Design and analysis of nonlinear numerical algorithm for seismic response of structures based on HVSR algorithm

Earthquake is one of the main factors causing structural disasters in current buildings. Under earthquake action, adjacent building structures are generally in different vibration stages, and collisions may occur in the structures, which may cause serious damage to the structure. In order to prevent certain earthquakes from damaging the designed buildings, this article mainly introduced the design and analysis of a numerical algorithm for seismic nonlinear structural dynamic response based on the HVSR algorithm. This article evenly divided the acceleration response time series into 15 time periods and then selected the position corresponding to the peak point of instantaneous amplitude within each period as the selected data point position. The same seismic load can be applied at the bottom of the established nonlinear model to extract the dynamic response data of the top layer of the structure, and then, the instantaneous amplitude and corresponding instantaneous phases and frequencies of the main components of the structural dynamic response can be extracted through the time-varying filter and Hilbert transform based on the discrete analytic mode decomposition. Under the influence of these four ground motions, the collision force within the range of 0-50 kN accounted for over 87% of the total number of collisions. In the comparison results of collision response to peak displacement, the four ground motions all led to structural collision, and the collision inhibited the positive peak displacement response of node 1512. Compared with noncollision, the peak displacement was reduced by 27.273, 33.675, 27.727, and 37.248%, respectively. The peak displacement of 1512 nodes was suppressed and reduced by 18.856%. The results indicate that the HVSR algorithm can obtain the instantaneous characteristic parameters of nonlinear structural dynamic response and achieve model correction.