Dynamic response of a viscously damped two adjacent degree of freedom system linked by inerter subjected to base harmonic excitation

The study investigates the dynamic response of a viscously damped two adjacent single degree-of-freedom (2-ASDOF) system coupled by a connection that includes an inerter element. The dynamical model of a pair of simple oscillators coupled with various connection elements is synthetic but also representative to describe different classes of structures (i.e. contiguous buildings, adjacent walls and frames and so on). The specific kind of connection fundamentally alters the dynamic behavior of the entire system. Coupling elements typically studied are springs, dampers, linear or non-linear, passive, semi-active or active, e.g. [1,2]. The inerter is a novel device able to generate a resisting force, proportional to the relative acceleration of its terminals, equivalent to a force produced with an apparent (inertial) mass two orders of magnitude greater than its own physical (gravitational) mass [3]. In this study, a non-conservative connection, realized with a spring-inerter-viscous damper elements, adjusted in parallel, is considered as linking scheme for the 2-ASDOF system. In order to perform modal analysis, the first order state-space representation is adopted and the modal equations for the viscously damped system are derived. By solving the eigenvalue problem, the attention is focused on how modal parameters, i.e. the natural frequencies, the modal damping ratios and modes are affected by the connection. The system is then subject to harmonic base excitation and frequency response functions are depicted showing the influence of the link (through spring stiffness, inertance and damping coefficient) on the dynamic response. From the analysis with the different linking schemes, it emerges that the specific kind of connection influences the system dynamic characteristics.