Vibration control of an elastic strip by a singular force

Vibration characteristics of an elastic plate in the shape of an infinite strip are changed by applying a lateral concentrated force to the plate. The homogeneous, isotropic, elastic plate is infinite in the x-direction and the sides are simply supported. The size of the force is changed in proportion to the displacement measured at a certain point of the plate. The proportionality constant serves as the control parameter. The mathematical formulation of this distributed control problem and its analytical solution in terms of the vibration frequencies of the plate are given. The vibration frequencies are plotted as a function of the control parameter.