Modal analysis and dynamic response of a two adjacent single degree of freedom systems linked by spring-dashpot-inerter elements

This paper illustrates the dynamics of a novel structural configuration represented by a two adjacent single-degree-of-freedom (2-ASDOF) systems coupled by a connection with spring-dashpot-inerter elements arranged in parallel. The connection is conservative if the link is realized only with spring and/or inerter, whereas becomes nonconservative when also the dashpot is added. The first part of the study concerns the system modal analysis: different linking schemes are considered in order to investigate the influence of each connection parameter on the coupled system modal properties. It is shown that, for conservative connection, modal properties are analytically derived because the eigenvalue problem admits closed-form solutions. For nonconservative connection, instead, the state-space description is adopted and the complex modal analysis is carried out (deriving pseudo-frequencies, pseudo-damping factors and complex modes). Admissible and not-admissible zones for the frequencies of the coupled system are individuated: frequencies are positioned on the left, on the right or within the uncoupled ones, depending on the values chosen for the connection parameters. Associated to each case, typical patterns for mode shapes are depicted. Peculiar behaviors of the system, advantageous for structural control purposes, emerge when the connection parameters assume specific values. The second part of the paper illustrates the system dynamics to very simple input conditions: the response to free vibration with initial conditions and to base harmonic motion is carried out. Based on the findings obtained from modal analysis, it is highlighted that it is possible to properly select the connection parameters in order to have: (i) the most rapid decay of the structural response in case of free vibrations and (ii) the minimum response amplification for both oscillators in case of harmonic motion.