Scattering of the Fundamental Lamb Modes in Bent Metallic Plates

Guided elastic waves, propagating through curved waveguides, have attracted significant attention in the recent past, both from the perspectives of assessment of structural integrity and generating novel designs of acoustic waveguides. This article presents investigation of the interaction of the fundamental Lamb modes with a cylindrical bend in thin metallic plates. A hybrid numerical method is exposited, which combines the computational efficacy of the semi-analytical finite element method in modeling the long straight portions of the plate and the versatility of the conventional finite element method in modeling the bent portion. The predictive capabilities of the proposed method are validated using transient finite element simulations. Appropriate modifications to the hybrid method, needed for simulating the multimodal incidence resulting from the point-force actuation, are discussed. Using the hybrid method, the scattering and mode-conversion behavior, imparted by the cylindrical bend, is studied when the two fundamental Lamb modes are used as the incident interrogation signals. The extents of equi-modal and cross-modal contributions in both the reflected as well as transmitted waveforms are quantified in terms of the respective modal energy ratios. Explicable contour charts are presented for comprehending the scattering behavior over a wide range of frequencies and bend angles that span from 0 deg to 180 deg. For two representative cases, the modal displacement patterns inside the bend region are presented and discussed. The present investigation can find its potential use in the analysis of geometrically irregular structures leading to the design of novel acoustic waveguides.