderately thick plates including small and large transverse displacements, into a single reference. The figures adequately illustrate the boundary and loading conditions associated with the development of the governing equations. None of the equations are numbered making it difficult at times to follow the mathematical presentation sequence across sections and chapters. The inclusion of references to specific works by some investigators would enhance the author’s presentation and comments within the text of the book. Analysis of Composite Structures should be a good reference for purchase by graduate students and practicing scientists and engineers.

Simulation of beam collector nonuniformities in gyro-amplifiers

The spiraling beams employed in gyro-amplifiers can create regions of enhanced local heating on the beam collector surface as a result of the turning-point behavior of the electron orbits. Although guiding center spread and the spread in Larmor radii will usually smooth out these irregularities, hot-spotting can reappear as a result of small transverse displacements or angular misalignments between the collector axis and the system magnetic axis, or from transverse magnetic fields in the electron gun. This paper presents a new, general procedure to efficiently simulate the spatial distribution of electron impacts in misaligned gyro-amplifier beam collectors, using adiabatic theory and analytic geometry. The procedure is used to investigate the distributions associated with various types of misalignments and the results are compared with experimental collector maps obtained from a high-average power, 94-GHz gyroklystron.

Stability of a vortex in a trapped Bose-Einstein condensate.

Based on the method of matched asymptotic expansions and on a time-dependent variational analysis, we study the dynamics of a vortex in a three-dimensional disk-shaped nonaxisymmetric condensate in the Thomas-Fermi limit. Both methods show that a vortex in a trapped Bose-Einstein condensate has formally unstable normal mode(s) with positive normalization and negative frequency, corresponding to a precession of the vortex line around the center of the trap. In a rotating trap, the solution becomes stable above an angular velocity Omega(m), characterizing the onset of metastability with respect to small transverse displacements of the vortex from the central axis.

Multimode Analysis of the Hollow Plasma Channel Wakefield Accelerator

The hollow plasma channel is analyzed as an accelerating structure. The excitation of the channel by an ultra-relativistic beam is analyzed. Coupling to the fundamental and all higher order azimuthal modes of the excited electromagnetic fields is derived. Implications of this work for plasma-based accelerators, including beam loading and beam breakup, are discussed. Small initial transverse displacements of the beam are shown to couple to deflecting modes in the channel. The asymptotic growth rate of the resultant beam breakup instability is analyzed and a method for reducing the growth is proposed.

Displacement-Limited Buckling of an Optical Fiber

Buckling of an optical fiber within a confining connector housing is analyzed under the restriction that the transverse deflection profile be shallow. Fibers with pinned ends and with clamped ends are treated. The three stages of buckling are discussed: sufficiently small transverse displacements that contact is not made with the housing wall; point contact with the wall; and finite-length contact with the wall. Explicit expressions for responses as functions of relative longitudinal displacement of ends are obtained for the first and third stages. For the second stage, longitudinal displacement and maximum fiber curvature are expressed in terms of buckling load. Except for a portion of the point-contact stage, contact with a confining wall causes more severe stresses in the fiber than would otherwise be the case.

Boundary controllability of nonlinear beams to bounded states

SynopsisConsidered is a nonlinear model which describes the dynamic behaviour of the not necessarily small longitudinal and transverse displacements of a thin, cantilevered beam. The motion of the beam is driven by a bending moment, an axial force and a vertical shear force that act at the free end of the beam. The main goal is to describe the reachable set of the system, that is, the set of all states that can be reached by varying the end forces within a certain set of admissible controls.

Theoretical diffraction efficiency of nearly unslanted volume multiplexed amplitude holograms

Kogelnik's coupled wave differential equations are solved for many incoherent amplitude transmission holograms superimposed in a photosensitive medium and recorded with small equiangular transverse displacements [Formula: see text] between them. Firstly, the case of two transmission amplitude volume overlaid holograms is analysed and a generalization for the case of N incoherently superimposed holograms is presented. Diffraction efficiency and wave amplitude formulas arc given for incidence "near" and "at the Bragg angle."

The deformation of a nearly straight thread in a shearing flow with weak Brownian motions

As a model of an almost fully extended macromolecule, a small, flexible, inextensible, nearly straight thread in a shearing flow with weak Brownian motions is considered. The hydrodynamic resistance to motion is included using the slenderbody theory for Stokes flow. The variation of the small transverse displacements along the thread is expressed as a truncated sum of Fourier components, with appropriately chosen modal functions. A diffusion equation is derived in the Fourier space and solved. The expected deformation of the thread is then given for axisymmetric and two-dimensional straining flows. The transverse displacement of the ends and the small shortening of the projected length of the thread are both found to be sensitive to the truncation of the Fourier representation, although it becomes clear on physical grounds that the ratio of the shortening to the typical transverse distortion should increase with the number of degrees of freedom. In simple shear flow the deformation increases as the thread aligns with the flow, until the analysis breaks down when the entire thread is no longer in the extensional quadrants. The influence of the 2:1 ratio of the resistance coefficients from the slender-body theory is found to be a small numerical factor.

Real time measurement of very small transverse displacements of diffuse objects by random moiré 2: Experiments

We first briefly describe a realization of the random moiré displacement transducer (Part 1 of this paper). The principal problems arising in practical measurements, namely, stability and noise, are then discussed. Finally, results of several vibration measurements are presented, with various waveforms and amplitudes (2 A to 3 microm peak to peak).

Real time measurement of very small transverse displacements of diffuse objects by random moiré 1: Theory

Illumination of a random diffuse object by a fringe pattern produced by two symmetrical laser beams leads to phenomena that are usually studied with speckle interferometric techniques. We first show that these phenomena are analogous to moiré. We then propose to apply this method for measuring the transverse vibrations of a diffuse surface in real time with interferometric sensitivity. Further, we show that the discussed system can work as a linear displacement transducer; the theoretical aspects of this so-called random moire transducer are investigated.

On the dissipation of energy in a chain of coupled harmonic oscillators

The article deals with processes which occur in coupled oscillator chains following an initial impulse imparted to any one of the atoms. In considering one-dimensional chains of coupled harmonic oscillators, their obvious deficiencies are analyzed and taken into account. The effects which energy dissipation losses and transverse vibrations have on propagation of collision waves through a one-dimensional atom chain are evaluated. It stands to reason, of course, to consider only small transverse displacements of atoms in a chain, since otherwise the simplest models become obviously inadequate.

Impulsive loading of fully clamped beams with finite plastic deflections and strain-rate sensitivity

A review is given of earlier work on the plastic response to impulsive loading of a beam clamped against end rotations and axial displacements, taking account of small finite transverse displacements and of strain-rate dependence of the yield stress. New solutions are derived from rigid-plastic analysis which include both effects in simple approximate ways. Deflections are compared as obtained from these formulas, from experiments described here on mild steel beams and from finite-difference numerical solutions using the M.I.T. rod model with elastic-plastic strain-rate sensitive behavior. The significance of agreements observed is discussed.

A thin circular plate normally and uniformly loaded over a concentric elliptic patch

ABSTRACTThis paper is concerned with the small transverse displacement of a thin circular plate elastically restrained along the circular boundary and subject to uniform normal pressure distributed over the area of an ellipse concentric with the plate. The method of complex potentials is used and the general assumptions relating to the small deflexion theory of thin plates are adopted. Explicit formulae for the bending and twisting moments and shearing forces are given at any point on the boundary and at the centre of the plate.