Free vibration of rotating hollow spheres containing acoustic media

Description

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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1. http://encore.tut.ac.za/iii/cpro/DigitalItemViewPage.external?sp=1001765

Tags

Vibrating patterns

Vibration frequency

Additional Fields

Identifer	oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:tut/oai:encore.tut.ac.za:d1001765
Date	16 April 2008
Creators	Shatov, MY, Joubert, SV, Coetzee, CE, Fedotoc, IA
Publisher	Elsevier
Source Sets	South African National ETD Portal
Language	English
Detected Language	English
Type	Text
Format	Pdf
Rights	c2008 ElsevierLtd.
Relation	Journal of Sound and Vibration