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April 30, 1963 G. KURTZE 3,087,568 VIBRATION-DAMPED STRUCTURE Filed March 23. 1959 INVEN TOR. BY UEN Tl-IER KURTZE A T'TOI‘FNEV 3,087,568 United States Patent 0 " ice Patented Apr. 30, 1963 1 2 3,687,568 viscosity means no motion of the medium; i.e. ?rm coupling of rthe plates 1 and 3. It has been found that VIBRATION-DAMPED STRUCTURE Guenther Kurtze, Arlington, Mass, assignor to Bolt Beranek and Newman, inn, Cambridge, Mass, a cer poration of Massachusetts Filed Mar. 23, 1959, Ser. No. 301,197 7 Claims. (Cl. 181-33) there exists an optimum value of the viscosity for which maximum damping is obtained. Analysis shows that the damping, expressed by the loss tangent 1; of the composite structure 1, 3, 5, increases with square of frequency, passes a maximum, and then decreases sub stantially linearly with further increasing frequency. The present invention relates to vibration-damped Under the condition cIEZCZ, the vibrational (angular) structures and, more particularly, to damping with the 10 frequency w of maximum attenuation is approximately aid of viscous media. given by Damping of structure-borne sound vibrations is usually obtained by covering the structural elements with layers ._ ps1 is 2%;2 or coatings of sound-dissipative materials. in this way, energy is withdrawn from the sound~vibration waves by 15 and the loss tangent at this frequency is irreversible deformations of these coatings. The terms ‘° _d1vI2<\/Z+ pd pd 2) 1r/)\1 “sound” and “vibrations,” as herein employed, are in tended to connote generically all types of elastic vibra tions and the like, whether audible, sub-audible or super audible. 20 where The present invention, on the other hand, is more par ticularly concerned with the damping of double-walled p=density of the viscous medium 5, improved vibration-damped structure. Mzbending wavelength in plate ‘1. (1) (2) d=thickness of the viscous medium 5, structures and the like, and involves the use of viscous n=viscosity of the medium 5, materials as dissipative media. An object of the invention is to provide a new and 25 M2=mass per unit area of plate 3, and A further object is to provide for the damping of double walls, partitions, panels, surfaces and the like, all hereinafter referred to by the generic term “plates and the like.” Still an additional object is to provide a novel appar atus for damping vibrations traveling along any pair of vibration-wave propagating paths, whether of plate con?guration or of other con?guration for permitting the passage of sound or vibration waves therealong. Equation 2 shows that the maximum obtainable damp ing its proportional to 1/)“ and hence decreases with de creasing frequency. This may be disadvantageous when 30 damping at low frequencies is desired. For such cases, ; the disadvantage can be obviated, in accordance with the invention, by partitioning or subdividing the medium 5 with partitions, such as, for example, foam plastic separators 7, FIG. 2, with closed, air-?lled cells 9. A 35 representative embodiment employed steel plates 1, 3 Other and further objects will be discussed hereinafter that were each 1 cm. thick, but with stiffness differing by and will be more particularly pointed out in the appended a factor of ten, and a liquid medium 5 of silicon oil 1 claims. cm. thick and of viscosity ,uz668. The invention will now be described in connection The partitions 7 are disposed at intervals I only along with the accompanying drawing, FIG. 1 of which is a 40 one direction (shown longitudinally spaced), the distance transverse section of a damped double-plate structure or separation I being much less than the wavelengths of constructed in accordance with the present invention; the band of frequencies to be damped. The partitions and 7 may also be of other materials, though they must have FIG. 2 is a similar view of a preferred modi?cation. the property of being soft or highly compressible com Referring to the drawing, the invention is illustrated pared With the viscous liquid or other medium 5 in order as applied to a double-plate structure, though it is to be to decouple adjacent medium regions from one another. understood that the teachings hereof may equally well The construction of FIG. 2 yields a wider or broader be applied to other pairs of vibration-propagating path band frequency range of effective damping than for the structures, including rods, tubes, pipes and the like, to construction of FIG. 1. Assuming again, that clé2cg, mention but a few. the frequency w of maximum damping is given sub The plates 1 and ‘3 are shown gen erally co-extensive and of somewhat dilferent thickness so that the vibration-propagation or bending-wave ve locity along the plates, say from one end to the other, is substantially different; in this case, the velocity C1 stantially by 12” 1 “ pdz \/1+ 1201M2 p12 ( along the plate 1 is faster or greater than the velocity C2 along the plate 3. Different velocities can also be and the maximum obtainable loss tangent is obtained in other ways, as by using different materials, 1 diiferent temperatures, and other techniques. (4) 7]='—'———__——-_: Where different bending wave velocities are involved, P12 p12 60 there will be phase shifts between the bending-wave motion of the two plates which increase with increasing According to Equation 4, 7; no longer depends on fre distance from the source end, resulting in relative mo quency so that the same amount of maximum damping tions of the two plates with respect to each other. If can be obtained at any frequency by proper choice of these two plates 1 and 3 are coupled over a substantial [.L in Equation 3. portion of the region separating them by a viscous If the plates 1 and 3 are made of light-transmitting medium 5, as of viscous liquid, plastic, semi-solid ma— material, such as transparent or translucent glass and the terial, etc., an alternating ?ow will be generated by this like, and the medium 5 is also light-transmitting, such relative motion, and the viscosity of the medium 5 will as, for example, a clear mineral oil of su?icient viscosity, give rise to energy losses. It will be observed that losses do not occur in the 70 a sealed unit 1, 3. 5 could well serve as a vibration damped window or the like. theoretical limiting cases of zero and in?nite viscosity, Further modi?cations will occur to those skilled in since zero viscosity means no dissipation, and in?nite ZN/WI; 12am“) 3,087,568 4 a the art and all such are considered to fall within the spirit and scope of the invention as de?ned in the ap pended claims. The terms “steel-like” and “liquid-oil like” as employed in the claims are intended to embrace materials which are like steel or like liquid oil, respec tively, in the function performed by the designated ele ments in the panel of the invention. For example, as stated above the spaced layers may be formed of gl-ass, which is “steel-like” as to stif?ness and rigidity when stantially greater than the overall bending stiffness of the other layer, whereby the acoustic bending wave prop agating velocity 01 of one layer is substantially greater than the acoustic bending wave propagating velocity 02 of the other layer and the phases of acoustic vibrations along said layers are different, and a plurality of spaced partitions extending between said layers and dividing said viscous material, the compressibility of said parti tions being substantially greater than that of said viscous compared to a viscous liquid-oil-like material, including l0 material, said panel having maximum damping at said predetermined acoustic frequency determined substan the oils, plastics, or semi-solids described. tially by the relationship: What is claimed is: 1. An acoustic panel for damping a predetermined acoustic frequency f with a maximum degree of damping pd2 / 1203M» and frequencies above and below said predetermined 15 ,,_ _____ frequency with substantial, but lesser damping, compris p ing a pair of layers of stiff steel-like sheet material spaced apart, and a body of viscous liquid-oil-like material be tween and continuously contacting said layers, both‘ said layers being much more rigid than said viscous material, 20 where w=21rf, p is the density of the viscous material, one of said layers having an overall bending stiffness partitions. :1 is the thickness of the viscous material, a is the viscosity of the viscous material, M2 is the mass per unit area of this slower-velocity layer, and l is the spacing of the substantially greater than the overall bending stiffness of 5. The panel of claim 4, said partitions being formed the other layer, whereby the acoustic bending wave prop of soft cellular material. agating velocity C1 of one layer is substantially greater 6. The panel of claim 4, said partitions being formed than the acoustic bending wave propagating velocity C2 25 of foam plastic. of the other layer and the phases of acoustic vibrations 7. The panel of claim 4, the spacing of said partitions along said layers are different, said panel having maxi being less than the wave length corresponding to said mum damping at said predetermined acoustic frequency frequencies. determined substantially by the relationship: 30 References Cited in the ?le of this patent drag/913+ 1%)2%_a) “11M, 4 pd pd 2 where w:21rf, p is the density‘of the viscous material, d is the thickness of the viscous material, p. is the vis UNITED STATES PATENTS 1,193,013 2,407,400 2,724,670 Grant ________________ __ Aug. 1, 1916 Chamberlain ________ __ Sept. 10, 1946 Mason ______________ __ Nov. 22, 1955 unit area of the slower-velocity layer. 2. The panel of claim 1, said sheet material and said 2,850,109 Benjamin ___- _________ __ Sept. 2, 1958 viscous material being light-transmitting. 3. The panel of'claim 1, said layers having different 40 thicknesses. 754,299 1,135,422 Great Britain __________ __ Aug. 8, 1956 France ______________ __ Dec. 17, 1956 cosity of the viscous material, and M2 is the mass per 35 4. An acoustic panel for damping a predetermined acoustic frequency f with a maximum degree of damping and frequencies ‘above and below said predetermined FOREIGN PATENTS OTHER REFERENCES Cyril M. Harris: Handbook of Noise Control (Mc Graw-Hill Book Company, Inc., New York, 1957), pages frequency with substantial, but lesser damping, compris ing a pair of layers of stiff steel-like sheet material spaced 45 12-1, 12-2, 12-8 through 12-10 and 14-13 through and continuously contacting said layers, both said layers 14-18. S. Timoshenko: Vibration Problems in Engineering being much more rigid than said viscous material, one of said layers having an overall bending stiffness sub pages 210-220. apart, a body of viscous liquid-oil-like material between (D. Van Nostrand Company, Inc., New York, 1955), Third edition.