Maximum likelihood estimation of flexural wavenumbers in lightly damped plates

This paper describes the use of the maximum likelihood method to estimate the flexural wavenumber characteristics of a vibrating plate from experimental measurements. The motion of the plate is assumed composed of a set of plane propagating waves of unknown wavenumber and amplitude. The problem of determining the wavenumbers and amplitudes that provide the ‘best’ fit to the measured data is posed as a nonlinear least-squares problem in which the nonlinear and linear variables can be separated. The maximum likelihood method is then used to solve this problem.The method is demonstrated in simulations of infinite and finite plates, and the effects of nearfields, damping and measurement noise are investigated. Practical implementation issues, including model deficiency, model adequacy and determining convergence are discussed.The method is then applied to experimental measurements on both a steel plate and a composite (orthotropic) panel, and the results are compared with theoretical predictions. It is shown that the proposed approach can give a good indication of the propagating wavenumber characteristics of lightly damped plates.