Optimal design of an inerter isolation system considering the soil condition

Previous studies on structures isolated by inerter-based systems have been conducted assuming they are constructed on a fixed base and neglecting the soil condition and impact of soil structure interaction (SSI) on the structural performance. To this end, this paper proposes an optimal design method for an inerter isolation system (IIS) considering the soil condition in a demand-oriented design framework. Initially, an analytical model of a structure with an IIS installed under fixed-base and flexible-soil conditions is developed in the frequency domain, wherein an SSI model is established using the frequency-dependent stiffness and damping elements. Within a probabilistic framework analysis, the stochastic responses of the structure isolated by the IIS are determined by both considering and ignoring the effects of SSI. A parametric analysis is conducted to study the variation in the structural performance with respect to the IIS parameters and to comprehensively investigate the effect of SSI on the vibration mitigation effect of the IIS; the superstructure deformation, base shear force, and base isolation displacement are the employed performance indices. A demand-oriented optimal design strategy is then proposed to determine the IIS parameters for a structure on a fixed base and further developed for a structure on flexible soil. The analysis results show that the SSI effect should be considered for structures equipped with an IIS and installed on flexible soil. Moreover, because of the SSI effect, the IIS is designed assuming that a fixed base will fail to behave as expected, particularly in terms of its vibration mitigation and damping enhancement effects. The proposed design method enables the structure to achieve the target base shear force response, regardless of the type of soil foundation, by incorporating the SSI effect into the IIS design for structures on flexible soils.