Measuring combination mode vibration patterns by hologram interferometry

Abstract

In this paper the authors offer an explanation for the holographic observation of vibration patterns that do not agree with the classical mode theory of vibrating objects. The equations are derived for the formation of hologram vibration interference fringes under the assumption that an object may vibrate in any linear combination of its permissible modes, even while executing forced vibration at a single frequency. The modes appear to combine by phasor addition in these equations to give fringe loci that depend strongly on the relative phase of the combining modes. A set of experiments are reported which demonstrate this behaviour and allow quantitative comparison to the theory. Finally, the equations are derived for combinations of modes vibrating with independent frequencies, and again a set of experiments is reported which demonstrates this behaviour and permits quantitative comparison. Here the resultant fringes appear as the product of the fringe patterns of the component modes.