Passive control and damage assessment with a pendulum tuned mass damper using mean square equations and second-order eigen-perturbation techniques

This paper proposes a novel framework for damage detection and retuning of a Pendulum Tuned Mass Damper (PTMD) addressing effects of stochasticity via mean-square equations and establishing rapid change detection. The framework was made possible via a Stochastic Differential Equation (SDE) formulation of the equations of motion considering a two degree of freedom base and structure system equipped with a PTMD. The system was assumed to be excited at the base with Gaussian white noise and the solutions were computed using a stochastic integration scheme. A Second Order Eigen-Perturbation (SOPS) estimate is used to carry out detection of sudden stiffness reduction in the base floor of the structure. Once damage is detected, mean square equations on monitored displacements were used to retune the PTMD by adapting the length of the pendulum. It was found that damage could be detected rapidly and successive retunings were able to minimize the mean square displacement of the damaged structure and stabilise it over time.