A standard method of introducing damping or balancing forces is the application of a Tuned Mass Damper (TMD)
Excitation forces are compensated by mass forces so that parts of the structure (main construction) remain almost at rest in a specific frequency range. In vibration damping, an additional oscillator consisting of mass and stiffness (undamped absorber) or of mass, stiffness, and damping (damped absorber) is attached to the main structure for calming.
The undamped absorber is usually used for stationary harmonic oscillation problems, where the absorber natural frequency fT is tuned to the excitation frequency. Theoretically, the vibration amplitudes of the main system can be reduced to zero if no damping is present.
For stationary broadband excitation, which is essential in the range of a natural system frequency, the use of an optimally damped absorber is useful. The natural frequency wT, opt and the damping ratio Dopt of the optimally damped absorber can be designed according to the formula of the Den Hartog formula: