Structural optimization of tapered composite sandwich plates partially treated with magnetorheological elastomers

This study investigates the optimal locations of magnetorheological elastomer (MRE) segments in partially treated tapered composite MRE sandwich plates to maximize the natural frequencies and the loss factors. Various partially treated tapered composite MRE sandwich plate configurations are developed by dropping-off the plies longitudinally in top and bottom orthotropic (composite) layers with uniform core layer thickness. The core layer is made of natural rubber and MRE. The classical laminated plate theory is used to derive the governing differential equations of motion of the various partially treated MRE tapered composite sandwich plate configurations. The equations of motion are solved by using finite element formulation. Various cases of optimization problems are formulated and solved using genetic algorithm (GA) in order to obtain optimal locations to yield maximum natural frequencies and loss factors corresponding to the first five modes. The proposed methodology is validated by comparing the results evaluated in identifying optimal locations of MR fluid pockets filled in between uniform composite face layers, available in literature. It is observed that according to the user/designer requirements on achieving the optimal functions and their maximum value, the optimal locations of MRE pockets vary. It has also been demonstrated that the end conditions of the sandwich plate could play an important role in identifying the optimal locations of the MRE pockets. Further, it is observed that the optimal locations of MRE pockets are influenced by the ply drop off and resin locations. Hence it is concluded that the efficient design layout of a partially treated tapered composite MRE sandwich plate configurations would provide the guidelines for the designer to control the vibration effectively.