Output Only Modal Analysis of a Nonuniform Beam Experiment by Using Decomposition Methods

This work explores the application of reduced-order mass-weighted proper orthogonal decomposition (RMPOD), state variable modal decomposition (SVMD), and smooth orthogonal decomposition (SOD) for extracting approximations of linear normal modes (LNMs) of a free vibrating thin lightly damped nonuniform beam experiment. The application of these decomposition methods involves organizing sensed outputs into ensemble matrices. The ensemble matrices are utilized to create correlation matrices, which are used in solving an eigenvalue problem. This is realized experimentally by sensing a thin nonuniform cantilevered beam, a saw blade, with eleven equally spaced accelerometers, during free vibration. The first mode was filtered out since its frequency was below the threshold of reliable accelerometers performance. RMPOD was able to extract the second, third, and fourth mode as implied by modal assurance criterion (MAC) in a comparison with an analytical approximation of the nonuniform Euler-Bernoulli beam modes. SVMD was able to extract an approximation to the LNMs and natural frequencies for the second, third, and fourth modes. SOD was able to extract the second, third, and fourth modes and natural frequencies successfully.