A novel optimization method for transducer array in Lamb wave detection of variable cross-section structures

Structures with complex cross-sections are widely applied in aerospace manufacturing and developing a Lamb wave-based structural health monitoring method for the structure has attracted interest. However, the complex nature of geometry makes dispersion calculation and transducers arrangement difficult. The variation in the thickness of the structural cross-section gives rise to disparities in the group velocity of Lamb waves. Consequently, the wave propagation leads to an uneven distribution of energy, which poses challenges for the applications of structural health monitoring (SHM). Although traditional phased arrays can be employed to address the issue of energy focusing, the implementation often complicates the in-situ monitoring process and consequently increases the associated costs. This article presents an efficient optimization method for flexible transducer array placement of Lamb wave detection. A real titanium alloy engine fan blade is employed to demonstrate and validate the proposed method. For better Lamb wave detection performance without cumbersome large-scale random sampling in array layout, the moment quadrature method is introduced to generate representative sparse samples for simulation. The process of the semi-analytical finite element (SAFE) method, which is improved by continuous cross-sections mapping, is conducted to analyze Lamb wave dispersion and select the desired mode. The dynamic simulation is employed to study the wave motion, especially the effects of optimized parameters on wave focusing. The simulation results are applied to build a polynomial model of focused energy and further obtain the optimized schemes for transducers arrangement. Validations in both simulations and experiments are performed to verify the performance of the proposed method.