Lamb Wave-Based Nondestructive Evaluation of Voided Adhesive Interfaces Using Chebyshev Spectral Dispersion Modeling

A reformulated model for Lamb wave propagation in an aluminium/adhesive/aluminium sandwich plate is presented, where the adhesive core is described using the theory of Linear Elastic Materials with Voids (LEMV). A Chebyshev spectral collocation scheme is employed to assemble, at prescribed real wavenumbers γ, the generalized eigenvalue problem K(γ)v=ω^2 Mv. This approach enables computation of the complete set of propagating branches without sequential mode-tracking and incorporates the porosity field φ as an additional kinematic variable within the coupled formulation. To reduce reliance on phenomenological parameter selection, the LEMV coefficients associated with porosity are related to the measurable void volume fraction f of the adhesive through a microstructure-informed calibration procedure. Dispersion relations and corresponding group velocity curves v_g=∂ω/∂γ are computed from the resulting eigenstructure. Zero Group Velocity (ZGV) points are identified and examined as functions of f. The results indicate systematic variations of selected ZGV frequencies with increasing void fraction, suggesting their potential relevance for quantitative nondestructive evaluation of bonded interfaces, within the assumptions of the present LEMV framework.