Quasibound states in the continuum for flexural waves

Bound states in the continuum (BICs) and their quasibound counterparts (QBICs) have emerged as powerful tools to engineer sharp resonances and extreme field confinement in wave systems. Here, we investigate the formation and tunability of BICs and QBICs for flexural waves in thin elastic plates decorated with a one-dimensional array of pointlike resonators. By designing a diatomic unit cell and varying the relative angle of the two resonators, we achieve precise control over the coupling between the guided modes of the plate and the radiation continuum. This simple geometric tuning enables the transition from a symmetry-protected BIC at the center of the Brillouin zone to a family of high-Q QBICs at finite Bloch wave vectors. We develop an analytical multiple-scattering model to compute the transmission and reflection coefficients of a plane flexural wave interacting with the array, and we demonstrate that the resulting resonances manifest as angle-dependent Fano line shapes in the scattering spectra. Furthermore, by employing a lumped-element description of the resonators, we propose a feasible physical realization of the system and validate our theoretical predictions against full finite element simulations, obtaining excellent quantitative agreement. Our results provide both a fundamental understanding and a practical route to engineer ultranarrow resonances and elastic metasurfaces with tailored dispersion, paving the way for advanced control of flexural waves in thin plates.