Movable Rigid Scatterer Model for Flexural Wave Scattering on Thin Plates

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
Liang-Wu Cai ◽  
Stephen A. Hambric
Keyword(s):  
Volume Fraction ◽  
Mass Density ◽  
Stop Band ◽  
Body Motion ◽  
Thin Plates ◽  
Flexural Wave ◽  
Fixed Structure ◽  
Limiting Case ◽  
Flexural Wave Scattering ◽  
Lower Frequencies

Rigid scatterers are fundamentally important in the study of scattering of many types of waves. However, in the recent literature on scattering of flexural waves on thin plates, a “rigid scatterer” has been used to represent a clamped boundary. Such a model physically resembles riveting the plate to a fixed structure. In this paper, a movable model for a rigid scatterer that allows rigid-body motion is established. It is shown that, when the mass density of the movable rigid scatterer is much greater than that of the host plate and at high frequencies, the movable rigid scatterer approaches the limiting case that is the riveted rigid scatterer. The single- and multiple-scattering by such scatterers are examined. Numerical examples show that, at the extreme end of lower frequencies, the scattering cross section for the movable model vanishes while that of the riveted models approaches infinity. An array of such movable rigid scatterers can form a broad and well-defined stop band for flexural wave transmission. With a volume fraction above 50%, the spectrum is rather clean: consisting of only an extremely broad stop band and two groups of higher frequency Perot–Fabry resonance peaks. Increasing either scatterer’s mass density or the lattice spacing can compress the spectral features toward lower frequencies.

Chaos in body–vortex interactions

2010 ◽  
Vol 466 (2119) ◽  
pp. 1871-1891 ◽  
Author(s):  
Johan Roenby ◽  
Hassan Aref
Keyword(s):  
Body Shape ◽  
Mass Density ◽  
Relative Equilibrium ◽  
Large Body ◽  
Point Vortex ◽  
Cylindrical Body ◽  
The Body ◽  
Body Motion ◽  
Single Vortex ◽  
Vortex Interactions

The model of body–vortex interactions, where the fluid flow is planar, ideal and unbounded, and the vortex is a point vortex, is studied. The body may have a constant circulation around it. The governing equations for the general case of a freely moving body of arbitrary shape and mass density and an arbitrary number of point vortices are presented. The case of a body and a single vortex is then investigated numerically in detail. In this paper, the body is a homogeneous, elliptical cylinder. For large body–vortex separations, the system behaves much like a vortex pair regardless of body shape. The case of a circle is integrable. As the body is made slightly elliptic, a chaotic region grows from an unstable relative equilibrium of the circle-vortex case. The case of a cylindrical body of any shape moving in fluid otherwise at rest is also integrable. A second transition to chaos arises from the limit between rocking and tumbling motion of the body known in this case. In both instances, the chaos may be detected both in the body motion and in the vortex motion. The effect of increasing body mass at a fixed body shape is to damp the chaos.

scholarly journals CuO–Water Nanofluid Magnetohydrodynamic Natural Convection inside a Sinusoidal Annulus in Presence of Melting Heat Transfer

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
M. Sheikholeslami ◽  
R. Ellahi ◽  
C. Fetecau
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Natural Convection ◽  
Hartmann Number ◽  
Volume Fraction ◽  
Melting Heat ◽  
Melting Heat Transfer ◽  
Limiting Case ◽  
Good Agreement ◽  
Melting Parameter

Impact of nanofluid natural convection due to magnetic field in existence of melting heat transfer is simulated using CVFEM in this research. KKL model is taken into account to obtain properties of CuO–H2O nanofluid. Roles of melting parameter (δ), CuO–H2O volume fraction (ϕ), Hartmann number (Ha), and Rayleigh (Ra) number are depicted in outputs. Results depict that temperature gradient improves with rise of Rayleigh number and melting parameter. Nusselt number detracts with rise of Ha. At the end, a comparison as a limiting case of the considered problem with the existing studies is made and found in good agreement.

An Experimental Study of Internal Hygrocysts

1976 ◽  
Vol 98 (4) ◽  
pp. 688-692 ◽  
Author(s):  
R. T. Balmer ◽  
T. G. Wang
Keyword(s):  
Secondary Flow ◽  
Weber Number ◽  
Critical Speed ◽  
Body Force ◽  
Volume Fraction ◽  
Anomalous Behavior ◽  
Body Motion ◽  
Fluid Systems ◽  
Correlation Models ◽  
Lateral Body

The onset of the stable laminar secondary flow (hygrocysts) that arises when a partially filled container is rotated about a horizontal axis has been experimentally studied. Nearly 500 sets of data on thirteen fluid systems were obtained and analyzed using a multiple linear regression computer program. Numerous dimensionless correlation models were investigated, the best being a power law relationship between the Reynolds number, volume fraction, and Weber number. Anomalous behavior was observed in that as the volume fraction approached unity, the critical speed of the onset of the secondary flow approached zero, indicating non-rigid body motion (driven by the lateral body force) in completely filled horizontal rotating containers.

scholarly journals Hydrogen diffusion and the percolation of austenite in nanostructured bainitic steel

2014 ◽  
Vol 470 (2168) ◽  
pp. 20140108 ◽  
Author(s):  
L. C. D. Fielding ◽  
E. J. Song ◽  
D. K. Han ◽  
H. K. D. H. Bhadeshia ◽  
D.-W. Suh
Keyword(s):  
Hydrogen Diffusion ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Bainitic Ferrite ◽  
Effective Diffusivity ◽  
Steel Sample ◽  
Thin Plates ◽  
Heat Treated ◽  
Diffusion Of Hydrogen

The diffusion of hydrogen in austenite is slower than in ferrite. Experiments have been conducted to study the behaviour of hydrogen in a nanostructured steel sample consisting of a mixture of thin plates of bainitic ferrite and intervening films of retained austenite, with the latter phase present in a quantity larger than the percolation threshold, i.e. it has three-dimensional connectivity. The structure was then heat treated to control the fraction of austenite, and hence to study the role of hydrogen when the austenite decomposes below the value required to sustain percolation. The experiments have involved both thermal desorption analysis and permeation, and when combined with theoretical analysis, indicate a significant influence of percolating austenite in hindering the passage of hydrogen into the steel during hydrogen charging, and its permeation through the composite nanostructure. The effect is not as large as might be expected from a simple comparison of independent data on the diffusivities of hydrogen in the two lattices, because the effective diffusivity in ferrite is found to be much smaller than in the defect-free ferrite, owing to trapping effects. The morphology of the austenite is demonstrated to play a role by comparing with a sample containing a larger volume fraction of austenite but present as isolated grains which are ineffective to the permeation of hydrogen.

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