Seismic response analysis of multi-degree-of-freedom structures with a series-parallel layout Ⅰ inerter system

Aiming at the problem of insufficient research on the application and arrangement scheme of an inertial -capacity system in multi-degree-of-freedom structures, the calculation method for the response frequency domain solution and the spectral moment of the multi-degree-of-freedom inertial capacitance system was proposed, based on which the arrangement scheme of the inertial capacitance system was determined. By introducing state variables, the structural equations of motion and the differential-type intrinsic structure relations of the series-parallel layout I inerter system were transformed into state equations expressed in matrix form. And a unified solution in frequency domain was derived for the serial responses of structural displacements, velocities, and interstory displacement angles. Then, the quadratic decomposition method (QDM) was used to convert the response power spectrum into a quadratic decomposition formula (linear combination form of the inverse of the sum of square of the circular frequency and the square of complex eigenvalue). Substituting the power spectral equation into the defining equation of the spectral moment, the 0 -2nd order spectral moment of the serial response of displacement, velocity, etc. was obtained. Finally, an 18-story structure was used as an example to verify the correctness of the proposed closed solution; the influence of the number of complex eigenvalues on the accuracy of the structural response was analyzed; the feasibility of the arrangement scheme of the inertial capacity system in a multi-story structure was explored. The results show that; the proposed closed solution for the spectral moments is correct and applicable; the influence of higher-order vibration patterns on the structural response is weak, and a high calculation accuracy can be achieved by considering only the first few vibration patterns. The arrangement scheme of the inertial capacitance system proposed in the paper has the features of simple and easy implementation and good effect. © 2023 Chinese Vibration Engineering Society. All rights reserved.