Analytic Solutions for the Stationary Seismic Response of Three-Dimensional Structures with a Tuned Mass-Inerter Damper and Bracket

The ultimate goal of research on seismic mitigation technologies is engineering application. However, current studies primarily focus on the application of dampers in planar structures, while actual engineering structures are three-dimensional (3D) in nature. A type of damper, making up tuned mass d...

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Bibliographic Details
Main Authors: Lin Deng, Cong Yao, Xinguang Ge
Format: Article
Language:English
Published: MDPI AG 2025-07-01
Series:Buildings
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Online Access:https://www.mdpi.com/2075-5309/15/14/2483
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Summary:The ultimate goal of research on seismic mitigation technologies is engineering application. However, current studies primarily focus on the application of dampers in planar structures, while actual engineering structures are three-dimensional (3D) in nature. A type of damper, making up tuned mass dampers (TMDs) and inerters, has excellent vibration mitigation performance and needs brackets to connect to structures. In this work, a coupled dynamic model of an energy dissipation system (EDS) comprising a TMD, an inerter, a bracket, and a 3D building structure is presented, along with analytical solutions for stochastic seismic responses. The main work is as follows. Firstly, based on D’Alembert’s dynamics principle, the seismic dynamic equations of an EDS considering a realistic damper and a 3D structure are formulated. The general dynamic equations governing the bidirectional horizontal motion of the EDS are further derived using the dynamic finite element technique. Secondly, analytical expressions for spectral moments and variances of seismic responses are obtained. Finally, four numerical examples are presented to investigate the following: (1) verification of the proposed response solutions, showing that the calculation time of the proposed method is approximately 1/500 of that of the traditional method; (2) examination of spatial effects in 3D structures under unidirectional excitation, revealing that structural seismic responses in the direction along the earthquake ground motion is approximately 10<sup>4</sup> times that in the direction perpendicular to the ground motion; (3) investigation of the spatial dynamic characteristics of a 3D structure subjected to unidirectional seismic excitation, showing that the bracket parameters significantly affect the damping effects on an EDS; and (4) application of the optimization method for the damper’s parameters that considers system dynamic reliability and different weights of the damper’s parameters as constraints, indicating that the most economical damping parameters can achieve a reduction in displacement spectral moments by 30–50%. The proposed response solutions and parameter optimization technique provide an effective approach for evaluating stochastic seismic responses and optimizing damper parameters in large-scale and complex structures.
ISSN:2075-5309