Steady forced vibration of a non-conservative system with variable mass; a pumping system

Abstract

There is an interesting class of vibratory systems in which the mass is a function of the velocity of the system. This paper treats, both theoretically and experimentally, the steady forced vibration of a single-degree-of-freedom system, with stepwise variation in mass, and by which external work is done. The deep-well reciprocating pump has been used as an example of such a system although in doing so it is necessary to consider the pump a highly idealized, undamped system with lumped parameters. The main purpose has been to study the effect of variation in mass. The theory considers two linear systems, one of mass M, the other of mass M + m, the boundary conditions of which must be made to agree. Four distinct “Classes of Motion” are shown; three of them involve an over-travel of the secondary mass, m. The experimental apparatus is mechanical.