Measurement of longitudinal vibrations in a slender rod by optical heterodyne interferometry

Abstract

The vibration of a slender rod subject to a longitudinal harmonic perturbation without physical contact and near the first resonance frequency is experimentally analyzed. The rod is excited by a magnetic field which produces an harmonic force acting on a small ferromagnetic disc glued at the end of the rod. The detection technique applied is based on the optical heterodyne speckle interferometry, which permits both the normal-to-surface displacement and the tangential displacement to be detected sequentially. The out-of-plane technique is used to estimate the first eigenfrequency. By means of the in-plane technique the amplitude and phase for different frequencies near resonance are measured and the displacements of 17 equidistant points on the lateral surface of the rod are plotted as a function of time. The comparison between the experimental results and the prediction of the classical theory shows a good agreement, making apparent the usefulness of the speckle interferometry for the vibration analysis. In addition, Young's modulus is calculated and Poisson's ratio is estimated from the measurement of both the out-of-plane and in-plane displacements of two opposite lateral points of the rod.