| Summary: | Abstract
When avibratingstructureisrotatedwithrespecttoinertialspace,thevibratingpatternrotatesatarateproportionalto
the inertialrateofrotation.Bryanfirstobservedthiseffectin1890.Theeffect,calledBryan’seffectinthesequel,has
numerous navigationalapplicationsandcouldbeusefulinunderstandingthedynamicsofpulsatingstarsandearthquake
series inastrophysicsandseismology.Bryan’sfactor(thecoefficientofproportionalitybetweentheinertialandvibrating
pattern rotationrates)dependsonthegeometryofthestructureandthevibrationmodenumber.The‘‘gyroscopiceffects’’
of ahollowisotropicsolidspherefilledwithaninviscidacousticmediumareconsideredhere,butthetheoryisreadily
adapted toahollowisotropicsolidcylinderfilledwithaninviscidacousticmedium.Alineartheoryisdevelopedassuming,
among othermildconditions,thattherotationrateisconstantandmuchsmallerthanthelowesteigenfrequencyofthe
vibrating system.Thuscentrifugalforcesareconsideredtobenegligible.Beforecalculatingsolutionsforthedisplacement
of aparticleintheisotropic,spherical,distributedbody,Bryan’sfactorisinterpretedusingacomplexfunction.Hereitis
demonstrated thatneitherBryan’seffectnorBryan’sfactorisinfluencedbyincludinglight,isotropic,viscousdampingin
the mathematicalmodel.Hencedampingisneglectedinthesequel.Twoscenariosarethenidentified.Firstly,wemay
assume thattheacousticmediumiscompletelyinvolvedintherotation(thespheroidalmode).Secondly,wemayassume
that theacousticmediumremainsstaticwithrespecttotheinertialreferenceframe(thetorsionalmode).Weinvestigatethe
spheroidal modeusinganumericalexperimentthatcomparestherotationalangularrateofasphere(filledwithaninviscid
acoustic medium)withthoseofitsvibratingpatternsatbothhighandlowvibrationfrequency.
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