Structural Dynamics
Tuned Mass Damper Simulator
Simulate vibration absorption via harmonic tuning of a secondary mass. Sweep excitation frequency, visualize primary and TMD mass response, and export frequency response data.
Model
2-DOF TMD
Harmonic forcing
Mesh
50 pts
Frequency sweep
Output
CSV
Export ready
Parameters
Configuration preset
Frequency sweep animation
Governing Equations
Equation of Motion (Primary)
m₁ẍ₁ + (c₁+c₂)ẋ₁ + (k₁+k₂)x₁ - c₂ẋ₂ - k₂x₂ = F₀cos(ωt)
Equation of Motion (TMD)
m₂ẍ₂ + c₂ẋ₂ + k₂x₂ - c₂ẋ₁ - k₂x₁ = 0
Natural Frequencies
ωn₁ = √(k₁/m₁) = 4.47, ωn₂ = √(k₂/m₂) = 4.47
Mass ratio μ = m₂/m₁ = 0.100. Tuning ratio f = ωn₂/ωn₁ = 1.000.
For optimal tuning, set ωn₂ ≈ ωn₁ and μ = 0.01–0.10.
TMD System Diagram
Primary Amplitude
0.2709m
ωn₁ (Primary)
4.47rad/s
ωn₂ (TMD)
4.47rad/s
Mass Ratio
0.100m₂/m₁
Frequency Response (X₁ vs ω)
Frequency Response Data
| ω (rad/s) | Amplitude (m) | Amplitude (mm) |
|---|---|---|
| 0.1 | 0.2501 | 250.14 |
| 0.5 | 0.2535 | 253.49 |
| 0.9 | 0.2617 | 261.70 |
| 1.3 | 0.2758 | 275.85 |
| 1.7 | 0.2981 | 298.09 |
| 2.1 | 0.3327 | 332.75 |
| 2.5 | 0.3892 | 389.22 |
| 2.9 | 0.4924 | 492.38 |
| 3.3 | 0.7371 | 737.07 |
| 3.7 | 2.0017 | 2001.68 |
| 4.1 | 0.7682 | 768.21 |
| 4.5 | 0.2709 | 270.93 |
| 4.9 | 0.6256 | 625.60 |
| 5.3 | 1.2486 | 1248.62 |
| 5.7 | 0.6194 | 619.45 |
| 6.1 | 0.3765 | 376.48 |
| 6.5 | 0.2673 | 267.29 |
| 6.9 | 0.2054 | 205.37 |
| 7.3 | 0.1654 | 165.37 |
| 7.7 | 0.1374 | 137.39 |
| 8.1 | 0.1167 | 116.72 |
| 8.5 | 0.1009 | 100.85 |
| 8.9 | 0.0883 | 88.31 |
| 9.3 | 0.0782 | 78.17 |
| 9.7 | 0.0698 | 69.81 |