Use of the sub-structuring method in the analysis of vibrating structures with layered damping technologies

This research focuses on a composite constructed from a polymer matrix reinforced with stiff platelets. The platelets are relatively large and are located within the matrix in three layers, where individual platelets are staggered relative to those in adjacent layers. This composite is interesting because it combines the damping ability of the polymer with the rigidity created by the structured assembly of platelets. When loaded, the high difference in elastic modulus between the stiff platelets and soft polymer results in a zigzag strain field. This work presents an analytical model that can estimate the equivalent flexural modulus of the soft-stiff staggered system and evaluates the effectiveness of such a construction in reducing vibration. The analytical model estimates the bending angle of a unit cell of the composite involving a region around the middle of the central platelets. The estimation is achieved by a method called the “Effective Bending Moment Method” (EBMM) which obtains the bending deflection from the contributions of parts through the cross section. The suitability of the model is evaluated experimentally using a beam constructed from an epoxy matrix and reinforced using steel platelets. Predicted system loss factors and flexural modulus values are compared with results measured using free vibration and cyclic 3-point bend tests. Also, digital image correlation (DIC) is used to examine the real zigzag strain distribution through the cross-section during flexure and therefore to validate the assumptions made when developing the model. The final part of the work considers the effectiveness of the staggered platelet composite in vibration reduction. A simplified model, representing the swing-modes of an automotive oil pan, is used to demonstrate the reductions in vibration level than can be achieved using the same epoxy-steel combination employed during the model validation stage.