Time-frequency characterization of lamb waves for material evaluation and damage inspection of plates

• Present a finite-element technique for computing dispersion curves and different modes.
• Present a conjugate-pair decomposition method for time-frequency analysis of Lamb waves.
• Time-frequency analysis can separate symmetric and antisymmetric modes.
• Time-frequency analysis can locate the interaction of different modes.
• Time-frequency analysis can reveal damage-induced small wave packets.

Guided wave-based technique is one major approach for damage inspection of structures. To detect a small damage, an elastic wave׳s wavelength needs to be in the order of the damage size and hence the frequency needs to be high. Unfortunately, high-frequency wave dynamics always involves complicated wave reflection, refraction and diffraction, and it is difficult to separate them in order to perform detailed examination and system identification. This paper investigates dynamic characteristics of Lamb waves in plates in order to be used for material evaluation and damage inspection of thin-walled structures. A one-dimensional finite-element modeling and analysis technique is developed for computing dispersion curves and all symmetric and antisymmetric modes of Lamb waves in isotropic and multi-layer plates. Moreover, the conjugate-pair decomposition (CPD) method is introduced for time-frequency analysis of propagating Lamb waves. Results show that, under a k-cycle sine-burst excitation at a plate׳s edge, the time-varying frequency of a surface point׳s response can reveal the Lamb wave propagating inside the plate being a symmetric or an antisymmetric mode. The frequency of the measured wave packet increases from the wave front to the trailing edge if it is a symmetric mode, and the frequency decreases from the wave front to the trailing edge if it is an antisymmetric mode. Moreover, interaction of two different wave packets results in a peak in the time-frequency curve. These characteristics can be used for accurate separation of wave packets and identification of different wave speeds to enable fast and accurate material evaluation and damage inspection. Transient finite-element analysis of Lamb waves in finite plates with crack/delamination show that k-cycle sine-burst probing waves are good agents for guided wave-based damage inspection of structures. Although crack and delamination introduce different waves into and complicate the probing wave packet, time-frequency analysis makes it possible to separate such damage-induced small waves from the probing wave and enable fast and accurate damage inspection of thin-walled structures.