Dynamic profilometry without out-of-plane conversion to measure vibration frequency of a cantilever beam

Abstract

A new technique to measure oscillation frequencies and modal shapes of an Euler–Bernoulli cantilever beam using dynamic profilometry and phase extraction techniques is presented. The proposed technique does not require a fixed reference or out-of-plane conversion, and works on nonstop vibration. A binary pattern is projected on the cantilever beam surface mechanically forced to vibrate harmonically in a natural mode. The Fourier transform method is employed to obtain the phase difference between two consecutive frames, in particular it is applied to four consecutive frames so that three consecutive phase differences are available. Finally, the three-step temporal phase-shifting technique is applied to measure the vibration's eigenvalues and eigenfunctions. This paper presents the analysis of the underlying theory and the experimental results obtained.