WO1990001645A1

WO1990001645A1 - Vibration damping materials

Info

Publication number: WO1990001645A1
Application number: PCT/GB1989/000869
Authority: WO
Inventors: John Richard House; Ann Elizabeth Hilliar
Original assignee: UK Secretary of State for Defence
Current assignee: UK Secretary of State for Defence
Priority date: 1988-08-02
Filing date: 1989-07-31
Publication date: 1990-02-22
Anticipated expiration: 1991-02-02
Also published as: AU4043189A; EP0427766A1; GB9102136D0; GB8818331D0; GB2241300A

Abstract

For areas with restricted access such as box sections (3), pipes and wall sections etc, vibration damping poses a problem as it may be difficult or impossible to apply conventional damping such as tiles and the use of lead shot or sand presents a weight problem. By using a vibration damping material consisting of a plurality of viscoelastic spheres (1) the ease of application is improved and effective damping achieved especially if a high density filler is included in the viscoelastic material. Application of viscoelastic spheres can be made to damp the vibration of any structure where the viscoelastic spheres can be suitably confined.

Description

VIBRATION DAMPING MATERIALS

The invention relates to materials for damping vibrations in structures, particularly but not exclusively hollow structures such as box sections, pipes, wall sections etc.

The damping of structural vibrations by means of applied tiles constructed either wholly or in part of viscoelastic polymers iswell known. Hcwever, there are situationswhere these techniques arenotpractical, such as hollow cavity-like structures where it is physically impossible to gain access for tileapplication. In such situations ithasbeencommonpractice to use granular fillings such as sand or lead shot to damp these structures. These treatments, however, are heavy and it is advantageous to use viscoelastic polymermaterials as substantial savings inweight can be made.

The damping effect of viscoelastic layers is affected by motion of the layer in its "thicknesswise" direction. Damping can be improved by increasing the density of the layer or by increasing the layer thickness. Conventionallyaviscoelasticlayer ismade intheformof ahomogeneouslayer which has a high loss factor in the frequency and temperature range of interest andmay be cast in situas a closedcell foam. Making thelayer as a foam reduces the effective moduli of the layer and hence reduces the wave velocity. Thicknesswise resonances can then occur at low frequencies and it is also possible to make the layer thinner. A similar effect can be achieved by increasing the layer density by, for example, the addition of a high density filler.

These kind of viscoelastic treatments could be useful in damping cavities (eg box-section tubing) where the thickness of the layer will be controlled by the depth of the cavity. jftny tuning of the damping performance has, therefore, to be done by variation of thewavevelocity (c) which can be achieved by altering the volume fraction of air iό) . To tune for very low frequencies itbecomes necessary to have a large air content but it can be shown that c will reach a limiting valuewhere further increase in the air content is ineffective. Furthermore, increasing the air content reduces the layer density, to the detriment of good overall damping performance. It therefore becomes necessary to increase the layer density by the addition of high density fillers. This does have the additional benefit of lowering cbut the reinforcing effect of the filler on the polymer modulus tends to counteract this, and there is also a limit to the amount of filler that can be added.

The object of the invention is to provide a vibration damping material having a lcwer wave velocity than an air filled foambut which also maintains a density comparable to or greater than a solid viscoelastic polymer material.

The invention provides a vibration damping material comprising a plurality of viscoelastic spheres.

Spherescanbeusedtofillanysizeorshapeofstructureandcanalso be removed easily if required. There is no requirement for the mixing of materials as with foams and spheres of different materials can be used for different damping requiranents. Preferably the diameter of each sphere is verymuch less thanthewavelengths of thevibrations tobedamped. For the damping of frequencies below 1kHz a maximum diameter of about 14mm is advantageous. Typicallyauseful rangeof spherediameters isabout10mmto 15mm.

Advantageously the spheres used to damp a particular structure are all of a single size and polymer type. If the spheres are of a single size they can be close packed within the structure to give the maximum packing density. The small point areas of contact between individual spheres results in a layer of high compliance but the damping material retains a relatively high density determined by the packing density of the spheres (this is typically >0.6 x the density of the spheres¹ material).

Preferably the spheres aremade of aviscoelasticpolymermaterial. Any material that is in its viscoelastic state at the operational temperatures and frequency can be used, for example, epoxy resins or polyurethane. A typical example of the type of epoxy resin used is EP 25 which is available from essexResins andAdhesives Ltd andwhichconsistsof EL 5 epoxy resin 100 g , EL 1 epoxymodi ier 100 gmand EHT 3 hardener 75 gm. Ifextraweight isacceptable, ahighdensityfiller ispreferablyincluded in the material as this improves the overall damping factor, which is dependent on the mass ratio of the spheres to the structure. Alternatively the spheres may be a high density material, such as steel or glass, coated with a layer of viscoelastic material.

The invention will now be described, by way of example only, with reference to the accompanying drawings, of which:

Figure 1 illustrates the effect on the damping factor of the thickness of a viscoelastic layer; Figure 2 illustrates the effect on damping of increasing the density of the viscoelastic layer; Figure 3 illustrates the effect on damping of increasing the thickness of the viscoelastic layer; Figure 4 illustrates the effect on wave velocity of increasing the air content of the viscoelastic layer; Figure 5 shows an experimental arrangement of spheres packed on a steel beam; Figure6 illustrates thepredictedandmeasureddamping factors for the steel beam shown in Figure 5 packed with viscoelastic spheres to a depth of 30mm; and Figure7 illustrates thepredictedandmeasureddamping factors for the steel beam shewn in Figure 5 packedwith viscoelastic spheres to a depth of 80mm; Figure 8 illustrates the frequency response of undamped10mmthick steel; Figure 9 illustrates the frequency response of the same steel as in

Figure8 butdampedwithlowdensityviscoelastic spheres; Figure 10 illustrates the frequency response of the same steel as in Figures 8 and 9 but damped with high density polyurethane spheres; Figure 11 illustrates the frquency against damping factor for various types of beam containing viscoelastic spheres of composition EP 25 as mentioned herein;

The damping factor for a thick homogeneous viscoelastic layer when applied to a plate can be given by:

where: ^}- = He_ffH m = mass of the plate

•? eff ⁼ effective density of the viscoelastic layer H = thickness of the viscoelastic layer k¹, k" = real and imaginary parts of the cc-mpressional wave number where k = 2ttf/c f = frequency c = cαmpressional wave velocity

^2 ⁼ viscoelastic layer loss factor Figure 1 illustrates a computation of this equation for aviscoelasticlayer applied to a steel plate. It canbe shown that the frequency (f ) atwhich the first damping factor peak occurs is related to approximately a X/4 resonance in the layer thickness and that subsequent peaks occur at every (2n - 1) X/4 thus:

where P_e f = t e effective plate modulus of the layer.

Furthermore, thedampingcanbe improvedby increasing themass ratio u either as a resultof increasingthedensityofthelayer, as shown inFigure 2, or by increasing the layer thickness, as shown in Figure 3.

Increasingtheaircontentof thelayer reducestheeffectivemodulus andhence reduces thewavevelocityinthelayer. Thicknesswiseresonances can therefore occur at lew frequencies and it is also possible to make the layer thinner. A similar effect can be achieved by increasing the layer density, for example by the addition of a high density filler. Thus:

eff c = (3) eff where P_eff = Keff + 4G_eff

^Keff = K(l - jό)/(l + (3Kιό)/(4G)) and

G_eff = G/Q + 150(1 - J)/((1 - ϋ) (l - 50))]

Where K = polymer bulk modulus (complex)

G = polymer shear modulus (complex) c = Poisson's Ratio

6 = volume fraction of air in the foam

When viscoelastic treatments are used to damp cavities, the thickness of thelayer iscontrolledby thedepth of thecavity. Anytuning of thedampingperformance, therefore, hastobedonebyvariationofthewave velocity (c), whichcanbe achievedbyalteringthevolumefractionoftheair (6) . Totuneforverylowfrequencies itwouldappeartobeadvantageousto havealargeair contentbut itcanbeshownthatcwill reachalimitingvalue wherefurtherincreaseintheaircontent is ineffective. Typically, awave velocity of 210 m/ε for an effective density of 250kg/m-*ⁱ is the best achievable for an unfilled polymer in the middle of its transition region. Figure 4 illustrates the effect for an epoxy resin polymer (consisting of epoxy resin, epoxy modifier and hardener in the proportions by weight of 100:100:75) at 200Hz and 20°C where:

Increasing the air content also reduces thelayerdensity, reducing the mass ratio μι to the detriment of good overall damping performance.

Figure 5 shows an experimental arrangement of a damping treatment according to the invention. Alayer ofviscoelasticspheres1, of a single size andmade of aviscoelastic polymer material, isclose-packedon asteel beam2 andheld inplacebyabox3. Thesmallpointareasofcontactbetween individual spheres results in a layer of high compliance which, however, retains a relatively high density determined by the packing density of the spheres. The effective density of the layer istypicallygreaterthan 0.6 x the density of the material of the spheres.

If the assumptions are made that: a) the spheres are identical; b) the viscoelastic material is homogeneous and isotropic; c) the packing is statistically homogeneous and isotropic; d) the viscoelastic material has an infinite coefficient of friction; e) the diameter of the spheres is very much less than the wavelength; and f) there is a confining pressure to the packing that ensures good contact between individual spheres; then itcanbeshownthatpackedspheres canbetreatedasahomogeneousmedium with equivalentphysical propertieswhere theequivalentbulk modulus K* can be expressed as:

where E¹ = the dynamic Young's Modulus of the polymer n = the number of contact points p = the hydrostatic confining pressure c-_gff = σV2(5 - 3o0 = 0.07 (assuming rough spheres ie coefficient of friction = 1) ύ = packing fraction of spheres

Hence:

where - 2cT_eff)K*

From observation, n is seen to be around 12 which implies that thepacking is face centred cubicwith avolumefractionof0.74. Fromtheseformulaeand using the samepolymer as forthefoamreferredtowith respecttoFigures1 to 4, a wave velocity of about 40m/s is obtained for an effective density of 925kg/m³ at 200Hz. Applying this to the thickness effect damping equation(1) , predicted damping curves can be derived. Figures 6 and 7 show predicted and measured damping curves for 14mm diameter spheres of the polymer, on 10mm thick steel plate at 20°C, for a packing depth of the spheres of 30mm and 80mm respectively. In each case the^~\/4 resonance is clearly illustrated at approximately 160Hz for the 80mm layer and 380Hz for the 30mm layer.

Figure 8 demonstrates the typical response of undamped 10 mm thick steel up to 1.6 KHz and Figure 9 shews the clear improvement in damping to be achieved by damping with low density viscoelastic spheres. Hcwever Figure 10 demonstrates particularly good levels of damping which can be achieved under the right conditions over a wide frequency range at least up to1.6 KHz by utilising high density viscoelastic spheres.

From Figure 11 it can be seen that damping factor changes with frequency and the dimensions of the object being damped.

It can be seen from the Figures that a packing of viscoelastic spheres can result in significant damping factors. The peak in the damping factors is related to aλ/4 thicknesswise resonance across the depth of the spheres though variation of the depth of the spheres is, in practice, restricted by the size of the cavity to be filled. However, the level of the overall damping factor is dependent on themass ratio of the spheres to the structure and this may be improved by raising the density of the sphere's material, either by the addition of a high density filler, for example a dispersion of particulate ironoxidethroughout theviscoelasticmaterial, orbyapplying a coating of a viscoelastic polymer to a high density sphere of, for example, steel or glass. This arrangementwill haveadvantageswherethelossofthe weight saving advantages of the use of a polymer is acceptable. Further improvements may be achieved by variation of the polymer modulus characteristics.

The damping material of the invention can be used in any hollow structurewheredamping is required, such aspipe structures, wall sections, box section beams etc. It can provide significant improvements indamping without causing significant increased weight problems.

Claims

1. A vibration damping material characterised in that it comprises a plurality of viscoelastic spheres.

2. Avibration dampingmaterial according to claim1 characterised in that the diameter of each sphere is very much less than the wavelengths of the vibrations to be damped.

3. Avibration dampingmaterial according to claim1 characterised in that the spheres are all of a single size and polymer type.

4. A vibration damping material according to any one preceding claim; characterised in that the spheres are made of a viscoelastic polymer material.

5. Avibration dampingmaterial accordingtoclaim4 characterised in that the viscoelastic polymer material is an epoxy resin.

6. Avibration dampingmaterial according to claim4 characterised in that the viscoelastic polymer material is polyurethane.

7. Avibrationdampingmaterial according to claim1 characterised in that a high density filler is included in the material.

8. Avibrationdampingmaterial according toclaim7 characterised inthat the high density filler is particulate iron oxide.

9. Avibrationdampingmaterial according to claim1 characterised in that thespheresaremadeofahighdensitymaterial, suchassteelorglass, coated with a layer of viscoelastic material.