Modal participation factor is a scalar that measures the relative contribution of a vibration mode to a system state for a linear system. The term "ratio" is less meaningful than the term factor "factor.

Consider a discrete dynamic system governed by the following equation

Mϋ + KU = F

where M, K, F have their usual meanings and U is the displacement.

Let A be the eigen vector matrix and L a coefficient matrix defined by

L = ATMUn

where Un is the vector of nodal displacements

The system's generalized mass is given by

MG = ATMA

Then the modal participation factor for mode i is given by

Γi = Li / MG(i,i)

The effective modal mass for mode i is given by

meff, i = Li2 )/ MG(i,i)

A mode that has a much higher effective mass than another can be readily more excited.

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