Optimal control of random vibration in plate and shell structures with distributed piezoelectric components

The state covariance assignment (SCA) method of Skelton and associates has been extended to the optimal random vibration control of large-scale complicated shell structures with distributed piezoelectric components and under nonstationary random excitations. It provides a direct approach for achieving performance goals stated in terms of the root-mean-square (RMS) values which are common in many engineering system designs. The large-scale shell structures with distributed piezoelectric components of complicated geometrical configurations are approximated by the hybrid strain or mixed formulation based lower order triangular shell finite elements developed in the present investigation. Each of these shell finite elements has three nodes. Every node has seven degrees of freedom (dof) which include three translational, three rotational and one electric potential dof. These elements are better alternatives to those based on the displacement formulation and that hinged on the truly hybrid strain formulation in that they eliminate locking problems commonly associated with displacement based lower order shell finite elements. Computed results applying the proposed approach for a plate and a cylindrical shell structures with distributed piezoelectric components and under stationary random excitations are included to demonstrate its simplicity of use and efficiency of implementing the proposed approach.