Multi-Objective Optimization of a Viscoelastic-Hysteretic Device for Vibration Mitigation in Two Coupled Oscillators

Dissipative coupling represents an efficient strategy to protect dynamically excited structures from damage while enhancing their resilience. However, selecting the optimal properties of the damping device remains challenging due to the need to balance conflicting objectives, such as minimizing displacements and accelerations. This study presents a simplified procedure for the preliminary design of an optimal viscoelastic-hysteretic damper coupling two simple oscillators. The optimization relies on the nonlinear stochastic response of the system - quantified through the standard deviations of displacements and accelerations - evaluated via equivalent linearization. The problem is formulated as a two-step multi-objective optimization. In the first step, Pareto fronts are derived to identify non-dominant solutions representing the trade-off between displacements and accelerations under low (serviceability) and high (safety) levels of white noise excitation. In the second step, a multi-objective metaheuristic algorithm is employed to determine the optimal damper configuration based on the outcomes obtained from the first step. The results are compared with traditional approaches, demonstrating the potential and effectiveness of the proposed procedure.