Optimization of segmented constrained layer damping with mathematical programming using strain energy analysis and modal data

A new method for enhancement of damping capabilities of segmented constrained layer damping material is proposed. Constrained layer damping has been extensively used since many years to damp flexural vibrations. The shear deformation occurring in the viscoelastic core is mainly responsible for the dissipation of energy. Cutting both the constraining and the constrained layer, which leads to segmentation, increases the shear deformation at that position. This phenomenon is called edge effect. A two-dimensional model of a cantilever beam has been realized for further investigations. An optimization algorithm using mathematical programming is developed in order to identify a cuts arrangement that optimizes the loss factor. The damping efficiency is estimated using the modal strain energy method. The Nelder–Mead simplex method is used to find the best distribution of cuts. In order to take into account geometrical limitations, the exterior point penalty method is used to transform the constrained objective function into an unconstrained objective function. As the optimization problem is not convex, a modal analysis is performed at each mode in order to identify initial cuts positions that lead to a global minimum. Over a large frequency range, the algorithm is able to identify a distribution of cuts that optimizes the loss factor of each mode under consideration.