Dynamic analysis of sliding structures with unsynchronized support motions. - Wang, Yen-Po (Earthquake engineering & structural dynamics.)
The dynamic analysis of sliding structures is complicated due to the presence of friction. Synchronization of the kinematics of all the isolation bearings is often granted to simplify the task. This, however, may lead to inaccurate prediction of the structural responses under certain circumstances. Stepped structures or continuous bridges with seismic isolation are notable examples where unsynchronized bearing motions are expected. In this paper, a logically simple and numerically efficient procedure is proposed to solve the dynamic problem of sliding systems with unsynchronized support motions. The motion equations for the sliding and non-sliding modes of the isolated structure are unified into a single equation that is represented as a difference equation in a discrete time state space form and the base shear forces between the sliding interfaces can be determined through simple matrix algebraic analysis. The responses of the sliding structure can be obtained recursively from the discrete time version of the motion equation with constant integration time step even during the transitions between the non sliding and sliding phases. Therefore, both accuracy and efficiency in the dynamic analysis of the highly non-linear system can be enhanced to a large extent. Rigorous assessment of seismic structures with unsynchronized support motions has been carried out for both a stepped structure and a continuous bridge. Effectiveness of friction pendulum bearings for earthquake protection of such structures has been verified. Moreover, evident unsynchronized sliding motions of the friction bearings have been observed, confirming the necessity to deal with each of the bearings independently in the analytical model.