简介：Thelinearandnonlineardynamicresponsesofavibratoryringgyroscopeareinvestigatedinthisstudyfocusingontheresponsemechanismofsuchavibratorygyroscope.Itisfoundthatthenonlinearequationsgoverningthedriveandsensedirectionsarecoupledthroughbothinertiallinearandgeometricnonlinearterms.Nonlinearresponsesarestudiedbasedonthefullcouplednonlineardynamicequations.Thevaryingamplitudeonthesensedirectionisanalyzedfordifferentinputangularrates.Theeffectofnonlinearityontheringgyroscopesystemisperformedbycomparingtheresultsofnonlinearresponsestothoseoflinearresponses.Thecontributionsofsomeparameterstotheamplituderesponsesandgyroscopesensitivityareanalyzed,theconclusionsofwhichprovideguidelinestoimprovethesensitivityofthevibratoryringgyroscopes.

简介：Stochasticdynamicanalysisofthenonlinearsystemisanopenresearchquestionwhichhasdrawnmanyscholars'attentionforitsimportanceandchallenge.Fokker–Planck–Kolmogorov(FPK)equationisofgreatsignificancebecauseofitstheoreticalstrictnessandcomputationalaccuracy.However,practicaldifficultieswiththeFPKmethodappearwhentheanalysisofmulti-degree-offreedom(MDOF)withmoregeneralnonlinearityisrequired.Inthepresentpaper,byinvokingtheideaofequivalenceofprobabilityflux,thegeneralhigh-dimensionalFPKequationrelatedtoMDOFsystemisreducedtoone-dimensionalFPKequation.Thenacellrenormalizedmethod(CRM)whichisbasedonthenumericalreconstructionofthederivedmomentsofFPKequationisintroducedbycoarseningthecontinuousstatespaceintoadiscretizedregionofcells.ThenthecellrenormalizedFPK(CR-FPK)equationissolvedbydifferencemethod.Threenumericalexamplesareillustratedandtheeffectivenessofproposedmethodisassessedandverified.

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