Semi-infinite Bar Research Articles

Transient Wave Analysis in a Linear Time-Dependent Material

We consider a body which under stress exhibits an elastic, a viscous, and a retarded elastic response. For the particular case of a constant velocity applied at the end of a semi-infinite bar, the transient stresses, strains and velocities are found by the method of characteristics. From this solution can also be obtained the stresses for the case of a constant stress applied at the end of a semi-infinite bar. By superposition we can also solve problems involving finite bars. For a constant velocity applied at the end of the bar an integral expression is derived for the stress at that end as a function of time.

On the axially-symmetric steady wave propagation in elastic circular rods

In the first part of this report we find an exact solution for the problem of steady wave propagation in an isotropic, elastic circular bar of infinite length, free of stress on its lateral surface and loaded by a harmonic body force, parallel to its axis, whose amplitude is a Dirac delta function. The solution of this problem gives at the same time the solution for a semi-infinite bar with a special prescribed load on its boundary plane.

A Note on a Problem in Conduction

The expression for the temperature distribution in a semi-infinite bar with heat supplied to the surface x=0 at a rate given by H=ktn(n=0, 1, 2 ···) is derived, assuming no radiation to the surrounding medium and an initial temperature of zero. Curves are given which enable the distribution in a bar of any material to be readily computed for n=0 and n=1. The solution serves equally well to determine the voltage variation in a semi-infinite non-inductive cable with entering current proportional to tn provided the heat constants are replaced by the appropriate electrical parameters.