Minimizing vibration response of cylindrical shells through layout optimization of passive constrained layer damping treatments

A layout optimization of passive constrained layer damping (PCLD) treatment for minimizing the vibration response of cylindrical shells is presented with consideration of broadband transverse force excitation. The equations governing the displacement responses, relating the integrated out-of-plane displacement over the whole structural volume, i.e., the structural volume displacement (SVD), of a cylindrical shell to structural parameters of base structure and multiple PCLD patches, are derived using the energy approach and assumed-mode method. Genetic algorithm (GA) based penalty function method is employed to find the optimal layout of rectangular PCLD patches with aim to minimize the SVD of the PCLD-treated cylindrical shell. Optimization solutions of the locations of patches for PCLD treatment are obtained under the constraint of total amount of PCLD materials in terms of percentage added weight to the base structure. Effects due to number of patches, their aspect ratios, and total amount of added PCLD weight are also studied. Examination of the optimal layouts reveals that the patches tend to increase their coverage in the axial direction and distribute over the whole surface of the cylindrical shell for optimal SVD reduction.