8,227 research outputs found
A Simple Multi-Directional Absorbing Layer Method to Simulate Elastic Wave Propagation in Unbounded Domains
The numerical analysis of elastic wave propagation in unbounded media may be
difficult due to spurious waves reflected at the model artificial boundaries.
This point is critical for the analysis of wave propagation in heterogeneous or
layered solids. Various techniques such as Absorbing Boundary Conditions,
infinite elements or Absorbing Boundary Layers (e.g. Perfectly Matched Layers)
lead to an important reduction of such spurious reflections. In this paper, a
simple absorbing layer method is proposed: it is based on a Rayleigh/Caughey
damping formulation which is often already available in existing Finite Element
softwares. The principle of the Caughey Absorbing Layer Method is first
presented (including a rheological interpretation). The efficiency of the
method is then shown through 1D Finite Element simulations considering
homogeneous and heterogeneous damping in the absorbing layer. 2D models are
considered afterwards to assess the efficiency of the absorbing layer method
for various wave types and incidences. A comparison with the PML method is
first performed for pure P-waves and the method is shown to be reliable in a
more complex 2D case involving various wave types and incidences. It may thus
be used for various types of problems involving elastic waves (e.g. machine
vibrations, seismic waves, etc)
Stochastic band structure for waves propagating in periodic media or along waveguides
We introduce the stochastic band structure, a method giving the dispersion
relation for waves propagating in periodic media or along waveguides, and
subject to material loss or radiation damping. Instead of considering an
explicit or implicit functional relation between frequency and
wavenumber , as is usually done, we consider a mapping of the resolvent set
in the dispersion space . Bands appear as as the trace of
Lorentzian responses containing local information on propagation loss both in
time and space domains. For illustration purposes, the method is applied to a
lossy sonic crystal, a radiating surface phononic crystal, and a radiating
optical waveguide. The stochastic band structure can be obtained for any system
described by a time-harmonic wave equation
Numerical analysis of seismic wave amplification in Nice (France) and comparisons with experiments
The analysis of site effects is very important since the amplification of
seismic motion in some specific areas can be very strong. In this paper, the
site considered is located in the centre of Nice on the French Riviera. Site
effects are investigated considering a numerical approach (Boundary Element
Method) and are compared to experimental results (weak motion and
microtremors). The investigation of seismic site effects through numerical
approaches is interesting because it shows the dependency of the amplification
level on such parameters as wave velocity in surface soil layers, velocity
contrast with deep layers, seismic wave type, incidence and damping. In this
specific area of Nice, a one-dimensional (1D) analytical analysis of
amplification does not give a satisfactory estimation of the maximum reached
levels. A boundary element model is then proposed considering different wave
types (SH, P, SV) as the seismic loading. The alluvial basin is successively
assumed as an isotropic linear elastic medium and an isotropic linear
viscoelastic solid (standard solid). The thickness of the surface layer, its
mechanical properties, its general shape as well as the seismic wave type
involved have a great influence on the maximum amplification and the frequency
for which it occurs. For real earthquakes, the numerical results are in very
good agreement with experimental measurements for each motion component.
Two-dimensional basin effects are found to be very strong and are well
reproduced numerically
Seismic site effects in a deep alluvial basin: numerical analysis by the boundary element method
The main purpose of the paper is the numerical analysis of seismic site
effects in Caracas (Venezuela). The analysis is performed considering the
boundary element method in the frequency domain. A numerical model including a
part of the local topography is considered, it involves a deep alluvial deposit
on an elastic bedrock. The amplification of seismic motion (SH-waves, weak
motion) is analyzed in terms of level, occurring frequency and location. In
this specific site of Caracas, the amplification factor is found to reach a
maximum value of 25. Site effects occur in the thickest part of the basin for
low frequencies (below 1.0 Hz) and in two intermediate thinner areas for
frequencies above 1.0 Hz. The influence of both incidence and shear wave
velocities is also investigated. A comparison with microtremor recordings is
presented afterwards. The results of both numerical and experimental approaches
are in good agreement in terms of fundamental frequencies in the deepest part
of the basin. The boundary element method appears to be a reliable and
efficient approach for the analysis of seismic site effects
Effective wave numbers for thermo-viscoelastic media containing random configurations of spherical scatterers
The dispersion relation is derived for the coherent waves in fluid or elastic
media supporting viscous and thermal effects and containing randomly
distributed spherical scatterers. The formula obtained is the generalization of
Lloyd and Berry's [Proc. Phys. Soc. Lond. 91, 678-688, 1067], the latter being
limited to fluid host media, and it is the three-dimensional counterpart of
that derived by Conoir and Norris [Wave Motion 47, 183-197, 2010] for
cylindrical scatterers in an elastic host medium.Comment: 11 page
Can crack front waves explain the roughness of cracks ?
We review recent theoretical progress on the dynamics of brittle crack fronts
and its relationship to the roughness of fracture surfaces. We discuss the
possibility that the intermediate scale roughness of cracks, which is
characterized by a roughness exponent approximately equal to 0.5, could be
caused by the generation, during local instabilities by depinning, of
diffusively broadened corrugation waves, which have recently been observed to
propagate elastically along moving crack fronts. We find that the theory agrees
plausibly with the orders of magnitude observed. Various consequences and
limitations, as well as alternative explanations, are discussed. We argue that
another mechanism, possibly related to damage cavity coalescence, is needed to
account for the observed large scale roughness of cracks that is characterized
by a roughness exponent approximately equal to 0.8Comment: 26 pages, 3 .eps figure. Submitted to J. Mech. Phys. Solid
Surface wave scattering at nonuniform fluid interfaces
Effects of spatially varying interfacial parameters on the propagation of
surface waves are studied. These variations can arise from inhomogeneities in
coverage of surface active substances such as amphiphillic molecules at the
fluid/gas interface. Such variations often occur in phase coexistence regions
of Langmuir monolayers. Wave scattering from these surface inhomogeneities are
calculated in the limit of small variations in the surface parameters by using
the asymptotic form of surface Green's functions in the first order Born
approximation. When viscosity and variations in surface elastic moduli become
important, modes other than transverse capillary waves can change the
characteristics of propagation. Scattering among these modes provides a
mechanism for surface wave attenuation in addition to viscous damping on a
homogeneous surfactant covered interface. Experimental detection of waves
attenuation and scattering is also discussed.Comment: 11 pages; 8 figures on reques
Supershear Rayleigh waves at a soft interface
We report on the experimental observation of waves at a liquid foam surface
propagating faster than the bulk shear waves. The existence of such waves has
long been debated, but the recent observation of supershear events in a
geophysical context has inspired us to search for their existence in a model
viscoelastic system. An optimized fast profilometry technique allowed us to
observe on a liquid foam surface the waves triggered by the impact of a
projectile. At high impact velocity, we show that the expected subshear
Rayleigh waves are accompanied by faster surface waves that can be identified
as supershear Rayleigh waves.Comment: 4 pages, 4 figures, 2 supplementary video
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