Visco-elastic coupling between a linear two-dof system and a rocking rigid block to improve the dynamic response

A two-degree of freedom linear system is used as a model for a multi-degree of freedom frame structure. Such a structure is coupled with a rocking rigid block to improve its dynamic response. The lowest part of the structure is connected to the block through a linear visco-elastic device. The nonlinear equations of motion of the couple system frame structure-block are obtained by a Lagrangian approach. Such equations are numerically integrated to analyze the behaviour of the coupled system. The coupling is considered effective if it reduces the displacements of the structure. Simulations are performed using a harmonic excitation as forcing term. An extensive parametric analysis is performed, and the results are summarized through behaviour maps. Such maps provide the ratio between the maximum displacements of the structure with and without the coupling with the rigid block for several combinations of system's parameters. When the ratio of the displacements is less than unity, the coupling is effective. Results show that the presence of the rocking rigid block improves the dynamics of the structure in large ranges of the parameters that characterize the coupled system.