Output-Only Modal Identification of a Nonuniform Beam by Using Decomposition Methods

Reduced-order mass weighted proper orthogonal decomposition (RMPOD), smooth orthogonal decomposition (SOD), and state variable modal decomposition (SVMD) are used to extract modal parameters from a nonuniform experimental beam. The beam was sensed by accelerometers. Accelerometer signals were integrated and passed through a high-pass filter to obtain velocities and displacements, all of which were used to build the necessary ensembles for the decomposition matrices. Each of these decomposition methods was used to extract mode shapes and modal coordinates. RMPOD can directly quantify modal energy, while SOD and SVMD directly produce estimates of modal frequencies. The extracted mode shapes and modal frequencies were compared to an analytical approximation of these quantities, and to frequencies estimated by applying the fast Fourier transform to accelerometer data. SVMD is also applied to estimate modal damping, which was compared to the estimate by logarithmic decrement applied to modal coordinate signals, with varying degrees of success. This paper shows that these decomposition methods are capable of extracting lower modal parameters of an actual experimental beam.