title: Analysis of 3-D vibrations from time-averaged holograms.
abstract: In a previous paper [R. Tonin and D. A. Bies, J. Sound Vib. 52(3), 315 (1977)] the theory of time-averaged holographic interferometry was extended to include simple harmonic motion in three orthogonal directions at a single frequency. The amended characteristic function formula was used to calculate the radial and tangential components of a vibrating cylinder by first determining the radial component and from this the tangential component of vibration. In this paper the analysis of the previous paper is improved by making use of a technique originally introduced for the investigation of static deflection using time-averaged holography [S. K. Dhir and J. P. Sikora, Exp. Mech. 12(7), 323 (1972)]. The improved procedure allows simultaneous determination of all vibration amplitude components. The procedure is used for the investigation of the low order resonant vibration modes of four cylinders of various sizes and materials with shear-diaphragm end conditions with good results. The procedure is quite general in its application and not restricted to the study of cylinders. It lends itself easily to the study of coupled-mode vibration problems and in fact many complex resonance phenomena.
authors.forename: R
authors.initials: R
authors.lastname: Tonin
authors.forename: D A
authors.initials: DA
authors.lastname: Bies