  The impedance matrix method is applied to study the scattering of flexural
waves propagating in an infinite thin plate containing an $N$-beam resonator.
The resonator consists of a circular hole containing a smaller plate connected
to the background plate by a number $N$ of rectangular beams. After
representing the boundary conditions in a modal multipole expansion form, a
compact expression is obtained for the T-matrix, which relates the incident and
the scattered transverse (out-of-plane) waves. The analysis of the scattering
cross-section reveals interesting scattering features, like resonances and
anisotropy, associated with this type of resonators. Numerical experiments
performed within the framework of the finite element method support the
accuracy of the model here developed.
