Modal coupling in one-dimensional electro-mechanical structured continua

A passive continuously distributed control of mechanical vibrations is proposed. The piezoelectric actuators are interconnected by a linear electric transmission line. We introduce coupling and internal resonance criteria to determine the optimal choices for electric parameters. These criteria can be found decomposing the differential operator appearing in the linear evolutions according to a partition of the state vector into mechanical and electrical parts. The results we find allow for the design of an experimental set up.