Steady-State Motions of Large Elastic Bodies. Part A: Damping in Steady-State Motions. Part B: A Steady-State Analogue to St. Venant's Principle

摘要

This report contains two parts. The first summarizes some results from the mathematical treatment of damping in steady-state motion. It is shown that the assumption of the complex modulus for so-called hysteretic or material damping does not lead to any results not implicit in the usual mathematical approach to linear elastic vibrations; further, viscous or viscoelastic behavior for steady-state motion leads to the same treatment. An experimental program to help to determine the proper physical hypothesis is suggested. The second part presents a tentative approach to the problem of establishing a sort of dynamic analogue, at least for steadystate motions, to the static St. Venant's principle of elasticity theory. The difficulties inherent in determining the pressure distribution between an indenter and a body lead one to want some way of finding the distance at which details of the distribution are no longer important. It is shown that total force and moment characteristics can be modeled and that these give the primary or lowest-order effects far from the loaded region. An estimation of the remainder effect, other than its order, is not as yet available. (Author)