“…With the purpose of maximizing TMD efficiency, over the years, numerous approaches have been proposed for the optimum design of TMD. After the work of Ormondroyd and Den Hartog (), several optimum design methods have been introduced in literature, aimed at minimizing the vibrations induced in mechanical and structural systems by various types of excitation sources (Crandall and Mark, ; Sadek et al ., ; Rana and Soong, ; Hoang and Warnitchai, ; Rundinger, ; Hoang et al ., ; Krenk and Høgsberg, ; Marano et al ., ; Marano and Greco, ; Greco and Marano, , ). In most of the above studies, the main structure is generally represented by an equivalent single degree of freedom system.…”