Modal analysis is established as one of the fundamental strategies in appro
aching structural dynamic problems. Despite its universal appeal, it is fun
damentally a linear theory and cannot be applied to significantly nonlinear
systems without incurring substantial difficulties in implementation and i
nterpretation of results. This paper documents a number of attempts to reco
ncile nonlinearity with modal analysis. Three main approaches are discussed
, each of which is characterized by a different philosophy.