Vibration isolation is defined as the process to isolate an object from sources of vibration. The theory of vibration isolation is to make the natural frequency of the system lower than the forced frequency and to suppress the resonance at the natural frequency of the system. As technology advances. a vibration isolation technique is essentially required to isolate vibrations from high-performance metrology tools.
Transmissibility (T) indicates the ratio of the amplitude of the vibration transmitted to an isolated payload to that of the exciting vibration. The efficiency of the vibration isolation improves with the lower natural frequency, meaning the lower transmissibility is the better vibration isolation performance.
The frequency ratio is a function of the forced frequency and the natural frequency of the system and is used as an evaluation criterion to determine vibration isolation performance.
As the frequency ratio reaches 1.414FN and T becomes less than 1 for all values greater than this, the isolation effect takes place. On the other hand. when the transmissibility ratio is smaller than 1.414. then vibration is amplified. Therefore. the transmissibility frequency (1.414FN) is reasonable value to determine the limit frequency of each natural frequency because the transmissibility frequency (1.414FN) is unaffected by the damping value. If the frequency ratio is equal to 1. then vibration amplitude is maximized (i.e. resonance occurs when the forced frequency and the natural frequency coincides).
Damping is reduction or restraining of mechanical oscillations by dissipating the energy stored in an oscillatory system. An un-damped spring leads the peaks of vibration amplitude at the resonant frequency. On the other hand. the damped spring decreases the vibration amplitude at resonance. However, there is a trade off between vibration isolation performance and damping that the vibration isolation performance degrades as damping increases.
Damping ratio is a system parameter denoted by ζ (zeta) that can vary from un-damped (ζ=0) to under-damped.