This paper proposes a flexible dry friction plate to mitigate the vibration of thin-walled structures for one resonance crossing. Based on a cantilever beam-friction damper finite element model, the geometry and material parameters of the friction plate are optimized numerically through steady-state response analyses by the widely-used Multi-Harmonic Balance Method (MHB-M). In order to further improve the damping effect, piezoelectric material is distributed to the flexible damper, and two types of dry friction and piezoelectric hybrid dampers are explored, namely semi-active and passive, respectively. For semi-active hybrid dampers, piezoelectric material is used as an actuator to adjust the normal load applied to the friction interface in real time, so that the friction damping is improved. For passive ones, piezoelectric material is used as a transducer, which dissipates the strain energy stored in the wave-like plate by the shunting circuit, additional shunted piezoelectric damping contributes to the total output damping accordingly. Better damping effect compared with the friction baseline is realized for the two types ideally. This damping module has a simple structure and avoids the problem of installation and maintenance of piezoelectric material which is generally bonded to the host structure. Technical challenges are: the semi-active type requires excessive voltage applied to the piezoelectric actuator, while the passive one needs to connect a programmable synthetic circuit.