Modal expansion analyses of ultrasonic Lamb waves generated by electromagnetic ultrasonic transducers

A modal expansion approach has been proposed for investigating generation of ultrasonic Lamb waves with electromagnetic acoustic transducers (EMATs). Based on the current distribution of the EMAT's meandering coil, the formal solution for Lorentz shear stress applied on the aluminum plate surface has been derived. Then the function of the wave-number spectral density of surface driving stress for generating ultrasonic Lamb waves can be obtained using the spatial Fourier transform. On this basis, with the modal expansion approach for waveguide excitation, the mathematical expression of Lamb wave's mode expansion coefficient has been deduced, which is closely related with the geometrical parameters of the EMAT's meandering coil. The mathematical relationship between Lamb wave's mode expansion coefficient and the EMAT's geometrical parameters, obtained in this paper, lays a theoretical foundation for exactly analyzing generation of Lamb waves with EMATs. Further, the numerical analyses performed indicate that the Lamb wave's mode expansion coefficient can be appropriately adjusted by changing the geometrical parameters of the EMAT's coil, and thus the unwanted Lamb wave modes can be effectively restrained. This result provides a theoretical basis for generating a single and pure Lamb wave mode with EMATs.