Abstract:

Frame-rocking wall was a composite self-resetting structure that could effectively improve the seismic resistance and toughness of buildings. To fully understand the random response characteristics of structures under earthquakes, a simplified nonlinear equation for a multi-degree-of-freedom frame-rocking wall structure was constructed, and an equivalent linear dynamic equation with time-varying parameters was constructed based on the assumption of pseudo harmonic behavior in response using equivalent linearization. Further, based on the principle of random averaging, the Fokker-Planck-Kolmogorov(FPK) equation could be derived to determine the time evolution form of probability density function(PDF) for controlling the amplitude of the response, and ultimately the first-order differential equation for the time-dependent variance of the random response could be obtained. Finally, a computational model was constructed using a framework of a certain teaching building as a sample for validation. The results show that the approximate analytical method has excellent accuracy, and while ensuring the accuracy of the random response time-related variance, it can improve the efficiency of analysis compared to traditional Monte Carlo simulation(MCS) methods. In the results of non-steady ground motion power spectrum models in separable and non-separable forms, the trend of the random response variance curve is related to the form of random seismic excitation, and its segmentation points show obvious unsmooth phenomena under the action of segmented modulation of non-stationary spectra. The results under different types of random seismic excitation disturbances demonstrate the excellent applicability of this method.

Key words: non-stationary, random earthquake, frame-rocking wall structure, response analysis, stochastic average