This study investigated the freeze–thaw resistance of ordinary and nano-TiO₂-modified concrete (NTC) based on mass loss, ultrasonic velocity, compressive strength, and fracture toughness. The compressive behavior and internal damage evolution were further analyzed using particle flow code in two dimensions (PFC^2D) simulations. The results show that, although neither material exhibited structural collapse after freeze–thaw cycling, visible surface damage was observed, particularly in ordinary concrete. After 100 cycles, NTC showed a 52.17% reduction in mass loss and a 37.31% increase in ultrasonic velocity compared to ordinary concrete. Compressive strength of ordinary concrete decreased by 24.28 MPa (from 41.53 MPa to 17.25 MPa), while that of NTC decreased by only 13.37 MPa, demonstrating that the incorporation of nano-TiO₂ effectively improves the compressive performance of concrete under freeze–thaw conditions. Fracture toughness after 100 cycles decreased by 89.7% in ordinary concrete and 80.9% in NTC, suggesting that while nano-TiO₂ mitigates damage, its effect on maintaining fracture load-carrying capacity remains limited. The PFC^2D simulations were consistent with the experimental results, effectively capturing peak compressive behavior and validating the model’s applicability for freeze–thaw degradation analysis.

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 10⁴ 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.