Study of Initial Conditions in Constant Velocity Impact

1960 ◽  
Vol 31 (12) ◽  
pp. 2188-2195 ◽  
Author(s):  
James F. Bell
Keyword(s):  
Constant Velocity ◽  
Initial Conditions ◽  
Velocity Impact

Thermoelasticity When the Material Coupling Parameter Equals Unity

1965 ◽  
Vol 32 (2) ◽  
pp. 378-382 ◽  
Author(s):  
O. W. Dillon
Keyword(s):  
Laplace Transform ◽  
Constant Velocity ◽  
Coupling Parameter ◽  
Step Function ◽  
Surface Strain ◽  
Coupled Thermoelasticity ◽  
Velocity Impact ◽  
One Dimensional ◽  
Laplace Transform Technique ◽  
The Laplace Transform

Analytical solutions of three problems in coupled thermoelasticity are presented for the case when the material coupling parameter equals unity. The problems considered are: (a) Danilovskaya’s problem of a step function in temperature at the surface; (b) a step function in surface strain; and (c) constant velocity impact. Solutions are presented for the case of thin bars (one-dimensional stress) and are obtained by the Laplace-transform technique. There is great simplification in the equations when the material coupling parameter equals unity which permits the straightforward inversion of the transformed solutions. The results demonstrate significant deviations from the corresponding uncoupled solutions.

Plastic Deformation of Semi-Infinite Beams Subject to Transverse Impact Loading at the Free End

1956 ◽  
Vol 23 (2) ◽  
pp. 239-243
Author(s):  
M. F. Conroy
Keyword(s):  
Plastic Deformation ◽  
Impact Loading ◽  
Constant Velocity ◽  
Bending Moment ◽  
Transverse Force ◽  
Square Root ◽  
Transverse Loading ◽  
Transverse Impact ◽  
Velocity Impact ◽  
Time Part

Abstract The object of this paper is to consider the plastic deformation of semi-infinite beams subject to dynamic transverse loading at the free end. The type of loading considered is that of a constant bending moment, together with a transverse force the magnitude of which is inversely proportional to the square root of time. Part 1 of the paper consists of a plastic-rigid analysis of the problem, based on the plastic-rigid analysis of infinite beams under transverse, constant velocity, impact loading developed by the author. Part 2 of the paper consists of an elastic-plastic solution of the problem, based on a theoretical analysis of the plastic deformation of infinite beams subject to transverse, constant-velocity impact loading developed by H. F. Bohnenblust. Specific problems are considered for which the deflection solutions obtained by elastic ideally plastic and rigid ideally plastic analyses are compared.

GENERALIZED SYNCHRONIZATION AND MEMORY EFFECT IN THE BURRIDGE–KNOPOFF SYSTEM OF THREE BLOCKS

2004 ◽  
Vol 15 (05) ◽  
pp. 629-636
Author(s):  
JACEK SZKUTNIK ◽  
KRZYSZTOF KUŁAKOWSKI
Keyword(s):  
Phase Space ◽  
Memory Effect ◽  
Constant Velocity ◽  
Initial Conditions ◽  
Numerical Results ◽  
Generalized Synchronization ◽  
The Third ◽  
Central Block ◽  
Second Mode ◽  
The One

Recently, synchronization in the Burridge–Knopoff model has been found to depend on the initial conditions. Here we report the existence of three modes of oscillations of the system of three blocks. In one of the modes, two lateral blocks are synchronized. In the second mode, the central block moves with almost constant velocity, i.e., it does not stick. Two lateral blocks do stick and they move in opposite phases. In the third mode, the blocks oscillate with aperiodic amplitude. The lateral blocks move in opposite phases and their frequency is lower than the one for the central block. The mode selected by the system depends on the initial conditions. Numerical results indicate that there is no modes in the phase space.

Three-dimensional viscous wakes

1962 ◽  
Vol 14 (2) ◽  
pp. 233-240 ◽  
Author(s):  
Martin H. Steiger ◽  
Martin H. Bloom
Keyword(s):  
Boundary Layer ◽  
Turbulent Flows ◽  
Axial Symmetry ◽  
Constant Velocity ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Velocity Fields ◽  
Axial Velocity Distribution ◽  
Fluid Properties ◽  
Laminar And Turbulent Flows

The velocity fields of three-dimensional viscous wakes are examined with the use of the boundary-layer approximations, Oseen's linearization of the convective terms, and the assumption of constant fluid properties. Transform methods yield solutions for general types of initial conditions. As an illustration, the axial velocity distribution of a wake whose initial isovels (lines of constant velocity) are of elliptic shape and their decay to axial symmetry are demonstrated. Both laminar and turbulent flows are considered.

Dynamics of Golf Ball-Hole Interactions: Rolling Around the Rim

1999 ◽  
Vol 121 (1) ◽  
pp. 88-95 ◽  
Author(s):  
Mont Hubbard ◽  
Tait Smith
Keyword(s):  
Initial Conditions ◽  
Golf Ball ◽  
Capture Process ◽  
Velocity Impact ◽  
Ball Rolling ◽  
Pure Rolling ◽  
Rolling Without Slipping ◽  
Impact Parameter Space ◽  
Roll Out ◽  
Perturbation Solutions

A previous study of a golf ball rolling on the rim of a cup neglected the spin of the ball about a line perpendicular to the plane of contact. The capture process is studied here by numerically solving the equations for rolling without slipping on the rim. The boundary in the velocity-impact parameter space separating roll-in and roll-out trajectories corresponds to initial conditions for a set of near guasi-equilibrium trajectories. Stability of the equilibrium trajectories is investigated using symbolic linearization of perturbation solutions from them. Although the locally unstable equilibrium trajectories themselves are not attainable from the two-space of pure rolling initial conditions, the boundary is nevertheless a “barrier” in that it corresponds to long contact times and large roll around angles.

An experimental study of laminar plumes

1993 ◽  
Vol 251 ◽  
pp. 581-601 ◽  
Author(s):  
Elisha Moses ◽  
Giovanni Zocchi ◽  
Albert Libchaberii
Keyword(s):  
Experimental Study ◽  
Potential Flow ◽  
Constant Velocity ◽  
Scaling Laws ◽  
Initial Conditions ◽  
Source Size ◽  
Turbulent Convection ◽  
Scaling Relations ◽  
Far Field

We present an experimental study of the scaling laws for the front (or cap) of an isolated, laminar starting plume. The scaling relations are formulated and measured experimentally over a range of power, fluids, and heaters. The results are that the cap rises at constant velocity, grows diffusively in width, and its temperature depends inversely on height. This extends analytic results by Batchelor (1954) for the column (stem) below the front. The source size determines initial conditions for the cap, but does not affect it in the far field. The shape of the front is fitted by a model of potential flow. The interaction between plume caps is complex, but with simple underlying dynamics. We conjecture that some of our conclusions can be applied to a distribution of plumes, as in soft turbulent convection.

Finite Size of the Electron and Runaway Solutions

1977 ◽  
Vol 32 (5) ◽  
pp. 383-389 ◽  
Author(s):  
J. Petzold ◽  
W. Heudorfer ◽  
M. Sorg
Keyword(s):  
Dirac Equation ◽  
Free Electron ◽  
Constant Velocity ◽  
Initial Conditions ◽  
Perturbation Expansion ◽  
Finite Size ◽  
Equation Of Motion ◽  
Local Equation ◽  
Causality Violation ◽  
Non Local

Abstract The problem of runaway solutions is studied within the framework of a non-local equation of motion for the classically radiating electron. It is found that the force-free electron oscillates down to a constant velocity under emission of radiation, if certain restrictions on the initial conditions are imposed. Causality violation is not present in this model, but penetrates into the theory as consequence of a false perturbation expansion leading to the notorious Lorentz-Dirac equation of motion.

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