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Viscoelastic dampers have been widely applied in the seismic and wind-resistant design of super high-rise buildings abroad. Their effectiveness in controlling structural responses to seismic and wind loads has been validated through extensive testing. Although research on their application in wind vibration control has increased in recent years, practical implementations remain limited. As a passive control device, viscoelastic dampers dissipate energy through the deformation of their internal molecular chain network during compression and relaxation. Installed within high-rise structures, they generate shear deformation when inter-story displacements occur due to vibrations, thus reducing the dynamic response on the main load-bearing system. Due to their simple construction and cost-effectiveness, they hold great potential for use in real-world engineering projects.
The complex stiffness matrix of a viscoelastic support element is typically represented as a type of support. The herringbone clock structure, with its oblique collapse form, is often used in pavilion designs. In some cases, sticky sticks are made from two steel rods, with the middle part consisting of wooden sticks and adhesive materials, controlled by three children. The toe nipple is constructed using steel plates sandwiched between two viscoelastic layers, which can be simplified into a mechanical model for pavilion analysis.
This study was supported by the Ministry of Science and Technology Fund Project 990313. The author, Ge, is from Banzhou, Jiangsu. According to Hooke’s law, shear strain occurs due to relative displacement between structural layers. This displacement corresponds to the angle between the viscoelastic support and the floor, with the shear area and thickness of the damping layer also playing important roles. The complex stiffness model is commonly used in structural vibration analysis, where the shear stiffness center of the viscoelastic material is considered.
It is assumed that the damping force of the material is proportional to the elastic force and leads in phase. The shear modulus of the viscoelastic material can be expressed in the complex plane, with G' representing the real part and G'' the imaginary part. The loss factor, η, is the ratio of damping force to elastic force, reflecting the material's energy dissipation capability.
The complex shear stiffness of the material is derived based on the assumption that the tensile stiffness of the steel rod is much greater than that of the damping layer, allowing its deformation to be neglected. The relationship between local and global coordinate systems for node displacements and forces is established, enabling the assembly of the overall complex stiffness matrix for the viscoelastic support bar.
The equivalent damping ratio of the structure is calculated based on the effective damping loss after installing the viscoelastic support. This involves comparing the original damping loss factor of the steel structure with that of the support system. The pulsating wind load vector along the wind direction is also considered in the motion equation of the steel frame building.
The motion equation for the steel structure is derived by combining equations (1) and (3). For each mode, the loss factor is calculated. By comparing equations 12 and 13, the formula for calculating the effective damping loss factor of the high-rise building is obtained. The relationship between the damping ratio in viscous damping theory and the loss factor in complex damping theory is also established.
The damping ratio for the seventh vibration mode is determined. Substituting equation 15 into equation 14 allows for the calculation of the effective damping ratio. To achieve optimal vibration control, damper parameters must be carefully selected. Two methods are commonly used: one involves adjusting the damping ratio until the structural response meets code requirements, while the other uses simplified formulas for shear-type high-rise buildings.
In a case study, a 12-story steel frame building with a total height of 37.5 meters was analyzed using time-history seismic response analysis. Each floor had two viscoelastic dampers, and the structure was modeled using beam elements. The maximum seismic wave amplitude was set at 358 cm/s², with an earthquake duration of 88 seconds. The structural damping ratio was calculated to be 0.02, showing improved performance after installation of the viscoelastic supports.
Based on the complex stiffness matrix and equivalent damping ratio, damper parameters were designed. A method suitable for general steel structures and a simplified approach for shear-type buildings were proposed. The results demonstrated the effectiveness of viscoelastic dampers in controlling seismic responses in high-rise steel buildings.
References:
1. Damping Vibration and Noise Reduction Technology, Xi'an Jiaotong University Press, 1986.
2. Qu Weilian, "Practical Design Method of Viscoelastic Damper for Wind Vibration Control of Steel High-Rise Buildings," Proceedings of the 1st National Conference on Wind Effects, Wuhan Huazhong University of Technology Press, 1997, pp. 65-78.
Editor-in-Chief: Zhou Jianlan