Simulation and Control of Floor Motions in Structures

Abstract

Floor motions in structures are substantially different than the ground motions exciting their foundations. Vibration amplifications of ground motions occur differently in the vertical and horizontal directions in these floors. Excessive motions influence adversely most of building contents and non-structural systems suspended on those floors. Shake table testing allows reproducing true effects of earthquake motions that can challenge a complex specimen, but their reproduction is usually imperfect because of the dynamics of the control system, the shake table controllers and the specimen dynamics, even when basic closed-loop control is used. This paper presents the analytical development and the experimental verification of an ‘openloop’ feed-forward iterative procedure for simulation of desired “floor motions” at any specific location of a test structure. As the first step, a well-known global feedforward procedure using transfer functions is reformulated for uni-axial systems. Subsequently, the same concept is extended to multi-directional systems using a newly developed 6×6 transfer function matrix. The compensation procedure was implemented and experimentally demonstrated, assuming uncoupled system in each axis of a 20ft×20ft×10ft test frame mounted on a shake table at the Structural Engineering and Earthquake Simulation Laboratory at the University at Buffalo. The procedure developed for a coupled system using the transfer function matrix is verified analytically. The developed ‘open-loop’ compensation procedure is limited to linear systems and is affected by the uncertainty and nonlinearity of the systems. Challenges of shake table-structure control observed in this study are also addressed. FLOOR MOTION SIMULATION In the experimental evaluation of non-structural components or in the qualification testing of electric devices, it is often required to produce a target spectrum at a specified location in a structure mounted on the shake table. Floor or roof motions are amplified differently in the vertical and horizontal directions when a structure is subjected to ground excitations as shown in Figure 1. At the top corner of a jth story, horizontal motion is amplified and the amplification can be expressed as the ratio