While base isolation successfully decreases the accelerations transmitted to a structure, a tradeoff is large unfavorable displacements in the isolation layer. This study investigates an innovative system, termed 'dual isolation', which applies two layers of isolation at the base and at mid-story to resolve this issue. A linear analytical solution for the equation of motion of the proposed system is developed on the basis of linear isolation theory. This creates a foundation to assess the behavior of various types of seismic protection systems and to select the damping and mass ratio that optimizes the performance of the proposed method. Dynamic response of an example dual isolated system to selected suites of ground motions is then examined. In addition to decreasing the displacement of the first isolation layer, the dual isolation system can greatly decrease floor accelerations of the upper portion of the building, further protecting building components and enhancing the comfort and safety of residents. displacement of the second floor, and when T 2 approaches T 1 , the mode shapes are approach 1 1 ! , and 1 À1 ! reduces the roof displacement of the system. This positive effect of increased mass ratio on the behavior of TMDs has been shown in other studies (Hoang et al., 2008;Taniguchi et al., 2008).
Dual isolation systemFrom the examination of the theoretical results of mid-story isolation and base isolation with TMD, it is seen that the displacement demands on the second DOF decrease with larger values of γ and increase with larger T 2 , while the increase in T 2 reduces the displacement demand of the first DOF. These insights are used to select the preliminary parameters for the proposed dual isolation system. The same two DOF model shown in Figure 1 is used for a numerical response spectrum study. As a starting point, the mass ratio γ of the dual isolation system is chosen as 0.5, locating the second isolation layer at the mid height of the building. The period of the first isolation layer, T 1 , is chosen as 3.5 s, and the damping ratio of the first and second DOFs, β 1 and β 2 , were chosen as 15%. This dual isolation system was then analyzed using response spectrum analysis for a design basis earthquake (DBE), the spectrum for which is shown in Figure 2. The spectrum is defined for 10% probability of exceedance in 50 years downtown Seattle, WA, USA (47.60, À122.34), and soil type D (ASCE 07, 2010). The lateral story drifts found are presented in Figure 3, varying the period of the second isolation layer, T 2 . The left side of the graph represents the traditional base isolation system in which the natural period of the first DOF is much longer than the second DOF. As the period of the second DOF increases, the drift of the first DOF is reduced with the concession of increased drifts in the second DOF. This finding is in line with the theory explored in the previous section. Compared with the classic base isolation system, the participation factor of the first mode is decreased, reducing the first DOF's d...