Maximizing modal damping in layered structures via multi-objective topology optimization

This paper presents a study on maximizing single and multiple modal damping ratios (MDR) of a structure by finding the optimal layouts of damping and/or base materials using an extended moving iso-surface threshold (MIST) topology optimization. Firstly, by using the Lagrange's equation, a general formulation of loss factor is derived and then used to extract MDR for classical and non-classical damping. Secondly, in the extended MIST, new general formulations for the physical response functions of individual mode are derived for the classical non-local damping and the non-classical damping, in which for non-classical damping modal strain energy (MSE) is used to estimate MDR and derive physical response function. Thirdly, to maximize multiple MDRs simultaneously or overcome the mode switching issue, a multi-objective optimization strategy is developed; and a concurrent design optimization of both base and damping layer is proposed to maximize MDR. Finally several numerical examples are presented to validate and illustrate the efficiency of the present extended MIST approach. (C) 2016 Elsevier Ltd. All rights reserved.