Coupled Vibration Mathematical Model of Special-Shaped Column Structure Considering Ground Rotation Effects
Abstract
1. Introduction
2. Seismic Response Analysis Model Considering Ground Rotational Components
2.1. Dynamics Model Considering Ground Rotational Components
2.2. Determination of Floor Torsional Stiffness
3. Lateral–Torsional Vibration Mathematical Mode
3.1. Establishment of Lateral–Torsional Coupled Motion Equations
3.2. Response Patterns of Lateral–Torsional Coupled Vibration
3.2.1. Natural Vibration Frequency Variation
3.2.2. Torsional Amplitude
3.2.3. Participation Coefficient
3.2.4. Relative Torsion Effect
3.2.5. Torsional Control Indicator
4. Shaking Table Test of the Special-Shaped Column Frame Structure
4.1. Test Survey
4.2. Lateral Vibration
4.3. Torsional Vibration
4.4. Seismic Shear
4.5. Column Shear
4.6. Column Torsional Stiffness
5. Comparison Between the Experimental Results and Theoretical Calculations
5.1. Comparison of the Natural Frequency Ratio
5.2. Comparison of the Torsional Effect
5.3. Comparison of Base Shear
5.4. Comparison of Special-Shaped Column Shear Force
5.5. Comparison of Torsional Stiffness
6. Conclusions
- (1)
- Considering the influence of ground rotation and eccentric torsion on the model, the lateral displacement of the structure and floor torsion is primarily induced by horizontal seismic components and floor eccentricity. The seismic torsion of the model is attributed to ground rotational components. The floor torsional angle is equivalent to the sum of the inter-story and pure torsional angles caused by eccentric torsion and ground rotation, respectively.
- (2)
- The natural vibration frequency of a structure, considering the influence of ground rotation, is a function of relative eccentricity ey/r, the lateral–torsional period ratio Tφt/Tu caused by ground rotation, and the lateral–torsional period ratio Tφe/Tu considering only eccentric torsion. The following conclusions are drawn from the variation analysis of the natural vibration frequency ratio, torsional amplitude ratio, mode participation factor ratio, and relative torsional index of the structure, considering the influence of ground rotation. When eccentricity ey/r is constant and Tφt/Tu remains unchanged, the peak points of the natural vibration frequency ratio and the lateral–torsional coupling coefficient, considering ground rotation, shift significantly compared to when considering only eccentricity under the same conditions. Once Tφe/Tu surpasses 1.0, the torsional amplitude increases remarkably, and the first vibration mode participation indicates elevated values compared to the scenario where only eccentricity is taken into account. When considering torsional dynamic effects, the accidental relative eccentricity of the SRC special-shaped structure in the Y-axis is less than 0.1.
- (3)
- The shaking table test results facilitate the acquisition of the natural characteristics, translational response, torsional response, and internal force distribution of the SRC special-shaped column frame structure. Under intense earthquake conditions, the inter-story stiffness of the structure degrades rapidly. The maximum displacement angle of the structure is observed to be 1/14, the maximum accidental eccentric torsional angle is measured at 18.8 × 10−7, and the maximum inter-story displacement angle resulting from lateral–torsional coupling is recorded as 1/48. Throughout the experimentation, the torsional response of the SRC special-shaped column remains within the elastic stage. For the special-shaped column structure that meets the height limitation requirement specified in the code, the influence of accidental eccentricity and lateral–torsional coupling on its seismic performance is relatively minimal.
- (4)
- By comparing experimental and theoretical values, the measured structural lateral–torsional natural frequency ratio considering ground rotation is close to the calculated results from the mathematical model. The maximum ratio of torsional displacement at the ground floor to the horizontal displacement in the X direction of the SRC special-shaped column frame structure under three-directional seismic action is 0.0007. The torsional effect, torsional stiffness, and internal force theoretical calculations of the special-shaped column correspond well to the experimental results, indicating that they can be used for analyzing lateral–torsional vibration response patterns of structures.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Hu, Z.; Xue, J. Coupled Vibration Mathematical Model of Special-Shaped Column Structure Considering Ground Rotation Effects. Buildings 2025, 15, 1300. https://doi.org/10.3390/buildings15081300
Hu Z, Xue J. Coupled Vibration Mathematical Model of Special-Shaped Column Structure Considering Ground Rotation Effects. Buildings. 2025; 15(8):1300. https://doi.org/10.3390/buildings15081300
Chicago/Turabian StyleHu, Zongbo, and Jianyang Xue. 2025. "Coupled Vibration Mathematical Model of Special-Shaped Column Structure Considering Ground Rotation Effects" Buildings 15, no. 8: 1300. https://doi.org/10.3390/buildings15081300
APA StyleHu, Z., & Xue, J. (2025). Coupled Vibration Mathematical Model of Special-Shaped Column Structure Considering Ground Rotation Effects. Buildings, 15(8), 1300. https://doi.org/10.3390/buildings15081300