Synthesis of passive interconnections in mass chains achieving a scale-free performance

This article is concerned with the synthesis problem of passive mechanical admittances that connect masses in a chain. The mass chain is excited at one boundary point, and the admittances are designed to suppress the disturbance independent of the length of the chain. The scalar transfer functions from the disturbance to a given intermass displacement are studied. The disturbance rejection performance is optimised over a class of arbitrary positive real mechanical admittances. The resulting admittance is synthesised mechanically using springs, dampers, and inerters only.