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Vibration dampingReading assignmentSupplementary readingMethods of vibration reductionSlide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Critical dampingSlide 17Slide 18Slide 19Slide 20Slide 21Viscous materialSlide 23Viscoelastic materialSlide 25Slide 26Slide 27Slide 28Slide 29ViscositySlide 31Slide 32Slide 33Slide 34Slide 35Slide 36Slide 37Slide 38Slide 39Slide 40Slide 41Slide 42Slide 43Slide 44Slide 45Slide 46Slide 47Slide 48Slide 49Slide 50Slide 51Constrained layer dampingDamping due to interfacesDamping due to defectsUse of interfaces for dampingHybrid composite compositionSlide 57Carbon nanofiberSlide 59Nanofiber as interlaminar fillerSlide 61Slide 62Slide 63Slide 64Slide 65Slide 66Slide 67Slide 68Slide 69Vibration dampingTopic 12Reading assignment1. http://www.sensorsmag.com/articles/0202/30/main.shtml Magnetorheological fluid damping2. No. 22 under “Publications: other” in http://www.wings.buffalo.edu/academic/department/eng/mae/cmrl3. Chung, Composite Materials, Ch. 12.4. Google: “Viscoelastic Damping 101”Supplementary readingNo. 124 under “Publications : cement” in http://www.wings.buffalo.edu/academic/department/eng/mae/cmrlMethods of vibration reductionIncrease damping capacity Increase stiffness (modulus).•http://www.kettering.edu/~drussell/Demos/SHO/damp.html•The black mass is undamped and the blue mass is damped (underdamped). After being released from rest the undamped (black) mass exhibits simple harmonic motion while the damped (blue) mass exhibits an oscillatory motion which decays with time.•Damping is the conversion of mechanical energy of a structure into thermal energy.•The amount of energy dissipated is a measure of the structure’s damping level.•Damping is very important with earthquakes since it dissipates the destructive energy of an earthquake which will help reduce the damage to the building.DooHysteresis loop for a viscoelastic materialD = energy dissipation per cycleStressStrainSuperelastic behaviorT > AfHysteresis loop means energy dissipation, hence vibration dampingStressThe more is the hysteresis in the stress-strain curve, the greater is the energy dissipation, and hence the higher is the damping ability.•Consider the suspension of your automobile, supporting the body mass. You have four springs. •You also have four friction elements, variously called dampers or dash pots or shock absorbers. Don’t try to drive without them! •Here are some friction elements – dampers – that you can see.SpringDashpot•Let’s diagram our hardware. We have a “sprung mass” M and a spring with stiffness K. •We also have a friction or damping element C. •C is not always visible, but is always present. No system exists without some damping•Damping is the decrease in amplitude with time due to the resistance of the medium to the vibration. •Damping occurs progressively as energy is taken out of the system by another force such as friction. •If the damping is enough that the system just fails to oscillate, then it is said to be critically damped. Damping more than this is referred to as over damping and less is similarly underdamped.Critical damping The minimum damping that will prevent or stop oscillation in the shortest amount of time.UnderdampedTransient responsemnnxxm ln1Log decrementQ = amplification factor (ratio of the response amplitude at resonance ω0 to the static response at ω = 0)oHalf-power bandwidth method (3 dB method)Loss factorVibration damping•Passive damping•Active dampingViscous materialA material in which the strain develops over a period of time and the material does not go to its original shape after the stress is removed.Viscoelastic material•A material in which the total strain developed has elastic and viscous components. •Part of the total strain recovers similar to elastic strain.•Some part of the total strain recovers over a period of time.•Examples: polymer melts.The combined viscous and elastic behavior (viscoelasticity) can be examined by determining the effect that an oscillating force has on the movement of the material.All the energy stored during loading is returned when the load is removed.Stress is proportional to strain.φ = 0°The material does not return any of the energy stored during loading. All the energy is lost once the load is removed.Stress is proportional to the strain rate.φ = 90°Some of the energy stored is recovered upon removal of the load; the remainder is dissipated in the form of heat.The angel φ (0 < φ < 90°) is a measure of the damping level.Viscosity•Measure of resistance to flow•Defined as the ratio of shear stress to shear strain rate•Unit: Poise or Pa.s•1 Pa.s = 10 P = 1000 cPThe viscosity (η) is the tendency of the fluid to resist flow and is defined by:(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.Shear-stress strain-rate relationships for Newtonian and non-Newtonian materialsiooeiEEE 21*Complex modulusG* = G' + iG''where G* is the complex shear modulus, G' is the in-phase storage modulus and G'' is the out-of-phase similarly-directed loss modulus; G* = √(G'2 + G''2).tan δ = G''/G' where tan δ (also called loss tangent) quantifies the balance between energy loss and storage. As tan 45° =1, a value for tan  greater than unity indicates more "liquid" properties, whereas one lower than unity means more "solid" properties, regardless of the viscosity.G* = G' + iG''G is the storage modulus and G'' is the loss modulus; The frequency where these parameters cross over corresponds to a relaxation time () specific for the material.Application of a Tuned Vibration Absorber (TVA) is sometimes the best option for control of unwanted noise/vibration. This countermeasure is particularly appropriate when the noise/vibration issue occurs for a single frequency, or across a very narrow frequency range.A variable damping system based on magnetorheological fluid sponges can help control the vibratory motion of a household washing machine during its spin cycle. Damping is switched on as the drum passes through resonance and off again at the highest speeds for optimum vibration isolation. The system permits the drum to rotate at speeds high enough to function as a centrifuge, but without the violent shaking familiar to every user.Conventional springs and


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UB MAE 438 - Vibration damping Topic 12

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