Abstract:To address the complexity in solving responses of high-rise structures with Tuned Liquid Dampers (TLDs) under random seismic excitations, using the finite element dynamic analysis and the quadratic decomposition method of the power spectrum, this study developed a simplified closed-form solution method for the spectral moments of the dynamic responses in high-rise structures with TLDs installed on the top floors under Hu Yuxian seismic excitation spectrum. Firstly, based on the linear mechanical model of TLD, the coupled seismic equations for the TLD-high-rise building structure were established. Then, finite element analysis technology was used to obtain the dynamic characteristics of the high-rise building structure. The equivalent dynamic equations for TLD-high-rise building structures expressed in real modes were reconstructed, resolving difficulties in acquiring the dynamic characteristics of complex controlled structures. Secondly, the simplified closed-form solutions for absolute structural displacements, inter-floor displacements, variance, and 0-2 order spectral moments of high-rise building structures were derived using the complex modal method and quadratic decomposition method. Finally, a real structure was used as a case study. The comparison between the floor and node spectral moments obtained by the proposed method and the results calculated by the virtual excitation method verified the correctness of the derived response spectral moments, and the effects of the number of structural vibration modes and the TLD parameters on vibration reduction performance were explored. The results showed that the first three orders of structural vibration modes could ensure the accuracy of the response results, and the seismic performance of high-rise structures could be effectively improved by appropriately increasing the length and height of the TLD and selecting a suitable damping ratio.
