Although　the　substitution　idea　has　been　used　occasionally　in　some　engineering　structures　to　study　vibration　characteristics,　it　is　still　short　of　systematic　study　in　the　vibrational　engineering　field.　We　summarize　the　techniques　of　the　substitution　method　in　this　paper　and　apply　such　skill　further　to　continuous　and　nonlinear　systems,　by　which　the　dimension　of　the　system　can　be　reduced.　By　illustrated　examples　of　frequency　analysis　on　Timoshenko　beam　and　composite　sandwich　structure,　the　substitution　method　has　verified　to　be　valid　and　efficient.　The　gyroscopic　systems,　represented　by　both　rotating　structures　and　orbits　around　libration　points　have　also　been　presented　to　show　the　power　of　substitution　method.　Illustrated　by　the　current　examples,　it　is　concluded　that　the　substitution　method　has　wide　potential　applications　via　studying　the　functional　relations　among　all　the　degreeof-freedoms　(DOFs)　of　non-gyroscopic　or　gyroscopic　systems.　(C)　2019　Elsevier　Ltd.　All　rights　reserved.