What Is the Dynamic Vibration Absorber (Tuned Mass Damper) Calculator?
A tuned mass damper counters cyclic structural excitation by vibrating in anti-phase relative to the host structure.
Den Hartog tuning flattens the frequency response function so both resonant peaks have equal minimal amplitude.
How Does the Dynamic Vibration Absorber (Tuned Mass Damper) Calculator Work?
Computes mass ratio mu = absorber mass / primary mass.
Calculates Den Hartog optimal frequency tuning ratio f_opt.
Determines required absorber spring stiffness k_a and optimal viscous damping ratio.
Dynamic Vibration Absorber (Tuned Mass Damper) Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
Den Hartog optimal tuning equations equalizing the two invariant resonance peaks.
How to Use the Dynamic Vibration Absorber (Tuned Mass Damper) Calculator
- Enter the host structure modal mass in kilograms.
- Enter primary modal stiffness in kN/m.
- Specify the proposed auxiliary absorber mass in kilograms.
Step-by-Step Example Calculation
Structural Floor Vibration Mitigation
Input Values:
Understanding Your Result
Absorber stiffness k_a indicates the exact spring stiffness required for resonant cancellation.
Optimal damping ratio prevents excessive absorber stroke while maximizing energy dissipation.
Factors That Affect the Result
- Mass ratio: Higher mass ratios (e.g. 5% vs 1%) produce broader frequency bandwidth protection and lower peak motion.
- Mistuning: Off-design shifts in primary structural stiffness severely degrade absorber effectiveness.
When Should You Use This Calculator?
- Tall building wind sway mitigation (e.g. Taipei 101 pendulum damper).
- Long-span pedestrian bridges and machine tool chatter suppression.
Assumptions & Limitations
- Assumes linear single-degree-of-freedom primary system with negligible inherent structural damping.
- Assumes steady-state harmonic base or force excitation.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Den Hartog formulation is the mathematically exact analytical optimum for undamped primary systems.