Report - PEER - University of California, Berkeley

The structure to be simulated is divided into a physical substructure and one ormore computational substructures. The interface forces between the physical andcomputational substructures are imposed by actuators and resulting displacements andvelocities are fed back to the computational engine. The earthquake ground motion,or motion of other computational substructures, is applied to the experimentalsubstructure by shake tables. A schematic of the RTDHT system is shown in Figure3. A detailed description of the implementation follows:5. SUBSTRUCTURING METHODSThe RTDHT implies first determining themodel of the physical substructure beingtested within the whole structural modelidentifying the interface parameters. Athree-story model is shown in Figure 4 withits parameters. If u g is the motion of theground with respect to the inertial referenceframe. u i and x i are the motions of the i thstory with respect to the fixed referenceframe and with respect to the groundrespectively, then ui = ug + xi. Definingthe first and third floor in Figure 4 ascomputational substructures and the secondfloor as the experimental substructure asshown also in Figure 4, the equations ofmotion in the inertial reference frame arethen given by:&& ( ) & & ( )&& & ( ) & &( )mu1 1+ c1+ c2 x1 − c2x2 + k1+ k2 x1 − k2x2= 0 →Computational Substructure 2mu2 2− cx2 1+ c2 + c3 x2 −cx 3 3− kx2 1+ k2 + k3 x2 − kx3 3= 0 →Experimental Substructuremu&& − cx& + cx&− kx + kx = 0 →Computational Substructure 12 2 3 2 3 3 3 2 3 3By considering the influence of the experimental substructure as externaldisturbance, the equations of the computational substructures may be written as:mx && + cx& + kx =− mu&& + k x − x + c x& −x&( ) ( )144442444431 1 1 1 1 1 1 g 2 2 1 2 2 1Force measured at the baseof experimental substructuremx &&3 3+ cx& 3 3+ kx3 3= − mu&& 3 g+ kx3 2+ cx&3 214243( k3*displacement +c 3*velocity) ofexperimental substructureThe equation governing the experimental substructure rearranged using therelative displacement x21 = x2 − x1. Then equation (2) becomes:( + ) + + = ( − )m u&& && x c x& k x k x x(3)2 1 21 2 21 2 21 3 3 2k 3k 2k 1c 3m 2c 2c 1m 3m 1Groupx 3 ,x 2 ,x 1 ,Figure 4. Three-story model.u g(1)(2)263