Proper Orthogonal Modes of a Beam Sensed with Strain Gages

Abstract

Proper orthogonal decomposition (POD) is a useful experimental tool in dynamical systems, for example in dimensionality studies 12 and reduced order modeling 3456. Application of POD in structural vibrations often involves sensed displacements, x1,x2,[[ellipsis]],xM, at M locations on the structure. These displacements are sampled N times at a fixed sampling rate to form displacement arrays xj=[xj(t1),[[ellipsis]],xj(tN)]T,j=1,[[ellipsis]],M. The means are often subtracted. An N×M ensemble matrix X=[x1,[[ellipsis]],xM] is then built. The M×M correlation matrix is R=XTX/N. Since R is real and symmetric, its eigenvectors form an orthonormal basis. The eigenvectors are the proper orthogonal modes (POMs) and the eigenvalues are the proper orthogonal values (POVs).