Proper Orthogonal Modes of a Beam Sensed with Strain Gages

Contributed by the Technical Committee on Vibration and Sound for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received November 2001; Revised January 2002. Associate Editor: A. F. Vakakis.

Proper orthogonal decomposition (POD) is a useful experimental tool in dynamical systems, for example in dimensionality studies 1,2 and reduced order modeling 3,4,5 6. Application of POD in structural vibrations often involves sensed displacements, $x1,$$x2,…,xM,$ at M locations on the structure. These displacements are sampled N times at a fixed sampling rate to form displacement arrays $xj=[xjt1,…,xjtN]T,$$j=1,…,M.$ The means are often subtracted. An $N×M$ ensemble matrix $X=[x1,…,x...$