Suppressing vibrational response of functionally graded truncated conical shells by active control and design optimization

A shear deformation shell theory including thickness stretching effects is used to formulate the minimization problem of the vibrational response of functionally graded truncated conical shells in different cases of boundary conditions. Mechanical control energy is introduced into the formulation as a functional containing a closed-loop control force. The optimization objective is taken as the sum of the control energy and the total energy of the shell. Based on Lyapunov-Bellman theory, optimum values for the control forces and deflections are obtained for shells with simply supported or clamped edges. A design procedure is applied to complete the minimization process for the control objective using material and geometric parameters. Numerical and graphical results are presented to show the importance of the inclusion of the thickness stretching effects into the formulation. An assessment for the current design and control approach in minimizing the optimization objective is performed.