This thesis consists of four papers concerning the audibledynamic stiffness of a vibration isolator; includingmeasurements and theoretical modeling. The study focus isrubber isolators, being the most popular material in theaudible frequency domain - though the measurement principlealso applies to other resilient elements.
Paper A seeks to establish an accurate audible stiffnessmeasurement method, including static preload, isolator platetranslation and rotation. Techniques, improving stiffnessaccuracy are discussed in some detail. The method is applied toa cylindrical vibration isolator at four axial preloads,resulting in smooth stiffness magnitude and phase curves,displaying antiresonances, resonances and the expected preloaddependence.
;Paper B offers a waveguide model of the axial dynamicstiffness for cylindrical vibration isolators, where influencesof higher order modes and structure borne sound dispersion areinvestigated in some detail. The problems of simultaneouslysatisfying the cylinder boundary conditions are removed, byadopting the mode matching technique, using the dispersionrelation for an infinite cylinder and approximately satisfyingthe boundary conditions at the lateral surfaces by acircle-wise fulfillment or a subregion method. The stiffnessresults are shown to converge. The rubber material is assumedto be nearly incompressible with deviatoric viscoelasticity.This work is verified by experiments on a rubber cylinder,equipped with bonded circular steel plates, in the frequencyrange 50 - 5 000 Hz, where model and measurements agreestrikingly well within the whole frequency range. Comparisonswith alternative material models are made. Approximate modelsare shown to diverge substantially from the presentedexacttheory, they are the long rod,the Love, theBishop, the Kynch, the Mindlin&Herrmann and the Mindlin&McNiven theories. To a great extent, the pertinent stressand displacement fields, derived from the presented model,explain the discrepancies reported for the approximatetheories.
The study focus in Paper C is on isolator stiffness radiusand length dependence. The results after a geometric shift of agiven isolator are compared to the results of a simple scalinglaw, which fails in modeling the stiffness alteration due to asingle length or radius shift, while successfully predictingthe results of an isolator shape invariant shift; the smalldeviations arise from a disregarded material propertyshift.
Paper D presents a non-linear preloaded dynamic stiffnessmodel. The problem of simultaneously modeling the rubberprestrain dependence and its audible short term response isaddressed. An incremental, nearly incompressible material modelis adopted, obeying decoupled spherical and deviatoricresponses, being elastic in dilatation while displayingviscoelasticity in deviation. The latter exhibits a time strainseparable relaxation tensor with a single function embodyingits time dependence. An updated Lagrangian non-linear finiteelement procedure solves the weak formulations corresponding tothe stiffness problem. The results applied to a cylindricalvibration isolator agree strikingly well with static anddynamic measurements at various preloads.
Keywords: Vibration isolator, dynamic stiffness,cylinder, rubber, waveguide, nearly incompressible, time strainseparable, viscoelasticity, stiffness measurement, modematching, subregion method, scaling law, prestrain, preload,translation, rotation, non-linear, finite element.
Stockholm: KTH , 1998. , 26 p.