Frictional Contact Between the Surface Wave and a Rigid Strip

1996 ◽  
Vol 63 (1) ◽  
pp. 15-20 ◽  
Author(s):  
O. Y. Zharii
Keyword(s):  
Surface Wave ◽  
Frictional Contact ◽  
Mixed Boundary ◽  
Closed Form Solution ◽  
Tangential Velocity ◽  
Form Solution ◽  
Load Force ◽  
Tangential Load ◽  
Normal Stress Distribution ◽  
Limiting Case

A problem of frictional contact between a running surface wave and a motionless rigid strip is considered. The corresponding mixed boundary value problem of elastodynamics is reduced to a singular integral equation for the normal stress distribution and a closed-form solution of it has been found. Boundaries of the contact zone are determined from a system of transcendental equations involving trigonometric functions. Also, simple formulae obtained for kinematic characteristics of solution (tangential velocity inside the contact area, velocity and slope of the free surface outside it). The problem considered represents a limiting case of operating ultrasonic motor when it is completely braked by an external tangential load force.

Adhesive Contact Between the Surface Wave and a Rigid Strip

1995 ◽  
Vol 62 (2) ◽  
pp. 368-372 ◽  
Author(s):  
O. Y. Zharii
Keyword(s):  
Integral Equation ◽  
Surface Wave ◽  
Stress Distribution ◽  
Contact Area ◽  
Mixed Boundary ◽  
Closed Form Solution ◽  
Adhesive Contact ◽  
Form Solution ◽  
Mixed Boundary Value Problem ◽  
Analysis Of Variation

A problem of adhesive contact between the running surface wave and a rigid strip is investigated. The mixed boundary-value problem of elastodynamics is reduced to a singular integral equation for a complex combination of stresses and an exact closed-form solution of it has been derived. Analysis of variation of contact area dimensions, stress distribution and rotor velocity on the frequency of excitation displayed significant differences between the results corresponding to conditions of adhesion and slipping in contact area. The origin of these differences is discussed.

Closed Form Solution for Outflow Between Corotating Disks

2016 ◽  
Vol 138 (5) ◽  
Author(s):  
Achhaibar Singh
Keyword(s):  
Closed Form ◽  
Stokes Equations ◽  
Closed Form Solution ◽  
Tangential Velocity ◽  
Form Solution ◽  
Navier Stokes ◽  
Published Data ◽  
Rotational Inertia ◽  
Viscous Losses ◽  
Present Solution

Mathematical expressions are derived for flow velocities and pressure distributions for a laminar flow in the gap between two rotating concentric disks. Fluid enters the gap between disks at the center and diverges to the outer periphery. The Navier–Stokes equations are linearized in order to get closed-form solution. The present solution is applicable to the flow between corotating as well as contrarotating disks. The present results are in agreement with the published data of other investigators. The tangential velocity is less for contrarotating disks than for corotating disks in core region of the radial channel. The flow is influenced by rotational inertia and convective inertia both. Dominance of rotational inertia over convective inertia causes backflow. Pressure depends on viscous losses, convective inertia, and rotational inertias. Effect of viscous losses on pressure is high at small throughflow Reynolds number. The convective and rotational inertia influence pressure significantly at high throughflow and rotational Reynolds numbers. Both favorable and unfavorable pressure gradients can be found simultaneously depending on a combination of parameters.

scholarly journals New Poisson's Type Integral Formula for Thermoelastic Half-Space

2009 ◽  
Vol 2009 ◽  
pp. 1-18 ◽  
Author(s):  
Victor Seremet ◽  
Guy Bonnet ◽  
Tatiana Speianu
Keyword(s):  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Mixed Boundary ◽  
Integral Formula ◽  
Closed Form Solution ◽  
Form Solution ◽  
Concentrated Force ◽  
Volume Dilatation ◽  
Type Integral

A new Green's function and a new Poisson's type integral formula for a boundary value problem (BVP) in thermoelasticity for a half-space with mixed boundary conditions are derived. The thermoelastic displacements are generated by a heat source, applied in the inner points of the half-space and by temperature, and prescribed on its boundary. All results are obtained in closed forms that are formulated in a special theorem. A closed form solution for a particular BVP of thermoelasticity for a half-space also is included. The main difficulties to obtain these results are in deriving of functions of influence of a unit concentrated force onto elastic volume dilatation and, also, in calculating of a volume integral of the product of function and Green's function in heat conduction. Using the proposed approach, it is possible to extend the obtained results not only for any canonical Cartesian domain, but also for any orthogonal one.

Closed-Form Solution of the Frictional Sliding Contact Problem for an Orthotropic Elastic Half-Plane Indented by a Wedge-Shaped Punch

2014 ◽  
Vol 618 ◽  
pp. 203-225 ◽  
Author(s):  
Aysegul Kucuksucu ◽  
Mehmet A. Guler ◽  
Ahmet Avci
Keyword(s):  
Contact Problem ◽  
Half Plane ◽  
Mixed Boundary ◽  
Closed Form Solution ◽  
Contact Problems ◽  
Form Solution ◽  
Orthotropic Materials ◽  
Principal Axes ◽  
The Coefficient Of Friction ◽  
Processing Techniques

In this paper, the frictional contact problem of a homogeneous orthotropic material in contact with a wedge-shaped punch is considered. Materials can behave anisotropically depending on the nature of the processing techniques; hence it is necessary to develop an efficient method to solve the contact problems for orthotropic materials. The aim of this work is to develop a solution method for the contact mechanics problems arising from a rigid wedge-shaped punch sliding over a homogeneous orthotropic half-plane. In the formulation of the plane contact problem, it is assumed that the principal axes of orthotropy are parallel and perpendicular to the contact. Four independent engineering constants , , , are replaced by a stiffness parameter, , a stiffness ratio, a shear parameter, , and an effective Poisson’s ratio, . The corresponding mixed boundary problem is reduced to a singular integral equation using Fourier transform and solved analytically. In the parametric analysis, the effects of the material orthotropy parameters and the coefficient of friction on the contact stress distributions are investigated.

View Factors in Radiation Between Two Parallel Oriented Cylinders of Finite Lengths

1982 ◽  
Vol 104 (2) ◽  
pp. 384-388 ◽  
Author(s):  
N. H. Juul
Keyword(s):  
Line Source ◽  
Closed Form Solution ◽  
Diffuse Radiation ◽  
Form Solution ◽  
View Factor ◽  
Double Integral ◽  
Integral Expression ◽  
View Factors ◽  
Limiting Case ◽  
Analytical Expressions

A simple double-integral expression for the diffuse radiation view factor, F12, between two parallel cylinders of finite lengths is derived. No closed-form solution appears possible except for the limiting case of infinite long cylinders for which an analytical expression for the view factor F12∞ is derived by applying the crossed string method. The accuracies of the line source approximations are evaluated, and the regions for which they are accurate to one percentage or better are identified. The view factor F12 between two opposing cylinders of equal length is computed by numerical integration and normalized by F12∞. The results are presented. Analytical expressions, which approximate the view factors between two opposite cylinders of finite length, are derived and their accuracy is evaluated over a useful parameter range. The range of their applications corresponds approximately to that for the line source approximation. This result is expected, because the errors are caused in part by blockage of radiation which is similar.

Two dimensional mixed boundary-value problems in a wedge-shaped region

1968 ◽  
Vol 64 (2) ◽  
pp. 503-505 ◽  
Author(s):  
W. E. Williams
Keyword(s):  
Integral Equation ◽  
Boundary Value Problems ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Closed Form Solution ◽  
Form Solution ◽  
Two Dimensional ◽  
Dual Integral Equations ◽  
Mixed Boundary Value Problems ◽  
Mellin Transforms

In a recent paper Srivastav (2) considered the solution of certain two-dimensional mixed boundary-value problems in a wedge-shaped region. The problems were formulated as dual integral equations involving Mellin transforms and were reduced to the solution of a Fredholm integral equation of the second kind. In this paper it will be shown that a closed form solution to the problems treated in (2) may be obtained by elementary means.

The Frictional Contact Problem of a Rigid Stamp Sliding over a Graded Medium

2016 ◽  
Vol 681 ◽  
pp. 155-174 ◽  
Author(s):  
M.A. Guler ◽  
M. Ozturk ◽  
A. Kucuksucu
Keyword(s):  
Contact Problem ◽  
Half Plane ◽  
Frictional Contact ◽  
Fourier Transforms ◽  
Closed Form Solution ◽  
Form Solution ◽  
Linear Elastic ◽  
Rigid Stamp ◽  
Sharp Edges ◽  
Parameter Coefficient

In this study, the contact problem for a graded elastic half-plane in frictional contact with a rigid stamp is considered. The plane contact problem is assumed to be linear elastic and the Poisson's ratio is assumed to be constant. Analytical formulation of the study includes Fourier transforms of the governing equations and boundary conditions. The resulting integral equation is solved numerically. Contact pressure, in-plane stress and the stress intensity factor at the sharp edges of the contact are evaluated and demonstrated for various stamp profiles. The results are compared with a closed form solution for homogeneous isotropic half-plane indented by rigid stamps. The effects of the nonhomogeneity parameter, coefficient of friction and stamp profiles on the contact and in-plane stresses are analyzed in detail.

Smooth Contact Between the Running Rayleigh Wave and a Rigid Strip

1995 ◽  
Vol 62 (2) ◽  
pp. 362-367 ◽  
Author(s):  
O. Y. Zharii ◽  
A. F. Ulitko
Keyword(s):  
Rayleigh Wave ◽  
Mixed Boundary ◽  
Closed Form Solution ◽  
Form Solution ◽  
Mixed Boundary Value Problem ◽  
Trigonometric Functions ◽  
Frictionless Contact ◽  
Dual Series Equations ◽  
Analytic Expressions ◽  
Smooth Contact

A problem of frictionless contact between the running Rayleigh wave and a rigid strip is investigated. The corresponding mixed boundary value problem of elastodynamics is reduced to a system of dual series equations involving trigonometric functions. On the base of the closed-form solution obtained, explicit analytic expressions for distributions of normal displacements and stresses and of tangential velocities on the surface have been derived.

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