ratios and frequencies can be defined and a modal control strategy can then be designed to adjust the closed-loop behaviour in some suitable way (Inman 2001, Daley et al 2004, Fang et al 2003). Performances that can be realised are dependent on the number of sensor and actuators available as well as their dynamics. It has widely been observed that an IMSC implementation typically requires the number of actuators to be equal to that of modelled modes (Nguyen 1991). The work presented here explores the possibility of realising an IMSC controller for mitigating human induced vibrations in floors. A structural model and input forces used in analytical simulations is introduced. A brief overview of the IMSC strategy used in this analytical work is shown and some results of analytical simulations for two different IMSC controllers setting are presented. IMSC controller 1 aims to target only the first mode of vibration of the reduced order model (ROM) of the laboratory structure while IMSC controller 2 aims to target both the first and second modes of vibration of the ROM. Some results and conclusions are finally presented. 2 STRUCTURAL MODEL AND INPUT FORCES 2.1 Structural Model The laboratory structure is a simply-supported in-situ cast post-tensioned slab strip of span 10.8m. Its total length is 11.2m, which includes 200mm overhangs over the knife-edge supports. It has a width of 2.0m, depth of 275mm, and weighs approximately 15 tonnes. The first and second modes of vibration have natural frequencies of 4.55 Hz and 17.02 Hz with modal damping ratios of 0.4 % and 0.2 %, respectively. The first mode is particularly prone to excitation by the second and third harmonics of walking excitation (Reynolds 2000). The IMSC controller design presented in these studies is formulated from a ROM of the laboratory structure. This ROM is developed based on uncontrollability and unobservability at node points of vibration modes of the laboratory structure (Seto and Mitsuta 1992). The mode order is chosen as two here and the node points of the third bending mode have been chosen as the locations of the masses for the lumped parameter system as shown in Fig. 1. Fig. 1 Laboratory structure grid, mode shapes and 2-DOF lumped mass model 10,800 200 200 Mode 1 Mode 2 Mode 5 2-DOF Lumped Mass Model M2 M1 K1 K2 K3 Y Controllable Observable Controllable Observable Uncontrollable Unobservable 1 1 2 3 2 3 A B C D A B C D 216
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