The Effect of Wave Propagation on Seismic Response at Transmitting Boundary of Discrete System

2018 ◽  
Vol 878 ◽  
pp. 110-114
Author(s):  
Sang Hun Lee ◽  
Takao Endo ◽  
Ryutaro Kawana
Keyword(s):  
Wave Propagation ◽  
Free Boundary ◽  
Boundary Conditions ◽  
Seismic Response ◽  
Ground Motion ◽  
Response Analysis ◽  
Free Boundaries ◽  
Propagation Condition ◽  
Free Boundary Conditions ◽  
Transmitting Boundary

When analyzing the seismic response of a very long elevated structure such as a Shinkansen viaduct, it is common practice to analyze a cutout of the structure under consideration and treat its both ends as free boundaries. This is attributable to the assumption that seismic response analysis assuming free boundary conditions is more conservative than one assuming non-free boundary conditions. In this study, after finding out that response to harmonic ground motion can be greater than under free-boundary conditions if outward energy dissipation occurs from the analysis domain, a series of numerical experiments was performed to determine whether such phenomena occur in seismic response. Then, after confirming that the frequency components of ground motion that satisfy the wave propagation condition greatly affect seismic response, the study showed that the area of the wave propagation condition region of the Fourier spectrum can be used as an indicator by which to judge the likelihood of occurrence of such phenomena.

Effect of an elastically restrained boundary on SV-wave radiation patterns

1968 ◽  
Vol 58 (2) ◽  
pp. 497-520
Author(s):  
Y. T. Huang
Keyword(s):  
Boundary Condition ◽  
Wave Propagation ◽  
Free Boundary ◽  
Boundary Conditions ◽  
Elastic Wave ◽  
Solid Earth ◽  
Elastic Constants ◽  
Wave Radiation ◽  
Free Boundary Conditions ◽  
Elastically Restrained

Abstract In the solution of elastic wave propagation equations applied to solid earth, it is customarily assumed that free boundary conditions are satisfied at a surface which is in contact with the atmosphere. Situations which depart from this boundary condition have now been studied for arbitrary combinations of the Lamé elastic constants. The solutions are given for a homogeneous, isotropic half space.

scholarly journals Reflection of Willmore Surfaces with Free Boundaries

2020 ◽  
pp. 1-18
Author(s):  
Ernst Kuwert ◽  
Tobias Lamm
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Critical Points ◽  
Free Boundaries ◽  
Willmore Functional ◽  
Boundary Constraints ◽  
Free Boundary Conditions ◽  
Immersed Surfaces ◽  
Willmore Surfaces

Abstract We study immersed surfaces in ${\mathbb R}^3$ that are critical points of the Willmore functional under boundary constraints. The two cases considered are when the surface meets a plane orthogonally along the boundary and when the boundary is contained in a line. In both cases we derive weak forms of the resulting free boundary conditions and prove regularity by reflection.

Using Elasticity to Correct for Boundary Effects in Calculations of Stress-Diffusion Coupling Parameters

2006 ◽  
Vol 978 ◽  
Author(s):  
Brian Puchala ◽  
Michael Falk ◽  
Krishna Garikipati
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Defect Formation ◽  
Correction Term ◽  
Periodic Boundary Conditions ◽  
Formal Proof ◽  
Free Boundaries ◽  
Slow Convergence ◽  
Free Boundary Conditions

AbstractThe effect of stress on diffusion during semiconductor processing becomes important as device dimensions shrink from microns to nanometers. Simulating these effects requires accurate parameterization of the formation and migration volume tensors of the defects that mediate diffusion on the atomistic scale. We investigate the effect of boundary conditions on the accuracy of atomistic calculations of defect formation energies and formation volume tensors. Linear elasticity provides a correction to the effect of the boundaries on the resulting relaxation volume tensor. By a formal proof we show that the correction term is zero for free boundaries and for periodic boundary conditions with zero mean boundary stress. This is demonstrated in the far field for periodic and free boundary conditions for an isotropic (vacancy) and an anisotropic (<110> intersitial) defect in Stillinger-Weber silicon. For periodic boundary conditions, formation volume tensor components converge to within 5% in a 216 atom simulation cell. For free boundary conditions, slow convergence of elastic constants results in slow convergence of formation volumes. Most significantly, this provides a new method to calculate the formation volume from constant volume calculations. This removes the need for relaxing boundaries, allowing for simpler and more efficient algorithms. We apply this method to both the vacancy and the <110> interstitial in Stillinger-Weber silicon.

scholarly journals High-frequency spectral analysis of thin periodic acoustic strips: Theory and numerics

2010 ◽  
Vol 21 (6) ◽  
pp. 557-590 ◽  
Author(s):  
S. D. M. ADAMS ◽  
K. D. CHEREDNICHENKO ◽  
R. V. CRASTER ◽  
S. GUENNEAU
Keyword(s):  
Surface Wave ◽  
Free Boundary ◽  
Boundary Conditions ◽  
High Frequency ◽  
Finite Thickness ◽  
Large Integer ◽  
Band Spectrum ◽  
Free Boundaries ◽  
Periodic Cell ◽  
Free Boundary Conditions

This paper is devoted to the study of the asymptotic behaviour of the high-frequency spectrum of the wave equation with periodic coefficients in a ‘thin’ elastic strip Ση=(0, 1)×(−η/2, η/2), η > 0. The main geometric assumption is that the structure period is of the order of magnitude of the strip thickness η and is chosen in such a way that η−1 is a positive large integer. On the boundary ∂Ση, we set Dirichlet (clamped) or Neumann (traction-free) boundary conditions. Aiming to describe sequences of eigenvalues of order η−2 in the above problem, which correspond to oscillations of high frequencies of order η−1, we study an appropriately rescaled limit of the spectrum. Using a suitable notion of two-scale convergence for bounded operators acting on two-scale spaces, we show that the limiting spectrum consists of two parts: the Bloch (or band) spectrum and the ‘boundary’ spectrum. The latter corresponds to sequences of eigenvectors concentrating on the vertical boundaries of Ση, and is characterised by a problem set in a semi-infinite periodic strip with either clamped or stress-free boundary conditions. Based on the observation that some of the related eigenvalues can be found by solving an appropriate periodic-cell problem, we use modal methods to investigate finite-thickness semi-infinite waveguides. We compare our results with those for finite-thickness infinite waveguides given in Adams et al. (Proc. R. Soc. Lond. A, vol. 464, 2008, pp. 2669–2692). We also study infinite-thickness semi-infinite waveguides in order to gain insight into the finite-height analogue. We develop an asymptotic algorithm making use of the unimodular property of the modal method to demonstrate that in the weak contrast limit, and when wavenumber across the guide is fixed, there is at most one surface wave per gap in the spectrum. Using the monomode property of the waveguide we can consider the gap structure for the nth mode, when doing so, for traction-free boundaries, we find exactly one surface wave in each n-band gap.

Asymptotic behaviour of solutions of free boundary problems for Fisher-KPP equation

2016 ◽  
Vol 28 (3) ◽  
pp. 435-469 ◽  
Author(s):  
JINGJING CAI ◽  
HONG GU
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Asymptotic Behaviour ◽  
Free Boundary Problems ◽  
Chemical Species ◽  
Travelling Wave ◽  
Free Boundaries ◽  
Kpp Equation ◽  
Free Boundary Conditions ◽  
Two Parameters

We study a free boundary problem for the Fisher-KPP equation: ut = uxx + f(u) (g(t) < x < h(t)) with free boundary conditions h′(t) = −ux(t, h(t)) − α and g′(t) = −ux(t, g(t)) + β for 0 < β < α. This problem can model the spreading of a biological or chemical species, where free boundaries represent the spreading fronts of the species. We investigate the asymptotic behaviour of bounded solutions. There are two parameters α0 and α* with 0 < α0 < α* which play key roles in the dynamics. More precisely, (i) in case 0 < β < α0 and 0 < α < α*, we obtain a trichotomy result: (i-1) spreading, i.e., h(t) − g(t) → +∞ and u(t, ⋅ + ct) → 1 with c ∈ (cL, cR), where cL and cR are the asymptotic spreading speed of g(t) and h(t), respectively, (cR > 0 > cL when 0 < β < α < α0; cR = 0 >cL when 0 < β < α = α0; 0 > cR > cL when α0 < α < α* and 0 < β < α0); (i-2) vanishing, i.e., limt→Th(t) = limt→Tg(t) and limt→T u(t, x) = 0, where T is some positive constant; (i-3) transition, i.e., g(t) → −∞, h(t) → −∞, 0 < limt→∞[h(t) − g(t)] < +∞ and u(t, x) → V*(x − c*t) with c* < 0, where V*(x − c*t) is a travelling wave with compact support and which satisfies the free boundary conditions. (ii) in case β ≥ α0 or α ≥ α*, vanishing happens for any solution.

On the Wave Propagation in an Elastic Hollow Cylinder With Long-Range Cohesion Forces

1986 ◽  
Vol 53 (1) ◽  
pp. 121-124
Author(s):  
J. L. Nowinski
Keyword(s):  
Wave Propagation ◽  
Free Boundary ◽  
Boundary Conditions ◽  
Long Range ◽  
Fourier Transforms ◽  
Frequency Equation ◽  
Considerable Decrease ◽  
Free Boundary Conditions ◽  
Short Waves ◽  
Stress Components

After a brief derivation of the formula for the nonlocal moduli, Fourier transforms of the stress components in their nonlocal aspect are established. Satisfaction of the traction-free boundary conditions leads to the frequency equation of the problem. A particular case involving longitudinal Lame´ modes is analyzed in more detail. A numerical example solved shows a considerable decrease of the speed and the frequency of the short waves as compared with those of long waves studied in the classical theory.

scholarly journals Local Well-Posedness for Free Boundary Problem of Viscous Incompressible Magnetohydrodynamics

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 461
Author(s):  
Kenta Oishi ◽  
Yoshihiro Shibata
Keyword(s):  
Free Surface ◽  
Free Boundary ◽  
Boundary Conditions ◽  
Stokes Equations ◽  
Mhd Flow ◽  
Transmission Conditions ◽  
Well Posedness ◽  
Anisotropic Space ◽  
Free Boundary Conditions ◽  
Incompressible Magnetohydrodynamics

In this paper, we consider the motion of incompressible magnetohydrodynamics (MHD) with resistivity in a domain bounded by a free surface. An electromagnetic field generated by some currents in an external domain keeps an MHD flow in a bounded domain. On the free surface, free boundary conditions for MHD flow and transmission conditions for electromagnetic fields are imposed. We proved the local well-posedness in the general setting of domains from a mathematical point of view. The solutions are obtained in an anisotropic space Hp1((0,T),Hq1)∩Lp((0,T),Hq3) for the velocity field and in an anisotropic space Hp1((0,T),Lq)∩Lp((0,T),Hq2) for the magnetic fields with 2<p<∞, N<q<∞ and 2/p+N/q<1. To prove our main result, we used the Lp-Lq maximal regularity theorem for the Stokes equations with free boundary conditions and for the magnetic field equations with transmission conditions, which have been obtained by Frolova and the second author.

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