Seismic response analysis of multi-degree-of-freedom structures with a series-parallel layout Ⅰ inerter system
LI Chuangdi1，WANG Ruibo1，JIANG Lifu1，GE Xinguang2
Author information+
1.School of Civil Engineering & Architecture, Guangxi University of Science and Technology, Liuzhou 545006, China;
2.College of Civil and Architectural Engineering, Liuzhou Institute of Technology, Liuzhou 545616, China
Aiming at the problem of insufficient research on the application and arrangement scheme of inertial-capacity system in multi-degree-of-freedom structures, the calculation method of response frequency domain solution and spectral moment of multi-degree-of-freedom inertial capacitance system is proposed. And the arrangement scheme of inertial capacitance system is determined based on the response frequency domain solution and spectral moment expression. By introducing state variables to transform the structural equations of motion and the differential-type intrinsic structure relations of the series–parallel layout I inerter system (SPIS-I) into state equations expressed in matrix form. Then, we derive a unified solution in the frequency domain for the series response of structural displacements, velocities, and interstory displacement angles. Next, the quadratic orthogonalization method(QOM) is used to convert the response power spectrum into quadratic decomposition formula (linear combination form of the inverse of the sum of the square of the circular frequency and the square of the complex eigenvalue). Immediately after substituting the power spectral equation into the defining equation of the spectral moment, the 0-2nd order spectral moment of the series response of displacement, velocity, etc. is obtained. Finally, an 18-story structure is used as an example to verify the correctness of the proposed closure solution; the influence of the number of complex eigenvalues on the accuracy of the structural response is analyzed; the feasibility of the arrangement scheme of the inertial capacity system in a multi-story structure is 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 the first few vibration patterns.The arrangement scheme of the inertial capacitance system proposed in this paper has the characteristics of simple and easy implementation and good effect.
LI Chuangdi1，WANG Ruibo1，JIANG Lifu1，GE Xinguang2.
Seismic response analysis of multi-degree-of-freedom structures with a series-parallel layout Ⅰ inerter system[J]. Journal of Vibration and Shock, 2023, 42(22): 19-28
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