A short note on equal peak design for the pendulum tuned mass dampers

Pendulum tuned mass dampers (PTMDs) are used to passively mitigate the vibrations of tall structures and buildings. The main objective of this short note is to introduce analytical formulae for the optimum design of the linear PTMD coupled to an undamped primary system. Den Hartog's equal peak method is applied to derive the optimum design. With the mass ratio between the primary system and the PTMD, the optimum length and optimum damping of the pendulum are calculated. The formulae are presented in both dimensional and non-dimensional forms and are simple to apply in real applications. It is also shown that the vibration mitigation performance of the proposed optimum design precisely matches the results obtained by numerical optimisation techniques.