Methods and apparatus are disclosed for analyzing structures by applying a continuous ultrasonic excitation and measuring steady state response of the structures using laser Doppler vibrometery, or other techniques. In one example, a method comprises applying a continuous signal having one or more periodic tones to the structure, generating measurements of wave response to the signal at each of a plurality of inspection points of the structure, and, for each of the periodic tones, estimating wavenumbers for a number of the inspection points of the structure based on the wave response measurements and the frequency of the periodic tones. The estimated wavenumbers can be used to determine properties of the structure, including defects, damage, or variation in thickness.
ACKNOWLEDGMENT OF GOVERNMENT SUPPORT
 This invention was made with government support under Contract No. DE-AC52-06NA25396 awarded by the U.S. Department of Energy. The government has certain rights in the invention.