Tuned Mass Damper (TMD)

1. Product Definition
The Tuned Mass Damper (TMD for short) is a sub-structural vibration reduction device attached to the main structure. It absorbs and dissipates structural vibration energy through the collaborative effect of a mass block, spring, and damper, thereby suppressing the vibration response of the main structure.

2. Core Components

• Mass unit: Generates inertial force to apply control force to the main structure. It is usually made of high-density materials (such as lead or steel), and the mass can be adjusted. The mass block is the core part of the TMD damper, and its mass size has a decisive impact on the damping effect, which can be adjusted as needed to match the natural frequency of the structure.
• Spring unit: Used to connect the mass block and the main structure, tune the natural vibration frequency of the TMD to match the target mode frequency of the main structure, ensure that the mass block can produce corresponding reverse movement when the structure vibrates, and provide a reset force. Metal springs or rubber springs are mostly used.
• Damper unit: Used to consume the relative motion energy between the mass block and the main structure, prevent energy accumulation in the system from causing greater vibration, and limit the displacement of the TMD. Common types include viscous dampers, friction dampers, or metal dampers.

3. Functional Advantages

• High-efficiency vibration reduction: It can reduce the peak acceleration of structural vibration by more than 70%.
• Adjustable frequency: Adapt to the vibration characteristics of different structures by optimizing parameters (mass ratio, frequency ratio, damping ratio).
• Convenient installation: It can be independently installed on the top of the structure, between layers, or below long-span components without major modification to the main structure.
• Wide adaptability: Suitable for vibration control of wind, earthquake, or human-induced vibrations in various structures such as high-rise buildings, long-span corridors, bridges, and equipment foundations.

1. Vibration Reduction Mechanism
When the main structure vibrates due to external excitation (such as wind, earthquake, or crowd activity), the TMD produces a relative motion opposite to the main structure due to inertia. The inertial force generated by its vibration acts on the main structure through the spring and damper, forming a "dynamic vibration absorption" effect. The specific performance is:

• The spring unit tunes the natural vibration frequency of the TMD to the target frequency of the main structure to produce a resonance effect, transferring the vibration energy of the main structure to the TMD.
• The damper unit dissipates the energy absorbed by the TMD, ultimately reducing the vibration amplitude of the main structure.

2. Theoretical Model
 

Where:
m1, m2: Mass of the main structure and TMD;
k1, k2: Stiffness of the main structure and TMD spring;
y1, y2: Displacements of the main structure and TMD;
c: Damping coefficient of the TMD;
P(t): External excitation (such as harmonic load (Psinώt)).

3. Key Parameter Optimization
 

1. Mass ratio (μ): μ = m2/m1, recommended value is 0.005~0.03. A larger mass ratio makes the vibration reduction frequency band wider, but the load limit of the main structure needs to be considered.
2. Optimal frequency ratio (δ_opt): δ_opt = , to match the vibration frequency of the TMD with the main structure frequency.
3. Optimal damping ratio (ζ_opt): ζ_opt = , to ensure high efficiency.

1. Conventional Model Parameters
 

2. Customized Parameter Design

• Frequency tuning range: 0.1~10.0Hz (can be precisely adjusted according to the natural frequency of the main structure).
• Damping ratio adjustment: 0.02~0.2 (optimized by damper type and damping fluid viscosity).
• Installation forms: Suspended type, supported type, embedded type (selected according to structural space).

3. General Parameter scope

4, Inspecting

1. Performance Advantages

• High vibration reduction efficiency: For the specific mode of the main structure, the vibration response can be reduced by 40%~80%, meeting the building comfort specification (such as vertical acceleration ≤0.15m/s²).
• Strong robustness: It has certain adaptability to structural parameter fluctuations (such as stiffness degradation and mass change). The Multiple Tuned Mass Damper (MTMD) can further broaden the vibration reduction frequency band.

2. Technical Innovations

• Active TMD (ATMD): Integrated with sensors and actuators, it can adjust the control force in real time, suitable for strong earthquake or complex load conditions (such as the PID control-based ATMD in Document 3, which improves the vibration reduction effect by 20%~30%).
• Physical model design: Optimizes structural details based on finite element analysis (such as ANSYS), considering the collaborative work of the mass block, spring, and damper, which is closer to the actual working conditions than the traditional particle model.

3. Economy

• Cost advantage: Compared with traditional structural reinforcement, the cost is reduced by 30%~50%, especially suitable for vibration reduction transformation of existing buildings.
• Long service life: The design life of the main components (mass block, spring) is ≥50 years, the damper can be replaced, and the maintenance cost is low.

1. Construction Engineering

• High-rise buildings: Control the top acceleration caused by wind vibration and improve living comfort.
• Long-span structures: Human-induced vibration control of long-span corridors and stadium roofs.
• Floor systems: Walking vibration control of office building and shopping mall floors to solve the "stepping vibration" problem.

2. Bridge Engineering

• Cable-stayed bridges and suspension bridges: Suppress wind-induced flutter and vortex-induced vibration.
• Pedestrian bridges: Prevent resonance caused by dense crowd walking and ensure traffic safety.

3. Industrial Equipment

• Foundations of large power equipment: Absorb vibrations generated by machine operation and protect equipment accuracy and surrounding structures.
• Pipeline systems: Suppress vibrations caused by fluid pulsation and reduce fatigue damage.

1. Installation Process

• Working condition analysis: Determine the natural frequency, mode shape, and most unfavorable vibration position of the main structure through modal analysis.
• Parameter design: Optimize TMD parameters according to the mass ratio and frequency ratio, and determine the number and position of installations.
• Fixed installation: Fix the TMD base on the structural beams, columns, or supports with high-strength bolts or welding to ensure connection stiffness.
• Debugging and acceptance: Test the working status of the TMD through an exciter, and adjust the damper parameters to achieve the best vibration reduction effect.

2. Maintenance Points

• Regular inspection: Inspect the bolt tightness, spring deformation, and damper oil leakage every 1~2 years.
• Damper replacement: Replace the damper in time when the damping force decays by more than 20% (usually the service life is 10~15 years).
• Parameter reset: If the main structure is modified (such as adding floors or reducing weight), re-evaluate and adjust the TMD parameters.

• Parameter matching: TMD parameters need to be precisely tuned with the main structure to avoid reducing the vibration reduction effect or even amplifying the vibration due to frequency mismatch.
• Installation space: Reserve enough movement space for the TMD (stroke ≥±50mm) to avoid collision with other components.
• Environmental adaptability: Anti-corrosion coatings (such as zinc-nickel alloy coatings) are required in humid environments, and high-temperature resistant damping fluid (temperature resistance ≥120℃) should be selected in high-temperature places.
• Safety redundancy: For important structures (such as lifeline projects), it is recommended to set up standby TMD or multiple tuning systems to improve reliability.

1. Vibration Reduction of Commercial Building Corridor

• Problem: The vertical natural vibration frequency of the 36m span corridor is 2.92Hz, and the peak acceleration under pedestrian load is 0.225m/s², exceeding the specification requirement (≤0.15m/s²).
• Solution: Install 1 TMD (mass 1521kg, stiffness 511.39kN/m, damping coefficient 2.389kN·s/m).
• Effect: The peak acceleration is reduced to 0.052m/s², a decrease of 76.89%, and the natural vibration frequency is adjusted to 2.78Hz, meeting the comfort requirements.

2. Wind Vibration Control of High-rise Buildings

• Project: A 200m high-rise office building with a top acceleration of 0.18m/s² under wind vibration (specification limit 0.15m/s²).
• Solution: Install 4 MTMDs on the top floor (total mass accounts for 0.5% of the structural mass), with a frequency coverage of 1.2~1.8Hz.
• Effect: The top acceleration is reduced to 0.12m/s², the wind vibration response is reduced by 33.3%, and indoor personnel have no obvious shaking sensation.

• Consulting and design: Provide structural vibration analysis, TMD parameter optimization, and scheme design, supporting finite element simulation (such as ANSYS, YJK).
• Customized production: Customize TMD specifications according to project needs, and provide 3D modeling and physical model testing.
• Installation and debugging: Professional team for on-site installation, equipped with a vibration monitoring system to optimize the vibration reduction effect in real time.
• After-sales guarantee: Provide a 5-year warranty, lifetime maintenance support, and regular return visits to detect equipment status.

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