Weak scattering formulation for flexural waves in thin elastic plates with point-like resonators

• A weak scattering formulation is developed for flexural waves in thin elastic plates with point-like resonators. • The Born approximation is rigorously justified via the spectral radius of the scattering matrix. • Geometric and physical contributions to scattering are separated and interpreted independently. • A dimensionless criterion for weak scattering is derived and validated with numerical examples. • The method provides insight into wave control in structured media and aids metamaterial design. We introduce a weak scattering formulation for flexural waves in thin elastic plates loaded by point-like resonators with an approach employing the Born approximation and far-field asymptotics of the Green’s function to characterize multiple scattering effects in this system. The response of the system to an incident wave is expressed as a power series expansion where each term introduces higher-order scattering components. The behaviour of this series is governed by the spectral properties of a specific matrix dictating the convergence and accuracy of the weak scattering approximation. By decomposing the scattering response into geometric and physical contributions, we establish a condition for weak scattering in terms of these two factors. This formulation provides a systematic framework for assessing the validity of low-order approximations and understanding wave interactions in complex media. Numerical examples illustrate the accuracy of the weak scattering approximation in periodic and random distributions of scatterers, highlighting implications for wave control and metamaterial design.