Multiple Scattering of Flexural Waves on Thin Plates

In this paper, the scattering of flexural waves on a thin Kirchhoff plate by an ensemble of through-thickness circular scatterers is formulated by using the concept of the T-matrix in a generalized matrix notation, with a focus on deterministic numerical computations. T-matrices for common types of scatterers, including the void (hole), rigid, and elastic scatterers, are obtained. Wave field properties in the multiple-scattering setting, such as the scattering amplitude, and scattering cross section, as well as properties of the T-matrix due to the energy conservation are discussed. After an extensive validation, numerical examples are used to explore the band gap formation due to different types of scatterers. One of the interesting observations is that a type of inclusion commonly referred to as the "rigid inclusion" in fact represents a clamped boundary that is closer to a riveted confinement than a rigid scatterer; and an array of such scatterers can block the wave transmission at virtually all frequencies.