Optimal control of vibration of beams and plates

In this thesis, we develop a procedure to find the distribution of the control input over the domain of the beam and plate that minimizes a cost functional and satisfies the given boundary conditions and initial conditions. We use the calculus of variation to derive the equations of motion and the boundary conditions for transverse vibrations of beam and plate. The necessary conditions are first derived and then solved by using the principle of separation of variables and by using modes function which satisfy the given boundary conditions and initial conditions.