Spider DSA User’s Manual
120
The relationship between input (force excitation) and output (vibration
response) of a linear system is given by:
where {Y} and {X} are the vectors containing the response spectra and the
excitation spectra, respectively, at the different DOFs in the model, and [H] is
the matrix containing the FRFs between these DOFs.
The equation above can also be written as:
where Yi is the output spectrum at DOF i, Xj is the input spectrum at DOF j,
and Hij is the FRF between DOF j and DOF i. The output is the sum of the
individual outputs caused by each of the inputs.
The FRFs are estimated from the measured auto- and cross-spectra of and
between inputs and outputs. Different calculation schemes (estimators) are
available in order to optimize the estimate in the given measurement situation
(presence of noise, frequency resolution, etc...).
For the classical case of a single input, the equation above gives the output at
any DOF i, with the input at DOF j, as:
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