2,510 research outputs found
Tuning gain and bandwidth of traveling wave tubes using metamaterial beam-wave interaction structures
We employ metamaterial beam-wave interaction structures for tuning the gain
and bandwidth of short traveling wave tubes. The interaction structures are
made from metal rings of uniform cross section, which are periodically deployed
along the length of the traveling wave tube. The aspect ratio of the ring cross
sections are adjusted to control both gain and bandwidth. The frequency of
operation is controlled by the filling fraction of the ring cross section with
respect to the period
Optimal lower bounds on the local stress inside random thermoelastic composites
A methodology is presented for bounding all higher moments of the local
hydrostatic stress field inside random two phase linear thermoelastic media
undergoing macroscopic thermomechanical loading. The method also provides a
lower bound on the maximum local stress. Explicit formulas for the optimal
lower bounds are found that are expressed in terms of the applied macro- scopic
thermal and mechanical loading, coefficients of thermal expansion, elastic
properties, and volume fractions. These bounds provide a means to measure load
transfer across length scales relating the excursions of the local fields to
the applied loads and the thermal stresses inside each phase. These bounds are
shown to be the best possible in that they are attained by the Hashin-Shtrikman
coated sphere assemblage.Comment: 14 page
Numerical convergence of nonlinear nonlocal continuum models to local elastodynamics
We quantify the numerical error and modeling error associated with replacing
a nonlinear nonlocal bond-based peridynamic model with a local elasticity model
or a linearized peridynamics model away from the fracture set. The nonlocal
model treated here is characterized by a double well potential and is a smooth
version of the peridynamic model introduced in n Silling (J Mech Phys Solids
48(1), 2000). The solutions of nonlinear peridynamics are shown to converge to
the solution of linear elastodynamics at a rate linear with respect to the
length scale of non local interaction. This rate also holds for the
convergence of solutions of the linearized peridynamic model to the solution of
the local elastodynamic model. For local linear Lagrange interpolation the
consistency error for the numerical approximation is found to depend on the
ratio between mesh size and . More generally for local Lagrange
interpolation of order the consistency error is of order
. A new stability theory for the time discretization is provided
and an explicit generalization of the CFL condition on the time step and its
relation to mesh size is given. Numerical simulations are provided
illustrating the consistency error associated with the convergence of nonlinear
and linearized peridynamics to linear elastodynamics
Sub-Wavelength Plasmonic Crystals: Dispersion Relations and Effective Properties
We obtain a convergent power series expansion for the first branch of the
dispersion relation for subwavelength plasmonic crystals consisting of
plasmonic rods with frequency-dependent dielectric permittivity embedded in a
host medium with unit permittivity. The expansion parameter is , where is the norm of a fixed wavevector, is the period of
the crystal and is the wavelength, and the plasma frequency scales
inversely to , making the dielectric permittivity in the rods large and
negative. The expressions for the series coefficients (a.k.a., dynamic
correctors) and the radius of convergence in are explicitly related to
the solutions of higher-order cell problems and the geometry of the rods.
Within the radius of convergence, we are able to compute the dispersion
relation and the fields and define dynamic effective properties in a
mathematically rigorous manner. Explicit error estimates show that a good
approximation to the true dispersion relation is obtained using only a few
terms of the expansion. The convergence proof requires the use of properties of
the Catalan numbers to show that the series coefficients are exponentially
bounded in the Sobolev norm
Uncertain Loading and Quantifying Maximum Energy Concentration within Composite Structures
We introduce a systematic method for identifying the worst case load among
all boundary loads of fixed energy. Here the worst case load is defined to be
the one that delivers the largest fraction of input energy to a prescribed
subdomain of interest. The worst case load is identified with the first
eigenfunction of a suitably defined eigenvalue problem. The first eigenvalue
for this problem is the maximum fraction of boundary energy that can be
delivered to the subdomain. We compute worst case boundary loads and associated
energy contained inside a prescribed subdomain through the numerical solution
of the eigenvalue problem. We apply this computational method to bound the
worst case load associated with an ensemble of random boundary loads given by a
second order random process. Several examples are carried out on heterogeneous
structures to illustrate the method
Dynamic Brittle Fracture as a Small Horizon Limit of Peridynamics
We consider the nonlocal formulation of continuum mechanics described by peridynamics. We provide a link between peridynamic evolution and brittle fracture evolution for a broad class of peridynamic potentials associated with unstable peridynamic constitutive laws. Distinguished limits of peridynamic evolutions are identified that correspond to vanishing peridynamic horizon. The limit evolution has both bounded linear elastic energy and Griffith surface energy. The limit evolution corresponds to the simultaneous evolution of elastic displacement and fracture. For points in spacetime not on the crack set the displacement field evolves according to the linear elastic wave equation. The wave equation provides the dynamic coupling between elastic waves and the evolving fracture path inside the media. The elastic moduli, wave speed and energy release rate for the evolution are explicitly determined by moments of the peridynamic influence function and the peridynamic potential energy
Influence of interfacial surface conduction on the DC electrical conductivity of particle reinforced composites
We describe new effects associated with electrical conduction along phase interfaces for particle reinforced conductors. For particles of general shape we introduce a new quantity β1 called the \u27surface to volume dissipation\u27 of a particle. This quantity is a measure of the particle\u27s ability to dissipate energy on its surface relative to the energy dissipated in its interior. It is described mathematically as the minimum value of a suitably defined Rayleigh quotient and is related to an eigenvalue problem posed on the particle surface. We consider the overall conductivity of a particle reinforced conductor when the particle conductivities are less than that of the matrix. It is shown that the overall conductivity will be increased by the presence of a specific particle when the particle\u27s \u27surface to volume dissipation\u27 lies above a critical value. We calculate the surface to volume dissipation for a sphere and for starlike particles we provide a lower bound in terms of particle dimensions. These estimates allow for the prediction of new particle size effects. Second, we present a new criterion on the particle size distribution for which the overall conductivity lies below the matrix conductivity. © 1998 The Royal Society
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