J. Gregory McDaniel
Kevin D. LePage
Nathan C. Martin
Bolt Beranek and Newman Inc., 70 Fawcett St., Cambridge, MA 02138
This work demonstrates a robust approach for computing complex wave numbers and amplitudes of waves in structures from experimental or numerical data. The approach postulates a wave field, which is a linear combination of damped waves. The number of waves and initial estimates of the complex wave numbers are based on any a priori physical knowledge and on the results of standard analyses of the data, such as wave-number transforms and spatial attenuation rates. Given these initial estimates of wave numbers, associated wave amplitudes are computed by linear least-squares inversion to data. Optimization algorithms improve these estimates by searching for complex wave numbers and amplitudes that minimize the normalized mean-square error between the data and the wave field. This approach is often more robust than Prony-based techniques, which require equally spaced data and are more sensitive to noise or unmodeled components. The approach is demonstrated on experimental vibration measurements of a damped box beam. Loss factors are computed for traditional flexural waves as well as plate waves, which involve flexural motions of the walls of the box beam. [Work supported by ONR.]