Additionally, this structure included a center column suspended from the 3rd floor, and a bumper mechanism attached on the 2nd floor as shown in Fig.2 (a). This system produces nonlinearity in the system response when the column impacts the bumper mechanism. The clearance (gap) between the bumper and the column can be adjusted to vary the extent of impacting that occurs during a particular excitation. This nonlinearity is intended to produce a small perturbation to an essentially stationary process, causing a nonlinear phenomenon. In the modeling, this nonlinearity can be described by adopting a kind of bilinear model in stiffness k4 as shown in Fig.2 (b), where kc is the summation of the bending stiffness of four assembled columns, and the kb is the bending stiffness of the suspended column, corresponding to a cantilever beam. In the modeling here, distance ' was defined to make a smooth transition between two stiffness states by a quadric function to satisfy C1-continuity. This transition area indicates that the actual structural condition should not show a complete discontinuous point at X=Gap because, in reality, some kinds of compliance should exist in the actual assembling system. 1st floor 2nd floor 3rd floor Base x-direction Shaker (a) Three-story share building set-up (b) 4DOF lumped-mass model Fig.1. Test-bed structure setup and its numerical model 2nd Floor 3rd Floor Gap Column Bumper (a) Bumper and suspended column mechanism (b) Bi-linear model for stiffness k4 Fig.2. Nonlinear behaviour mechanism between 2nd and 3rd floor 155
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