Analytical and numerical investigations of one-way mixing of Lamb waves in a thin plate

Abstract

This paper derives the resonance conditions for one-way resonant mixing of nonlinear Lamb waves. Two mode triplets are identified that satisfy such resonance conditions. It is also found that, when the primary waves are pulses of finite duration, the signal envelope of the corresponding resonant mixed wave is either a diamond or an elongated hexagon. The dimensions of these shapes are obtained explicitly in terms of the pulse lengths and group velocities of the Lamb modes in the mode triplet. These analytical results are verified by numerical simulations using the finite element method. Finally, a nondestructive evaluation method based on one-way mixing of Lamb waves is proposed for the inspection of a large area of a plate for damage distribution via a single access point. Numerical simulations of this nondestructive evaluation technique are conducted. It is found that using shorter pulses gives better spatial resolution, thus better suited for locating and sizing the damage zone, while using longer pulses gives a higher signal to noise ratio, thus better suited for quantifying the degree of damage in the damage zone. Results of this paper clarify some of the confusion in the existing literature regarding the resonance conditions for one-way mixing of nonlinear Lamb waves. They also provide a better understanding of the physical characteristics of the resonant mixed wave. Such understanding enables the design of optimal measurement systems for one-way mixing of Lamb waves for the purpose of conducting large area nondestructive evaluation of plate-like structures from a single access point. This proposed one-way mixing nondestructive evaluation technique can be extended to pipes.