When the
foundation of structure vibrates due to external source, the response of
structure needs to take such movement into account, rather than considering
only the reaction of the dynamic components. For this reason, we need to use
relative displacement and velocity when writing our equilibrium equation.
The steady state response of structure can be related to the excitation motion amplitude by introducing the term transmissibility. When the frequency ratio is zero and square root of two, the transmissibility is one, denotes the amplitude of steady state response is the same as that for excitation motion. However, there are cases where the value of transmissibility is less than one. For such cases, we can say the isolation of vibration is in place.
The following shows the derivation related to harmonic excitation of foundation due to motion excitation. Watch the video above for full details.
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