Inerter-added transmissibility to control base displacement in isolated structures

A solution to the large base displacement problem in isolated structures under seismic loads is proposed; it is based on a displacement transmissibility formulation that includes the inerter device. The solution is also based on a novel spectral characterization of ground displacement; it should be clear that if the problem is displacement, the focus must be on displacements, both, as the excitation: ground displacement (rather than acceleration which is the norm) and as isolator displacement, through a transmissibility that relates both input and output displacements, all of which is a new approach. The proposal can serve as a passive-control design procedure, either under near-field or far-field conditions, when an inerter at the base level is chosen to solve the large isolator displacement problem. An isolated structural model commonly used in the subject literature is employed to show that the base displacement level can be reduced to under the ground displacement level, which implies a positive comparison with previous passive and active control solutions, including inerter solutions; in fact, the design aim is a competitive 0.95 ratio for both displacements.