Resonant electromagnetic excitation and detection of ultrasonic waves in thin sheets

Abstract

A unified theory of the simultaneous electromagnetic excitation and detection of ultrasonic waves travelling in the through-thickness direction in conducting sheets in the presence of a static magnetic field is presented. What to our knowledge are the highest-frequency room-temperature measurements of this type are described for aluminium sheets of thickness as low as 20 μm for frequencies up to 120 MHz. Maxwell’s equations are solved for the geometry of a planar current sheet above a conducting sheet with sinusoidal time variation. It is shown how, from the solution of a single fourth-order differential equation for the magnetic vector potential, the coupled electromagnetic and elastic wave problem can be solved analytically. The effective transfer impedance is evaluated, a measure of the ultimate efficiency of the combined excitation and detection process. At acoustic resonance its amplitude is inversely proportional to the sum of the ultrasonic attenuation of the sample and the attenuation arising from the electromagnetic-elastic coupling. This high-frequency resonant method should open up a wide range of new applications for the nondestructive evaluation of thickness, ultrasonic attenuation, bonding, and delamination of thin sheets and coatings in the sub-10 μm to 1 mm thickness range.