Proceedings of Meetings on Acoustics Volume 9, 0 http://acousticalsociety.org/ ICA 0 Montreal Montreal, Canada - 7 June 0 Structural Acoustics and Vibration Session asa: History and Application of Constrained Layer Damping asa. An overview of constrained-layer damping theory and application Benjamin M. Shafer Corresponding author's address: Serious Energy, 6 N Rochester St, Tacoma, WA 98406, bshafer@seriousenergy.com Beginning in the early 90s a variety of theoretical and experimental research has been published regarding the development and use of damping. What began as an experiment to reduce noise and vibration in metals and plastics has become a common treatment in an amalgam of applications. Constrained-layer damping (CLD) is a specific method of treatment commonly used in the aerospace and military industries. CLD may be described as a type of shear-related energy dissipation achieved by interconnecting two or more structural materials using a relatively thin viscoelastic layer. Among the advantages of using CLD as a damping treatment are the ability to obtain high loss factors with relatively thin configurations and that the stiffness of the composite system is not markedly increased. The analytic development of constrained-layer damping will be presented along with a brief discussion of the applications of CLD throughout history. Published by the Acoustical Society of America through the American Institute of Physics 0 Acoustical Society of America [DOI: 0./.4800606] Received Jan 0; published Jun 0 Proceedings of Meetings on Acoustics, Vol. 9, 0650 (0) Page
THE KEY FOUNDING RESEARCHERS Although the concept of using damping to reduce vibratory response in structures has been recognized by scientists and engineers since the days of the Roman Empire, significant advances in the development of damping and its uses hadn t been made till the 90s,. War in the 940s created the need for further development with applications in both the naval and aerospace industries, leading to a relative blossom of development and innovation in the 950s and 60s 4. In 95, Oberst and Frankenfeld published a paper in the journal Acustica 5 entitled Uber die dampfung der biegeschwingungen dunner bleche durch fest haftendebelage, which, in the english language, may be translated as The damping of bending vibrations of thin plates by adherent cohesion. This paper served as the basis, or starting point for many subsequent developments, including research by Donald Ross, Edward Kerwin, and Eric Ungar 6. These brilliant scientists can be credited for the most well known, and simplest, set of equations developed for approximating the effect of damping on plates and beams, often referred to as the RKU equations. It will be shown that a form of the RKU equations can be used to characterize constrained-layer damping, or CLD. By the 950s it had become common to increase damping in beams and plates by attaching a secondary structural or constraining layer to the base structure using what was termed as damping tape 7. Edward Kerwin s 959 journal article was among the first published that provides a detailed theoretical explanation of this phenomenon with experimental data for validation of its usefulness 8. CONSTRAINED-LAYER DAMPING THEORY The layer referred to in the book Structure-Borne Sound and in Kerwin s 959 paper as damping tape is contemporarily termed a viscoelastic interlayer 9. As a composite CLD structure undergoes vibration, the viscoelastic interlayer between the two constraining materials is subjected to shear motion and the vibrational energy is converted into heat. The advantage of a CLD treatment is, for many applications, the ability to obtain an exceptionally high amount of dissipation in a beam or plate without significantly changing the stiffness or mass of the composite system. Although more complex systems may require more sophisticated methods of theoretical prediction and modeling such as finite element analysis, it is useful to understand the process of characterizing the loss of CLD treatments using the aforementioned RKU equations. These equations differ slightly between beams and plates, so a separate set of equations will be shown for both. The loss factor,, of the composite CLD material is essential in characterizing important parameters for highly damped materials, including the impedance, radiation efficiency, and transmission coefficient. For both beams and plates, the fundamental equations needed to approximate the loss factor are the shear parameter,, structural parameter, Y, and complex bending stiffness (flexural rigidity),. Before the RKU equations can be used for actual materials, the material characteristics listed in Table must be known or measured. TABLE. List of needed measured or known values for the CLD composite system before using the RKU equations Description Material Property Variable Designation Viscoelastic Interlayer loss factor shear modulus thickness length (beam) Constraining Layers Young s modulus moment of inertia cross-sectional Area thickness (plate) Composite Structure mass per length (beam) or mass per area (plate) distance between neutral axes Proceedings of Meetings on Acoustics, Vol. 9, 0650 (0) Page
The following equation apply to any three-layer beam CLD configuration. The shear parameter,, is calculated as Gb S, () p h where S E A +, () E A and B p ω μ, () where ω is the angular frequency. The structural parameter, Y, can be found using EI + E Y h The complex bending stiffness, B, is calculated using the equation where I. (4) ( E ) I + EI + + S Y B, (5) ( jβ ), (6) and the optimum shear parameter,, is calculated as / [( + Y )( + )] opt β. (7) The three-layer plate equation set is similar to that of the three-layer beam, where G S, (8) p h S E h +, (9) E h Proceedings of Meetings on Acoustics, Vol. 9, 0650 (0) Page
B p ω μ, (0) Eh + Eh S, () Y h Y ( ) E + h Eh + + B, () ( jβ ), () and / [( + Y )( + )] opt β. (4) The RKU equations for both three-layer scenarios can be solved using the iterative method proposed by Ungar and Zapfe in Chapter 4 of Noise and Vibration Control Engineering 9. The resulting parameters may then be input into the final loss factor equation βy η +. (5) ( + Y ) + ( + Y )( + β ) The same iterative method may also be used to approximate the loss factor of composite materials with many layers. CLD APPLICATIONS The foundation laid for constrained-layer damping in the 950s has led to some significant advances and varied application of CLD treatments, beginning with the relatively obvious application in naval vessels and aircraft both to reduce the radiation efficiency and transmission coefficient for inward and outward propagating sound waves and mechanical vibration. Vibrating computer hardware components can be a source of annoyance and stress in modern work environments. CLD has been used to reduce the vibration of various parts of the computer without significantly adding weight and thickness to the computer shell 0. The automotive industry has also benefitted from CLD research. One example is published wherein the vibration of an engine and engine compartment was dissipated using a viscoelastic interlayer applied between two formed engine covers. One unlikely application of CLD has recently been developed for the building construction industry. CLD drywall panels are used to reduce the transmission of sound through wall and ceiling partitions. Using the CLD treatment allows builders to achieve adequate transmission loss through partitions, often without drastically increasing the thickness and mass of the partition or assembly. Active CLD, many times using piezoelectric materials, has been modeled and implemented to reduce vibration in rotating beams and other sandwich beams and panels. Applications such as this may yet be discoverable as the technological world advances and brilliant scientists and researchers apply proper theory to application. Proceedings of Meetings on Acoustics, Vol. 9, 0650 (0) Page 4
REFERENCES. Craig Allen Gallimore, Passive viscoelastic constrained layer damping application for a small aircraft landing gear system, Master s thesis, Virginia Polytechnic Institute and State University.. O. Foppl, The practical importance of the damping capacity of metals, especially steels, J. Iron & Steel Inst. 4(), 9 4 (96).. N. N. Davidenkoff, Energy dissipation in vibrations, J. Tech. Phys. 8(6), 48 (98). 4. D. I. G. Jones, Response and damping of a simple beam with tuned dampers, J. Acoust. Soc. Am. 4(), 50 5 (967). 5. H. Oberst, Uber die dampfung der biegeschwingungen dunner bleche durch fest haftendebelage, Acustica, 8 94 (95). 6. D. Ross, E. E. Ungar, and E. M. Kerwin, Jr., Damping of plate flexural vibrations by means of viscoelastic laminae, Structural Damping, ASME Publication, pp. 49 88, New York (959). 7. L. Cremer, M. Heckl, E. E. Ungar (97). Structure-Borne Sound, Structural Vibrations and Sound Radiation at Audio Frequencies (Springer-Verlag, Berlin, Heidelberg). 8. E. M. Kerwin, Jr., Damping of flexural waves by a constrained viscoelastic layer, J. Acoust. Soc. Am. (7), 95 96 (959). 9. Istvan L. Ver and Leo L. Beranek (006). Noise and Vibration Control Engineering Principals and Applications, Second Edition (John Wiley & Sons, Inc.,Hoboken, New Jersey). 0. Peter Y. H. Huang, Per G. Reinhall, I. Y. Shen, and Vipin Kumar, Use of microcellular foam materials in constrained layer damping treatments, Cellular Polymers, 0(), 0 4 (00).. Nicholas J. Oosting, Julie Hennessy, David T. Hanner, Dave Fang (004), Application of a constrained layer damping treatment to a cast aluminum V6 engine front cover, SAE International.. A. Baz and J. Ro, Vibration control of rotating beams with active constrained layer damping, Smart Materials and Structures, 0(), (00). Proceedings of Meetings on Acoustics, Vol. 9, 0650 (0) Page 5