A simplified metaelastic model for coated sphere-filled random composites

2020 ◽  
pp. 108128652097761
Author(s):  
CQ Ru
Keyword(s):  
Displacement Field ◽  
Vibration Isolation ◽  
Average Distance ◽  
Rigid Sphere ◽  
Rigid Spheres ◽  
Simple Method ◽  
Long Wavelength ◽  
Random Composites ◽  
Characteristic Wavelength ◽  
Representative Unit Cell

A simplified metaelastic model is presented to study long-wavelength dynamics of random composites filled with coated rigid spheres under the condition that the characteristic wavelength of the displacement field is much larger than the average distance between adjacent coated rigid spheres. The model is characterized by a simple differential relation between the displacement field of the composite and the displacement field of the mass center of a representative unit cell. The validity and accuracy of the model are demonstrated by comparing its predicted bandgap frequencies with known numerical and experimental data. The efficiency and merits of the model are demonstrated by applying it to study vibration isolation of coated rigid sphere-filled composite rods and (periodic or non-periodic) free vibration caused by initial displacement or velocity disturbance of the embedded rigid spheres inside an otherwise static composite rod. The proposed model could offer a simple method to study various long-wavelength metaelastic dynamic problems of coated rigid sphere-filled random composites.

Inertial migration of rigid spheres in two-dimensional unidirectional flows

1974 ◽  
Vol 65 (2) ◽  
pp. 365-400 ◽  
Author(s):  
B. P. Ho ◽  
L. G. Leal
Keyword(s):  
Shear Flow ◽  
Simple Shear ◽  
Poiseuille Flow ◽  
Initial Position ◽  
Rigid Sphere ◽  
Simple Shear Flow ◽  
Two Dimensional ◽  
Lateral Migration ◽  
Rigid Spheres ◽  
Inertial Migration

The familiar Segré-Silberberg effect of inertia-induced lateral migration of a neutrally buoyant rigid sphere in a Newtonian fluid is studied theoretically for simple shear flow and for two-dimensional Poiseuille flow. It is shown that the spheres reach a stable lateral equilibrium position independent of the initial position of release. For simple shear flow, this position is midway between the walls, whereas for Poiseuille flow, it is 0·6 of the channel half-width from the centre-line. Particle trajectories are calculated in both cases and compared with available experimental data. Implications for the measurement of the rheological properties of a dilute suspension of spheres are discussed.

The Study in the Displacement Field near Crack of the Plexiglass by Frequency Domination Method of the White Speckle

2006 ◽  
Vol 306-308 ◽  
pp. 357-362 ◽  
Author(s):  
Xin Hua Ji ◽  
Fang Yu Xu ◽  
Jin Long Chen ◽  
Yu Wen Qin
Keyword(s):  
Light Source ◽  
Displacement Field ◽  
Vibration Isolation ◽  
Laser Speckle ◽  
Displacement Fields ◽  
Fracture Properties ◽  
Normal Environment

The fracture properties of Plexiglass bright the attentions of the researchers as it is the import material used in aero-planes industry The white speckle technique could obtain displacement fields nondestructively under the normal environment. Compare to the laser speckle method there are no interference light source and the vibration isolation needed. In the paper the principle of the technique is described and the displacement field near crack and SIF are measured. The results show that the technique is very suitable to the application in industry.

scholarly journals Migration of rigid spheres in a two-dimensional unidirectional shear flow of a second-order fluid

1976 ◽  
Vol 76 (4) ◽  
pp. 783-799 ◽  
Author(s):  
B. P. Ho ◽  
L. G. Leal
Keyword(s):  
Shear Rate ◽  
Outer Cylinder ◽  
Second Order ◽  
Rigid Sphere ◽  
Cylinder Wall ◽  
Two Dimensional ◽  
Lateral Migration ◽  
Lateral Variation ◽  
Rigid Spheres ◽  
Neutrally Buoyant

The lateral migration of a neutrally buoyant rigid sphere suspended in a second-order fluid is studied theoretically for unidirectional two-dimensional flows. The results demonstrate the existence of migration induced by normal stresses whenever there is a lateral variation of the shear rate in the undisturbed flow. The migration occurs in the direction of decreasing absolute shear rate, which is towards the centre-line for a plane Poiseuille flow and towards the outer cylinder wall for Couette flow. The direction of migration agrees with existing experimental data for a viscoelastic suspending fluid, and qualitative agreement is found between the theoretically predicted and experimentally measured sphere trajectories.

scholarly journals New Additive for Culture Media for Rapid Identification of Aflatoxin-ProducingAspergillus Strains

2001 ◽  
Vol 67 (10) ◽  
pp. 4858-4862 ◽  
Author(s):  
C. A. Fente ◽  
J. Jaimez Ordaz ◽  
B. I. Vázquez ◽  
C. M. Franco ◽  
A. Cepeda
Keyword(s):  
Culture Media ◽  
Uv Light ◽  
Rapid Identification ◽  
Fungal Culture ◽  
Simple Method ◽  
Long Wavelength ◽  
Cyclodextrin Derivative ◽  
Natural Fluorescence ◽  
Green Fluorescent ◽  
Bright Blue

ABSTRACT A new reliable, fast, and simple method for the detection of aflatoxigenic Aspergillus strains, consisting of the addition of a cyclodextrin (a methylated β-cyclodextrin derivative) to common media used for testing mycotoxin production ability, was developed. We propose the use of this compound as an additive for fungal culture media to enhance the natural fluorescence of aflatoxins. The production of aflatoxins coincided with the presence of a bright blue or blue-green fluorescent area surrounding colonies when observed under long-wavelength (365-nm) UV light after 3 days of incubation at 28°C. The presence of aflatoxins was confirmed by extracting the medium with chloroform and examining the extracts by high-pressure liquid chromatography with fluorescence detection.

Propagation of Low-Frequency Elastic Disturbances in a Composite Material

1974 ◽  
Vol 41 (1) ◽  
pp. 97-100 ◽  
Author(s):  
W. Kohn
Keyword(s):  
Composite Material ◽  
Wave Equation ◽  
Dispersion Relation ◽  
Displacement Field ◽  
Low Frequency ◽  
Local Strain ◽  
Airy Functions ◽  
Low Frequencies ◽  
One Dimensional ◽  
Long Wavelength

In the limit of low frequencies the displacement u(x, t) in a one-dimensional composite can be written in the form of an operator acting on a slowly varying envelope function, U(x, t): u(x, t) = [1 + v1(x)∂/∂x + …] U(x, t). U(x, t) itself describes the overall long wavelength displacement field. It satisfies a wave equation with constant, i.e., x-independent, coefficients, obtainable from the dispersion relation ω = ω(k) of the lowest band of eigenmodes: (∂2/∂t2 − c¯2∂2/∂x2 − β∂4/∂x4 + …) U(x, t) = 0. Information about the local strain, on the microscale of the composite laminae, is contained in the function v1(x), explicitly expressible in terms of the periodic stiffness function, η(x), of the composite. Appropriate Green’s functions are constructed in terms of Airy functions. Among applications of this method is the structure of the so-called head of a propagating pulse.

Shear versus vortex-induced lift force on a rigid sphere at moderate Re

2002 ◽  
Vol 473 ◽  
pp. 379-388 ◽  
Author(s):  
P. BAGCHI ◽  
S. BALACHANDAR
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Shear Flow ◽  
Lift Force ◽  
Lift Coefficient ◽  
Rigid Sphere ◽  
Free Rotation ◽  
Rigid Spheres ◽  
Linear Shear ◽  
Strong Lift

The lift forces on rigid spheres entrained in a vortex and a linear shear flow are computed using a direct numerical simulation. The sphere Reynolds number is in the range 10 to 100. The lift coefficient in a vortex is shown to be nearly two orders of magnitude higher than that in a shear flow. The inviscid mechanism is shown to be inadequate to account for the enhanced lift force. The effect of free rotation of the sphere is also shown to be too small to account for the enhanced lift force. Flow structure around the sphere is studied to explain the generation of the strong lift force in a vortex.

Dynamic Variational-Asymptotic Procedure for Laminated Composite Shells—Part II: High-Frequency Vibration Analysis

2008 ◽  
Vol 76 (1) ◽  
Author(s):  
Chang-Yong Lee ◽  
Dewey H. Hodges
Keyword(s):  
High Frequency ◽  
Vibration Analysis ◽  
Shell Theory ◽  
Low Frequency ◽  
Normal Displacement ◽  
Difficult Situation ◽  
Long Wavelength ◽  
First Approximation ◽  
Low Frequency Vibration ◽  
Characteristic Wavelength

Shell theories intended for low-frequency vibration analysis are frequently constructed from a generalization of the classical shell theory in which the normal displacement (to a first approximation) is constant through the thickness. Such theories are not suitable for the analysis of complicated high-frequency effects in which displacements may change rapidly along the thickness coordinate. Clearly, to derive by asymptotic methods, a shell theory suitable for high-frequency behavior requires a different set of assumptions regarding the small parameters associated with the characteristic wavelength and timescale. In Part I such assumptions were used to perform a rigorous dimensional reduction in the long-wavelength low-frequency vibration regime so as to construct an asymptotically correct energy functional to a first approximation. In Part II the derivation is extended to the long-wavelength high-frequency regime. However, for short-wavelength behavior, it becomes very difficult to represent the three-dimensional stress state exactly by any two-dimensional theory; and, at best, only a qualitative agreement can be expected. To rectify this difficult situation, a hyperbolic short-wave extrapolation is used. Unlike published shell theories for this regime, which are limited to homogeneous and isotropic shells, all the formulas derived herein are applicable to shells in which each layer is made of a monoclinic material.

The Contact Behavior Between Laminated Composite Plates and Rigid Spheres

1994 ◽  
Vol 61 (1) ◽  
pp. 60-66 ◽  
Author(s):  
Enboa Wu ◽  
Ching-Shih Yen
Keyword(s):  
Plate Thickness ◽  
Three Dimensional ◽  
Laminated Composite ◽  
Composite Plates ◽  
Anisotropic Elasticity ◽  
Rigid Sphere ◽  
Rigid Spheres ◽  
Shear Moduli ◽  
Contact Behavior ◽  
Young’S Moduli

The contact behavior between a composite laminate and a rigid sphere is discussed in this paper using a method derived from the three-dimensional anisotropic elasticity theory. Response of the plate and the force-indentation ( F − α ) relationship were obtained by constructing an exact Green’s function of the laminate. Agreement between the prediction and the experimental data reported by others is excellent before laminates are damaged. The F - α relationship is approximately proportional to the out-of-plane Young’s modulus and is influenced by the plate thickness. The effects of changing the in-place Young’s moduli, all the shear moduli, stacking sequences and span of the laminates are insignificant unless identation is large. Further, the modified Hertz law underestimates the contact force for the same indentation.

An Immersed Boundary Direct Numerical Simulation Study of the Wall Effect on the Dynamics of a Rigid Sphere

2017 ◽  
Author(s):  
Jason Gatewood ◽  
Zhi-Gang Feng
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Direct Numerical Simulation ◽  
Drag Coefficient ◽  
Particle Diameter ◽  
Laminar Flows ◽  
Wall Effect ◽  
Immersed Boundary ◽  
Rigid Sphere ◽  
Rigid Spheres

The presence of a wall near a rigid sphere is known to disturb the particle fore and aft flow field and thereby affect particle drag and lift. This effect has wide ranging implications in particulate flows such as the dynamics of blood cells in microvessels or the transport of particulates in channel and pipe flows. In this study, an Immersed Boundary Direct Numerical Simulation (IB-DNS) is used to predict the dynamics of a rigid spherical body in the presence of a wall at laminar flows. The wall effect is shown to be significant when the dimensionless ratio (L/D) of the particle diameter (D) to the wall distance (L) is less than 3, and when particle Reynolds number is less than 10. Based on the IB-DNS results, a correlation for the wall effect on drag coefficient is derived that can be used to predict the actual drag coefficient for rigid spheres under the influence of a wall for L/D between 0.75 and 3 and Reynolds number between 0.18 and 10. The data underlying the correlation developed herein is validated by comparison to published experimental, numerical, and analytical correlations. The application of the IB-DNS method to study the wall effect is both novel and significant. It is novel in that such an application is not yet demonstrated. It is significant in that it; (1) utilizes a uniform Cartesian fluid mesh and (2) requires no sub domains of higher grid resolution in the wall gap.

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