Vibrations resulting from earthquakes, machinery, or unanticipated shocks may be very damaging and costly to structures. To avoid such damage, designers need a structural system that can dissipate the energy caused by these vibrations. Using elastically buckled struts may be a viable means to reduce the harmful effects of unexpected vibrations. Post-buckled struts can support high axial loads and also act as springs in a passive vibration isolation system by absorbing or dissipating the energy caused by external excitation. When a base excitation is applied, the buckled strut may act to reduce the dynamic force transmitted to the system, thus reducing the structural damage to the system. Several models of buckled and pre-bent struts are examined with different combinations of parameters and end conditions. The models include pinned or fixed columns supporting loads above their buckling load, and columns with an initial curvature supporting various loads. The varying parameters include external damping, internal damping, and stiffness. The columns will be subjected to simple harmonic motion applied at the base or to a multi-frequency base excitation. The response of each model is measured by the deflection transmissibility of the supported load over a large range of frequencies. Effective models reduce the motion of the supported load over a large range of frequencies. / Master of Science

A vibration isolator is designed to reduce the vibration and structure borne noise transmitted from a vibratory source, such as machinery and equipment, to the supporting structure. The vibration and structure borne noise transmitted depends upon the dynamic properties of the foundation, the source mounting point and the vibration isolator. Therefore knowledge of the frequency dependent dynamic properties of vibration isolators is a necessary part of the acoustic prediction and control/reduction process. Vibration isolators may be characterised by measuring their four-pole parameters. A measurement procedure is proposed that employs the floating mass method, measures the direct forces and corrects for the errors introduced by the direct force measurement. Compared to the basic method, it extends the frequency limits of measurement in both directions. The development of a novel vibration isolator test facility that implements the proposed measurement procedure is described, and its satisfactory operation is experimentally demonstrated. The vibration isolator test facility is capable of characterizing vibration isolators commonly used in industrial and maritime applications, under service conditions. A method is proposed for measuring the four-pole parameters of a uni-directional asymmetrical vibration isolator under static load. The method is called the two masses method, and is suitable for determining the four???pole parameters of active vibration isolators with feedback control. The method is also applicable to uni-directional symmetrical and bi-directional symmetrical and bi-directional asymmetrical vibration isolators. It may be regarded as a universal method for characterising vibration isolators. Experimental data is presented and the method is validated. Modelling of vibration isolators is complicated by the highly non-linear nature of their rubber elements. The notion of an effective rubber cylinder is proposed to account for the barrelling of rubber elements under static load. Consequently, a general static compression model is proposed that applies to vibration isolators having unfilled and filled rubber elements of regular prismatic shapes. The model predicts the dependence of the four-pole parameters on the compression ratio of the rubber element. The predictions derived from the effective rubber cylinder and general static compression model agree excellently with experimental work of this study and other researchers.

A vibration isolator is designed to reduce the vibration and structure borne noise transmitted from a vibratory source, such as machinery and equipment, to the supporting structure. The vibration and structure borne noise transmitted depends upon the dynamic properties of the foundation, the source mounting point and the vibration isolator. Therefore knowledge of the frequency dependent dynamic properties of vibration isolators is a necessary part of the acoustic prediction and control/reduction process. Vibration isolators may be characterised by measuring their four-pole parameters. A measurement procedure is proposed that employs the floating mass method, measures the direct forces and corrects for the errors introduced by the direct force measurement. Compared to the basic method, it extends the frequency limits of measurement in both directions. The development of a novel vibration isolator test facility that implements the proposed measurement procedure is described, and its satisfactory operation is experimentally demonstrated. The vibration isolator test facility is capable of characterizing vibration isolators commonly used in industrial and maritime applications, under service conditions. A method is proposed for measuring the four-pole parameters of a uni-directional asymmetrical vibration isolator under static load. The method is called the two masses method, and is suitable for determining the four???pole parameters of active vibration isolators with feedback control. The method is also applicable to uni-directional symmetrical and bi-directional symmetrical and bi-directional asymmetrical vibration isolators. It may be regarded as a universal method for characterising vibration isolators. Experimental data is presented and the method is validated. Modelling of vibration isolators is complicated by the highly non-linear nature of their rubber elements. The notion of an effective rubber cylinder is proposed to account for the barrelling of rubber elements under static load. Consequently, a general static compression model is proposed that applies to vibration isolators having unfilled and filled rubber elements of regular prismatic shapes. The model predicts the dependence of the four-pole parameters on the compression ratio of the rubber element. The predictions derived from the effective rubber cylinder and general static compression model agree excellently with experimental work of this study and other researchers.

Vibrations are very common phenomenon. It influences structures and generates acoustic noise which might be harmful to human beings. The vibration isolator was invented to reduce the effect from vibrations. However, the behavior of rubber material, which many vibration isolators are made of, is hard to predict. Consequently, vibration tests are needed to obtain the dynamic properties of rubber isolator.In this case, a six-year old LORD 2204-5 rubber isolator provided by Atlas Copco was tested. The aim of this paper is to obtain the FRF (Frequency Response Function) diagram which can describe the property of the rubber material. Moreover, the influence of aging of rubber material on the dynamic properties was studied.As the vibration test should simulate the working environment of the isolators that are both a static load from the structure and a dynamic force from the engine, a new excitation method was designed. The camshaft with the shape of an epitrochoid induced the sinusoidal signal of the isolator and the frame transferred the static load from the hydraulic machine. The artificial aging was performed in a hot air oven in 90°C for 42 hours, which according to Arrhenius equation should be equivalent to six years of natural aging. The vibration isolator was tested again after being aged.The obtained data showed that the aging process decreased the stiffness of the material. The results were corresponding with other studies regarding aging of rubber.

The dynamic behaviour in the audible frequency range of magneto-sensitive (MS) rubber is the focus of this thesis consisting of five papers A-E. Paper A presents results drawn from experiments on samples subjected to different constant shear strains over varying frequencies and magnetic fields. Main features observed are the existence of an amplitude dependence of the shear modulus referred to as the Fletcher-Gent effect for even small displacements, and the appearance of large MS effects. These results are subsequently used in Paper B and C to model two magneto-sensitive rubber isolators, serving to demonstrate how, effectively, by means of MS rubber, these can be readily improved. The first model calculates the transfer stiffness of a torsionally excited isolator, and the second one, the energy flow into the foundation for a bushing inserted between a vibrating mass and an infinite plate. In both examples, notable improvements in isolation are obtainable. Paper D presents a non-linear constitutive model of MS rubber in the audible frequency range. Characteristics inherent to magneto-sensitive rubber within this dynamic regime are defined: magnetic sensitivity, amplitude dependence, elasticity and viscoelasticity. A very good agreement with experimental values is obtained. In Paper E, the magneto-sensitive rubber bushing stiffness for varying degrees of magnetization is predicted by incorporating the non-linear magneto-sensitive audio frequency rubber model developed in Paper D, into an effective engineering formula for the torsional stiffness of a rubber bushing. The results predict, and clearly display, the possibility of controlling over a large range through the application of a magnetic field, the magneto-sensitive rubber bushing stiffness. / QC 20100816

This thesis investigates the impact of vibration isolators on circuit boards during harsh vibrationenvironments that occur when they are mounted on the wings of a fighter jet. To examine thisphenomenon, a mathematical model and a simulated model were developed to determine theresonant frequencies of the circuit board under various boundary conditions. Subsequently, theresonant frequencies of the circuit board were validated through experimental tests, allowing forthe establishment of the material properties of the circuit board. In order to prevent structuralfailure, this thesis employs α-gel dampers as the damped attachments for the circuit board.These vibration isolators belong to the category of silicone gel dampers and were evaluatedthrough experimental vibration testing. The two employed vibration isolators are denoted asmodels A1 and A2, exhibiting respective damping ratios of 0.1 and 0.05. By utilizing thesevibration isolators during the experimental vibration tests, the structure demonstrated resilienceagainst natural frequency coupling, thereby preventing failure. / Den här masteruppsatsen undersöker effekten av vibrationsisolatorer på kretskort under detuffa vibrationsmiljöer som sker vid vingarna på ett stridsflyg. För att undersöka detta såanvänds en matematisk modell samt en simulerad modell för att hitta resonansfekvensernaför kretskorten vid olika randvillkor. Resonansfrekvenserna från modellerna jämfördes medresonansfrekvenserna som kom tillhanda efter vibrationsprover och med dem så kunde ävenmaterialegenskaperna bestämmas. För att unvika kollaps av strukturen användes α-geldämpare till kretskorten. Dessa dämpare är gjorde av silikongel och utvärderades genomexperimentella vibrationsprover. Dessa vibrationsisolatorer var av modell A1 och A2 ochkorresponderande modell hade dämpningsförhållande 0.1 respektive 0.05. Genom att användadessa vibrationsiolatorer under de experimentella virbationstesterna så undvek strukturenkollaps genom att resonansfrekvenserna inte triggades.

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Vibrations is a phenomenon that can cause problems to systems if not dealt with. In heavy duty trucks, vibrations are mainly caused by uneven roads and from the combustion engine. Vibrations can damage components, reduce their service life and cause discomfort for the driver. To manage the problem, vibration isolators can be used to absorb energy and thus reduce the vibrations. Rubber is a commonly used material for vibration isolators thanks to its viscoelastic properties. However, due to the characteristics of rubber, there are difficulties to make accurate simulation models of components such as vibration isolators. To improve the accuracy in simulations, physical testing can be performed to measure the material properties and characteristics such as hysteresis to get a better understanding of how the material and the component will behave. The purpose of the master thesis was to generate and develop concepts of a test rig for a specific vibration isolator from Scania where the force as a function of displacement in the component’s Z-direction should be measured as well as the force in the component’s Y-direction. Further, the component should be compressed in a vertical linear motion. Based on the background information, the following research questions were stated: - How can a hysteresis curve based on frequency input be found by performing physical testing? - How can a test rig be designed to test and measure the material properties of a rubber component in order to parametrize the material? The vibration isolator was investigated and analyzed. From the analysis, seven concepts were generated and were evaluated with a Pugh matrix. From the evaluation, two concepts were chosen to be further developed before a final evaluation using a desirability chart was made. The master thesis resulted in two concepts that were developed named Hinged beam and Guiding plates. Guiding plates was the concept that scored the best in the final evaluation, but the concepts had different strength and weaknesses. Both concepts fulfilled the requirement of compressing the vibration isolator in a vertical linear motion but the measurement of the force in the component’s Y-direction needs to be further investigated. / Vibrationer är ett fenomen som kan orsaka problem för olika typer av system om det inte hanteras. I lastbilar är vibrationer huvudsakligen orsakade av ojämnt underlag samt av förbränningsmotorn. Vibrationerna kan orsaka skada på komponenter, reducera deras livslängd och även orsaka obehag för föraren. Det här problemet kan hanteras genom användning av vibrationsisolatorer som minskar effekten fr.n vibrationerna genom att absorbera dess energi. Gummi är ett material som ofta används för att isolera vibrationer tack vare dess viskoelastiska egenskaper. Egenskaperna gör det dock svårt att skapa noggranna simuleringsmodeller av komponenter så som vibrationsisolatorer. För att öka noggrannheten i simuleringarna kan fysisk testning genomföras och materialegenskaper så som hysteres kan mätas för att få en bättre förståelse för hur både material och komponent beter sig med olika laster. Syftet med det här masterexamensarbetet var att generera och utveckla koncept för testriggar för en specifik vibrationsisolator tillhandahållen av Scania. Kraft som funktion av förskjutning i komponentens Z-riktning samt kraft i dess Y-riktning skulle vara möjligt att mätas. Utöver det var ett krav att komponenten endast ska komprimeras i en vertikal linjär rörelse. Baserat på bakgrundinformationen kunde följande forskningsfrågor formuleras: - Hur kan en frekvensbaserad hystereskurva tas fram genom fysisk testning? - Hur kan en testrigg designas för att kunna testa och mäta materialegenskaper hos en gummikomponent för att kunna parametrisera materialet? Vibrationsisolatorn undersöktes och analyserades. Efter analysen genererades sju koncept som utvärderades med en Pugh matris. Utvärderingen resulterade i att de två bäst presterande koncepten valdes för vidareutveckling innan en sista utvärdering genomfördes med hjälp av ett så kallat desirability chart. Masterexamensarbetet resulterade i två koncept som vidareutvecklades, ett som kallas Hinged beam och ett vid namn Guiding plates. Guiding plates var det konceptet som presterade bäst i den slutgiltiga utvärderingen, men de olika koncepten har dock olika styrkor och svagheter. Båda koncepten uppnådde kraven gällande att kompression av vibrationsisolatorn endast ska ske i en vertikal rätlinjig rörelse men hur krafterna i komponentens Y-riktning ska mätas behöver vidare undersökning.

The purpose of this research is to study a new type of vibration isolator, utilizing the post-buckled stiffness of elastic struts (or columns). The advantage of the post-buckled state is that ideally it can support more static load with a relatively small static deflection than traditional vibration isolators such as springs or rubber mounts, but can also exhibit a low axial stiffness when dynamic excitation is introduced. Three models consisting of buckled or pre-bent struts serving as vibration isolators which support a rigid bar are examined in this research. The three cases studied are 1) two buckled struts supporting a symmetric rigid bar, 2) two buckled struts supporting an asymmetric rigid bar, and 3) two pairs of buckled struts with a bonded filler supporting a symmetric rigid bar. The models are subjected to a harmonic excitation at the base, and external damping is included. The struts in all cases are modeled as an elastica, and the boundary conditions are clamped/clamped for all cases. Because the purpose of the struts is to reduce unwanted vibrations, determining the displacement transmissibility of the system is the main goal of this research. Transmissibility versus frequency plots are generated for all cases, with varying parameters such as stiffness, damping, and location of center of mass, to determine how they affect the behavior of the struts. Models that produce a large range of frequencies at which the transmissibility is well below unity are the most effective. Vibration shapes are also determined for certain frequencies so that the physical behavior of the system can be studied. / Master of Science

In this thesis, a process is developed for designing elastomeric vibration isolators in order to provide vibration isolation for sensitive equipment being used in ROKETSAN A.S.&rsquo / s products. For this purpose, first of all, similar isolators are examined in the market. After that, appropriate elastomeric materials are selected and their temperature and frequency dependent dynamic properties are experimentally obtained. Parametric finite element model of the isolator is then constituted in ANSYS APDL using the properties of elastomeric materials and the conceptual design of the isolator. Then, according to design requirements, final design parameters of the vibration isolator are determined at the end of design iterations. In the next step, vibration isolator that was designed is manufactured using the elastomeric material chosen, by a local rubber company. Finally, design process is verified by comparing analysis and test results.