This study deals with the optimisation of pendulum tuned mass damper parameters for different types of excitations and responses of the host structure to which it is attached. The study considers force excitation and base excitation with different types of output quantities to be minimised on the host structure. It also considers both harmonic motion with H ∞ optimisation of the different transfer functions and random white noise excitation where the variance of the output signal is minimised, leading to H2 optimisation. Although a lot of work has been done on optimisation of tuned mass dampers, there exists in the literature only a few solutions for optimisation of the pendulum tuned mass dampers not covering all possible types of loads and output quantities. The analogy between the mass spring tuned mass damper and pendulum tuned mass damper presented in this study allows to use all the tuning rules developed for tuned mass dampers in the case of pendulum tuned mass dampers. In addition, the existing tuning rules for tuned mass dampers are extended to cases which were not previously solved in the literature for H2 optimisation and validated by comparing with numerical optimisation. Finally, a discussion is presented where the different tuning rules are compared, and the performance degradation is assessed when the wrong tuning rule is used. This is representative of the case where, for example, both wind and earthquake excitation exist on the structure, and the pendulum tuned mass damper is tuned for just wind excitation.
Invariant slow manifolds of an Atomic Force Microscope system under the Derjaguin-Muller-Toporov forces and a slow harmonic base motion
