scholarly journals On the propagation, reflection, and transmission of transient cylindrical shear waves in nonhomogeneous four-parameter viscoelastic media

1973 ◽  
Vol 8 (3) ◽  
pp. 397-411 ◽  
Author(s):  
T. Bryant Moodie
Keyword(s):  
Material Properties ◽  
Outer Boundary ◽  
Shear Waves ◽  
Infinite Plate ◽  
Radial Distance ◽  
Viscoelastic Plate ◽  
Reflection And Transmission ◽  
Viscoelastic Media ◽  
Finite Plate ◽  
Arbitrary Thickness

The purpose of this paper is to study the propagation of cylindrical shear waves in nonhomogeneous four-parameter viscoelastic plates of arbitrary thickness. The plates have a transverse cylindrical hole and their material properties are functions of the radial distance from the center of this opening. They are initially unstressed and at rest. A suddenly rising shearing traction is applied uniformly over the boundary of the opening and parallel to the faces of the plates and thereafter steadily maintained; they are otherwise free from loading. We consider both the case of a finite plate with a stress-free cylindrical outer boundary, and an infinite plate composed of two media in welded contact along a cylindrical surface symmetrical with respect to the center of the opening. We find that a reflected pulse is produced at the outer boundary of the finite plate while reflected and transmitted pulses are produced at the interface in the infinite bi-viscoelastic plate. Ray techniques are used throughout, and formal asymptotic wavefront expansions of the solution functions are obtained.

scholarly journals Nanoparticles and the influence of interface elasticity

2008 ◽  
Vol 35 (1-3) ◽  
pp. 267-286 ◽  
Author(s):  
Mi Changwen ◽  
Demitris Kouris
Keyword(s):  
Material Properties ◽  
Axial Symmetry ◽  
Outer Boundary ◽  
Elastic Field ◽  
Interface Stress ◽  
Axially Symmetric ◽  
Displacement Potential ◽  
Surface And Interface ◽  
Stress Effects ◽  
Interface Elasticity

In this manuscript, we discuss the influence of surface and interface stress on the elastic field of a nanoparticle, embedded in a finite spherical substrate. We consider an axially symmetric traction field acting along the outer boundary of the substrate and a non-shear uniform eigenstrain field inside the particle. As a result of axial symmetry, two Papkovitch-Neuber displacement potential functions are sufficient to represent the elastic solution. The surface and interface stress effects are fully represented utilizing Gurtin and Murdoch's theory of surface and interface elasticity. These effects modify the traction-continuity boundary conditions associated with the classical continuum elasticity theory. A complete methodology is presented resulting in the solution of the elastostatic Navier's equations. In contrast to the classical solution, the modified version introduces additional dependencies on the size of the nanoparticles as well as the surface and interface material properties.

The measurement of surface tension by means of a vertical-plate balance

1970 ◽  
Vol 23 (11) ◽  
pp. 2153 ◽  
Author(s):  
JE Lane ◽  
DO Jordan
Keyword(s):  
Surface Tension ◽  
Experimental Error ◽  
Gravitational Force ◽  
Vertical Plate ◽  
Infinite Plate ◽  
Arbitrary Cross Section ◽  
Finite Plate ◽  
Fluid Surface ◽  
Additional Force ◽  
Infinite Height

A thermodynamic analysis of the measurement of surface tension using plates with either horizontal or vertical grooves of arbitrary cross section is presented. An exact description of the behaviour of horizontal grooves in a plate of infinite width and of vertical grooves in a plate of infinite height is given. The behaviour of a plate of finite height with vertical grooves can be the same as for an infinite plate, but in most instances this is not true. An approximate analysis of a finite plate with vertical grooves is developed and the errors in the curvatures of the resulting liquid-fluid surface are evaluated. In general, it is found that a grooved plate partly immersed in liquid requires a greater force to balance it than a smooth plate of the same overall dimensions and mass and with zero contact angle against the liquid and fluid phases. The additional force required to balance the grooved plate is approximately independent of the groove orientation but increases with width (pitch) of the groove. It is shown that if the measurements are made with the bottom of the plate at the level of the liquid-fluid surface at an infinite distance from the plate, the additional force almost equals the gravitational force on the mass of liquid adhering to the plate after complete immersion and withdrawal from the liquid, the agreement improving as the groove pitch is decreased. This conclusion helps explain the good results obtained for surface tension measurements using roughened plates with scratched surfaces. The important results are checked experimentally and in most cases the agreement is within the experimental error. The only exceptions to this are the results for finite plates with vertical grooves but even then the agreement is nearly quantitative.

Fragmentation of a Filamentary Cloud Threaded by Perpendicular Magnetic Field

2018 ◽  
Vol 14 (A30) ◽  
pp. 105-105
Author(s):  
Tomoyuki Hanawa ◽  
Takahiro Kudoh ◽  
Kohji Tomisaka
Keyword(s):  
Magnetic Field ◽  
Magnetic Force ◽  
Outer Boundary ◽  
Radial Distance ◽  
Radial Density ◽  
Radial Density Distribution ◽  
Model Cloud ◽  
Moderate Magnetic Field ◽  
Self Gravity ◽  
The Magnetic Field

AbstractFilamentary molecular clouds are thought to fragment to form clumps and cores. However, the fragmentation may be suppressed by magnetic force if the magnetic fields run perpendicularly to the cloud axis. We evaluate the effect using a simple model. Our model cloud is assumed to have a Plummer like radial density distribution, $\rho = {\rho _{\rm{c}}}{\left[ {1 + {r^2}/(2p{H^2})} \right]^{2p}}$ , where r and H denote the radial distance from the cloud axis and the scale length, respectively. The symbols, ρc and p denote the density on the axis and radial density index, respectively. The initial magnetic field is assumed to be uniform and perpendicular to the cloud axis. The model cloud is assumed to be supported against the self gravity by gas pressure and turbulence. We have obtained the growth rate of the fragmentation instability as a function of the wavelength, according to the method of Hanawa, Kudoh & Tomisaka (2017). The instability depends crucially on the outer boundary. If the displacement vanishes in regions very far from the cloud axis, cloud fragmentation is suppressed by a moderate magnetic field. If the displacement is constant along the magnetic field in regions very far from the cloud, the cloud is unstable even when the magnetic field is infinitely strong. The wavelength of the most unstable mode is longer for smaller index, p.

A Numerical Procedure for Estimating the Stress Intensity Factor of a Crack in a Finite Plate

1964 ◽  
Vol 86 (4) ◽  
pp. 681-684 ◽  
Author(s):  
A. S. Kobayashi ◽  
R. D. Cherepy ◽  
W. C. Kinsel
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
High Speed ◽  
Linear Equations ◽  
Infinite Plate ◽  
Numerical Procedure ◽  
Complex Stress ◽  
Theory Of Elasticity ◽  
Finite Plate

The advantages of the complex variable method are combined with the numerical procedure of collocation for estimating the stress intensity factors in finite, cracked plates subjected to in-plane loadings. In this approach, the complex stress functions for an infinite plate problem are modified to meet the boundary conditions for a finite plate with identical crack configuration. This procedure produces a system of linear equations which can be programmed readily on high-speed computers. The procedure is used to find the elastic stress intensity factor at the crack tip in a centrally notched plate in uniaxial tension. The resulting values are nearly identical to the stress intensity values determined analytically by the theory of elasticity. This numerical procedure should be useful for designers and analysts working in the fields of fracture mechanics and fail-safe concepts.

scholarly journals Interference Analysis between Crack and General Inclusion in an Infinite Plate by Body Force Method

2013 ◽  
Vol 577-578 ◽  
pp. 1-4
Author(s):  
Takuichiro Ino ◽  
Shohei Ueno ◽  
Akihide Saimoto
Keyword(s):  
Material Properties ◽  
Body Force ◽  
Infinite Plate ◽  
Inelastic Strain ◽  
Inclusion Problem ◽  
Interference Analysis ◽  
Force Method ◽  
Body Force Method

A Continously Embedded Force Doublet over the Particular Region can be Regardedas the Distributing Eigen Strain. this Fact Implies that many Sorts of Inelastic Strain can Bereplaced by the Force Doublet. in the Present Paper, the Force Doublet is Used to Alter the Localconstitutive Relationship. as a Result, a Method for Analyzing the General Inclusion Problem Inwhich the Material Properties of the Inclusion are Not only Different from those of the Matrixmaterial but also can be even a Function of Spacial Coordinate Variables is Proposed. Thetheoretical Background of the Present Analysis is Explained Followed by some Representativenumerical Results.

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