Lydik S. Jacobsen

Response of an elastically non-linear system to transient disturbances

Abstract Tje problem relates to an undamped, elastically non-linear, single-degree-of-freedom system subjected to three forms of ground motion pulses (rectangular, cosine and “skewed” cosine); each form consists of a single pulse, the duration of which has been varied over a wide range. The maximum relative displacements (maximum distortions) have been plotted in dimensionless form as functions of the pulse durations. Under some circumstances the non-linearity results in reduced maximum distortion, but in other cases it acts to increase it. Simple quantitative conclusions cannot be drawn.Analytical, graphical and experimental methods were employed; the graphical method has been presented in detail.

Steady forced vibrations of single mass systems with symmetrical as well as iinsymmetrical non-linear restoring elements

Abstract Part of the theory and all the experiments reported on in this paper were condensed into a four-page discussion or addendum to Professor Den Hartogs original paper on “Amplitudes of Non-Harmonic Vibrations” at the time of its presentation at the June Meeting of the A.S.M.E. in Chicago, 1933. Upon the instigation of Professor Den Hartog and the Editor of the Journal of the Franklin Institute , the original discussion has been brought into the present form.

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.