A Model for the Electromagnetic Generation and Detection of Rayleigh and Lamb Waves

TLDR

Existing solutions for the response of a solid to periodic surface stresses are applied to cases where the stresses arise from Lorentz forces on currents flowing in a static magnetic field. Calculations and measurements of the efficiencies of electromagnetic transducers for Rayleigh and Lamb waves are presented. The model describes transducer operation by passing current through surface‑bonded wires for insulating solids or inducing current via a nearby coil for conducting solids, provides expressions for transmission and reception efficiencies with reciprocity relations, and compares theoretical predictions to experimental results for 130 kHz flexural waves on aluminum and steel plates. The model accurately predicts transducer performance for both insulating and conducting solids, matching experimental data on aluminum plates without adjustable parameters, showing similar qualitative results for steel with comparable magnetostrictive and Lorentz force coupling, and correctly describing the dependence on plate separation.

Abstract

Calculations and measurements of the efficiencies of electromagnetic transducers for Rayleigh and Lamb waves are presented. Existing solutions for the response of a solid to periodic surface stresses are applied to cases where the stresses arise from Lorentz forces on currents flowing in a static magpetic field. Results are presented for both electri- cally insulating and conducting solids. In the former case, the current must be passed through wires bonded directly to the surface, while in the latter case they may be induced in the metal surface by a nearby coil with no physical contact. Included are expressions for the efficiencies of transmitting and receiving transducers along with a brief discussion of ap- propriate reciprocity relations and equivalent circuits. The theoretical predictions are compared to experimental results for the transduction of 130 kHz flexural waves on 3/8-in aluminum and steel plates. With no adjustable parameters, the theory closely predicts the absolute level of performance on the aluminum plate. Data on steel is qualitatively the same but suggests that magnetostrictive coupling is of comparable magnitude to the Lorentz force coupling mechanism. The dependence of transducer performance upon separation from the plate is also found to be accurately described by the model.