Stability of damped membranes and plates with distributed inputs

This paper proves the stability of boundary and distributed damped membranes and Kirchhoff plates under distributed inputs. Distributed viscous or Kelvin–Voigt damping ensures a weakly bounded response to a bounded transverse loading for pinned membranes and clamped plates. Damping on part of the boundary can also weakly stabilize the forced response, provided the damped and undamped boundary normals satisfy certain conditions. For example, damping on half and one side of the boundary is sufficient for circular and rectangular domains, respectively.