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Viscoelastic Damping Technologies: Finite Element Modeling and Application to Circular Saw Blades

  • Chapter
Vibration and Structural Acoustics Analysis

Abstract

A great deal of information on viscoelastic damping technologies, comprising surface mounted or embedded viscoelastic damping treatments, is nowadays available for the practical noise reduction of machinery, in general, and circular saw blades, in particular, for woodworking operations. Among the most efficient and appellative noise reduction techniques for low-noise woodworking circular saw blades demonstrated during the last decades, the use of viscoelastic damping technologies is an interesting possibility which did not receive sufficient attention and dissemination so far. These technologies are analyzed in this chapter in order to gain a preliminary insight into the interest of this noise control solution to further continuing developing more refined and efficient viscoelastic-based noise reduction designs towards the widespread use of low-noise circular saw tooling and industrial practices by woodworking companies. For that purpose, a more comprehensive and tutorial approach to the field is presented in this book chapter. Emphasis is put not also on the specific application to circular saws, which is used to illustrate the interest, applicability and design procedures of such technologies, but also on practical engineering aspects related with the use of computational tools and finite element (FE) modeling software for the mathematical modeling, design and assessment of the efficiency of damping treatments. In particular, different configurations of damping treatments, spatial FE modeling and meshing approaches, mathematical descriptions of viscoelastic frequency-dependent material damping and their implementation into FE frameworks and the use of different solution methods and commercial FE software are discussed.

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References

  1. Adhikari, S., Pascual, B.: Eigenvalues of linear viscoelastic systems. J. Sound Vib. 325(4–5), 1000–1011 (2009)

    Article  Google Scholar 

  2. Adhikari, S., Woodhouse, J.: Quantification of non-viscous damping in discrete linear systems. J. Sound Vib. 260(3), 499–518 (2003)

    Article  Google Scholar 

  3. Agnes, G., Napolitano, K.: Active constrained layer viscoelastic damping. In: Proceedings of the 34th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Reston Park, VA, US, pp. 3499–3506 (1993)

    Google Scholar 

  4. Ahmad, S., Irons, B.M., Zienkiewicz, O.C.: Analysis of thick and thin shell structures by curver finite elements. Int. J. Numer. Methods Eng. 2(3), 419–451 (1970)

    Article  Google Scholar 

  5. Alfrey, T., Doty, P.: The methods of specifying the properties of viscoelastic materials. J. Appl. Phys. 16(11), 700–713 (1945)

    Article  MathSciNet  Google Scholar 

  6. Allen, C.H.: Vibration damping method and means having non-contacting sound damping means (1982). US Patent 4323145, April 6, 1982

    Google Scholar 

  7. Allen, D.H., Holmberg, J.A., Ericson, M., Lans, L., Svensson, N., Holmberg, S.: Modeling the viscoelastic response of GMT structural components. Compos. Sci. Technol. 61(4), 503–515 (2001)

    Article  Google Scholar 

  8. Astley, R.J.: Infinite elements for wave problems: a review of current formulations and an assessment of accuracy. Int. J. Numer. Methods Eng. 49(7), 951–976 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  9. Astley, R.J.: Numerical acoustical modeling (finite element modeling). In: Crocker, M.J. (ed.) Handbook of Noise and Vibration Control, pp. 101–115. Wiley, Hoboken (2007)

    Chapter  Google Scholar 

  10. Azvine, B., Tomlinson, G.R., Wynne, R.J.: Use of active constrained-layer damping for controlling resonant vibration. Smart Mater. Struct. 4(1), 1–6 (1995)

    Article  Google Scholar 

  11. Bagley, R.L., Torvik, P.J.: Fractional calculus—a different approach to the analysis of viscoelastically damped structures. AIAA J. 21(5), 741–748 (1983)

    Article  MATH  Google Scholar 

  12. Bagley, R.L., Torvik, P.J.: Fractional calculus in the transient analysis of viscoelastically damped structures. AIAA J. 23(6), 918–925 (1985)

    Article  MATH  Google Scholar 

  13. Balmès, E.: Model reduction for systems with frequency dependent damping properties. In: 15th International Modal Analysis Conference (IMAC XV), vol. 1, pp. 223–229. Society for Experimental Mechanics, Orlando (1997)

    Google Scholar 

  14. Balmès, E., Germès, S.: Tools for viscoelastic damping treatment design. Application to an automotive floor panel. In: Sas, P., Hal, B. (eds.) International Conference on Noise and Vibration Engineering (ISMA), Leuven, pp. 461–470 (2002)

    Google Scholar 

  15. Baz, A.: Active constrained layer damping. In: Proceedings of Damping’93, San Francisco, CA, US, vol. 3, pp. IBB 1–23 (1993)

    Google Scholar 

  16. Baz, A.: Robust control of active constrained layer damping. J. Sound Vib. 211(3), 467–480 (1998)

    Article  Google Scholar 

  17. Baz, A.: Spectral finite-element modeling of the longitudinal wave propagation in rods treated with active constrained layer damping. Smart Mater. Struct. 9(3), 372–377 (2000)

    Article  Google Scholar 

  18. Baz, A.: Active constrained layer damping of thin cylindrical shells. J. Sound Vib. 240(5), 921–935 (2001)

    Article  Google Scholar 

  19. Baz, A.: Active damping. In: Ewins, D.J., Rao, S.S., Braun, S.G. (eds.) Encyclopedia of Vibration, pp. 351–364. Academic Press, Oxford (2001)

    Chapter  Google Scholar 

  20. Beaty, L.B.: Noise dampened rotary saw blade (1980). US Patent 4187754, February 12, 1980

    Google Scholar 

  21. Beljo-Lučić, R., Goglia, V.: Some possibilities for reducing circular saw idling noise. J. Wood Sci. 47(5), 389–393 (2001)

    Article  Google Scholar 

  22. Benjeddou, A.: Advances in hybrid active-passive vibration and noise control via piezoelectric and viscoelastic constrained layer treatments. J. Vib. Control 7(4), 565–602 (2001)

    Article  MATH  Google Scholar 

  23. Bert, C.W.: Material damping: an introductory review of mathematic measures and experimental technique. J. Sound Vib. 29(2), 129–153 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  24. Bettess, P.: Infinite Elements. Penshaw Press, Cleadon (1992)

    Google Scholar 

  25. Bhimaraddi, A.: Sandwich beam theory and the analysis of constrained layer damping. J. Sound Vib. 179(4), 591–602 (1995)

    Article  Google Scholar 

  26. Bianchini, E., Marulo, F., Sorrentino, A.: MSC/NASTRAN solution of structural dynamic problems using anelastic displacement fields. In: 36th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, New Orleans, LA, US, vol. 5, pp. 3063–3069 (1995)

    Google Scholar 

  27. Boltzmann, L.: Zur theorie der elastischen nachwirkung. Sitz. Math.-Naturwiss. Kl. Kaiserlichen Akad. Wiss. 70(2), 275–306 (1874)

    Google Scholar 

  28. Brown, E.W.: Attenuated vibration circular saw (1981). US Patent 4270429, June 2, 1981

    Google Scholar 

  29. Budke, R.L., Freeborn, L.C.: Noise-controlled circular saw blade (1978). US Patent 4114494, September 19, 1978

    Google Scholar 

  30. Cady, W.G.: Piezoelectricity: An Introduction to the Theory and Applications of Electromechanical Phenomena in Crystals. Dover, New York (1964)

    Google Scholar 

  31. Caldwell, D.B.: Sound-damped saw blade (1977). US Patent 4034639, July 12, 1977

    Google Scholar 

  32. Carrera, E.: \({C}_{z}^{0}\) Requirements—models for the two dimensional analysis of multilayered structures. Compos. Struct. 37(3–4), 373–383 (1997)

    Article  Google Scholar 

  33. Carrera, E.: A study of transverse normal stress effect on vibration of multilayered plates and shells. J. Sound Vib. 225(5), 803–829 (1999)

    Article  Google Scholar 

  34. Carrera, E.: Theories and finite elements for multilayered, anisotropic, composite plates and shells. Arch. Comput. Methods Eng. 9(2), 87–140 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  35. Carrera, E.: Historical review of zig-zag theories for multilayered plates and shells. Appl. Mech. Rev. 56(3), 287 (2003)

    Article  Google Scholar 

  36. Carrera, E.: Theories and finite elements for multilayered plates and shells: a unified compact formulation with numerical assessment and benchmarking. Arch. Comput. Methods Eng. 10(3), 215–296 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  37. Chattopadhyay, A., Gu, H.Z., Beri, R., Nam, C.H.: Modeling segmented active constrained layer damping using hybrid displacement field. AIAA J. 39(3), 480–486 (2001)

    Article  Google Scholar 

  38. Chaudry, A., Baz, A.: Vibration control of beams using stand-off layer damping: finite element modeling and experiments. In: Proceedings of the SPIE, vol. 6169, 61690R, San Diego, CA, US (2006)

    Google Scholar 

  39. Chen, C.P., Lakes, R.S.: Viscoelastic behaviour of composite materials with conventional- or negative-Poisson’s-ratio foam as one phase. J. Mater. Sci. 28(16), 4288–4298 (1993)

    Article  Google Scholar 

  40. Chen, Y.R., Chen, L.W., Wang, C.C.: Axisymmetric dynamic instability of rotating polar orthotropic sandwich annular plates with a constrained damping layer. Compos. Struct. 73(3), 290–302 (2006)

    Article  Google Scholar 

  41. Cho, H.S., Mote Jr., C.D.: Aerodynamic noise source in circular saws. J. Acoust. Soc. Am. 65(3), 662–671 (1979)

    Article  Google Scholar 

  42. Christensen, R.M.: Theory of Viscoelasticity: An Introduction, 2nd edn. Academic Press, New York (1982)

    Google Scholar 

  43. Cortés, F., Elejabarrieta, M.J.: Computational methods for complex eigenproblems in finite element analysis of structural systems with viscoelastic damping treatments. Comput. Methods Appl. Mech. Eng. 195(44–47), 6448–6462 (2006)

    Article  MATH  Google Scholar 

  44. Côté, A.F., Atalla, N., Guyader, J.L.: Vibroacoustic analysis of an unbaffled rotating disk. J. Acoust. Soc. Am. 103(3), 1483–1492 (1998)

    Article  Google Scholar 

  45. Cournoyer, B.: Modélisation analytique et numérique de plaques multicouches : application au traitement viscoélastique des disques encastrés-libres. M.Sc. thesis, Université de Sherbrooke, Québec (1995)

    Google Scholar 

  46. Cremer, L., Heckl, M., Petersson, B.A.T.: Structure-Borne Sound, 3rd edn. Springer, Berlin (2005)

    Book  Google Scholar 

  47. Cupial, P., Niziol, J.: Vibration and damping analysis of a three-layered composite plate with a viscoelastic mid-layer. J. Sound Vib. 183(1), 99–114 (1995)

    Article  MATH  Google Scholar 

  48. Di Taranto, R.A.: Theory of vibratory bending for elastic and viscoelastic layered finite-length beams. J. Appl. Mech. 32(4), 881–886 (1965)

    Article  MathSciNet  Google Scholar 

  49. Douglas, B.E.: The transverse vibratory response of partially constrained elastic-viscoelastic beams. Ph.D. thesis, Department of Mechanical Engineering, University of Maryland at College Park, Maryland, US (1977)

    Google Scholar 

  50. Douglas, B.E., Yang, J.C.S.: Transverse compressional damping in vibratory response of elastic-viscoelastic-elastic beams. AIAA J. 16(9), 925–930 (1978)

    Article  Google Scholar 

  51. Doyle, J.F.: Wave Propagation in Structures: Spectral Analysis Using Fast Discrete Fourier Transforms, 2nd edn. Springer, New York (1997)

    MATH  Google Scholar 

  52. Ellis, R.W., Mote, C.D.: A feedback vibration controller for circular saws. J. Dyn. Syst. Meas. Control 101(1), 44–49 (1979)

    Article  Google Scholar 

  53. Enelund, M., Lesieutre, G.A.: Time domain modeling of damping using anelastic displacement fields and fractional calculus. Int. J. Solids Struct. 36(29), 4447–4472 (1999)

    Article  MATH  Google Scholar 

  54. Eversman, W., Dodson, R.O.: Free vibration of a centrally clamped spinning circular disk. AIAA J. 7(10), 2010–2012 (1969)

    Article  MATH  Google Scholar 

  55. Everstine, G.C.: A symmetric potential formulation for fluid-structure interaction. J. Sound Vib. 79(1), 157–160 (1981)

    Article  Google Scholar 

  56. Everstine, G.C.: Finite element formulations of structural acoustics problems. Comput. Struct. 65(3), 307–321 (1997)

    Article  MATH  Google Scholar 

  57. Ewins, D.J.: Modal Testing: Theory, Practice and Application, 2nd edn. Research Studies Press, Baldock (2000)

    Google Scholar 

  58. Ewins, D.J.: Disks. In: Ewins, D.J., Rao, S.S., Braun, S.G. (eds.) Encyclopedia of Vibration, pp. 404–413. Academic Press, Oxford (2001)

    Chapter  Google Scholar 

  59. Fahy, F., Gardonio, P.: Sound and Structural Vibration: Radiation, Transmission and Response, 2nd edn. Academic Press, Amsterdam (2007)

    Google Scholar 

  60. Felippa, C.A., Park, K.C.: Model based partitioned simulation of coupled systems. In: Sandberg, G., Ohayon, R. (eds.) Computational Aspects of Structural Acoustics and Vibration, pp. 171–216. Springer, Udine (2009)

    Google Scholar 

  61. Ferry, J.D.: Viscoelastic Properties of Polymers, 3rd edn. Wiley, New York (1980)

    Google Scholar 

  62. FFT: Actran 2007 User’s Guide. Free Field Technologies (www.fft.be). Mont-Saint-Guibert (2007)

  63. Fung, Y.C., Tong, P.: Classical and Computational Solid Mechanics. World Scientific, Singapore (2001)

    MATH  Google Scholar 

  64. Galucio, A.C., Deü, J.F., Ohayon, R.: Finite element formulation of viscoelastic sandwich beams using fractional derivative operators. Comput. Mech. 33(4), 282–291 (2004)

    Article  MATH  Google Scholar 

  65. Galucio, A.C., Deü, J.F., Ohayon, R.: A fractional derivative viscoelastic model for hybrid active-passive damping treatments in time domain—application to sandwich beams. J. Intell. Mater. Syst. Struct. 16(1), 33–45 (2005)

    Article  Google Scholar 

  66. Galucio, A.C., Deü, J.F., Mengue, S., Dubois, F.: An adaptation of the gear scheme for fractional derivatives. Comput. Methods Appl. Mech. Eng. 195(44–47), 6073–6085 (2006)

    Article  MATH  Google Scholar 

  67. Gandhi, F., Remillatt, C., Tomlinson, G., Austruy, J.: Constrained-layer damping with gradient polymers for effectiveness over broad temperature ranges. AIAA J. 45(8), 1885–1893 (2007)

    Article  Google Scholar 

  68. Gibson, W.C., Smith, C.A., McTavish, D.J.: Implementation of the Golla-Hughes-McTavish (GHM) method for viscoelastic materials using MATLAB and NASTRAN. In: Proceedings of the SPIE, San Diego, CA, US, vol. 2445, pp. 312–323 (1995)

    Google Scholar 

  69. Golla, D.F., Hughes, P.C.: Dynamics of viscoelastic structures—a time-domain, finite element formulation. J. Appl. Mech. 52(12), 897–906 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  70. Guedri, M., Lima, A.M.G., Bouhaddi, N., Rade, D.A.: Robust design of viscoelastic structures based on stochastic finite element models. Mech. Syst. Signal Process. 24(1), 59–77 (2010)

    Article  Google Scholar 

  71. Gupta, K.K., Meek, J.L.: Finite Element Multidisciplinary Analysis, 2nd edn. AIAA Education Series, Reston, VA, USA (2003)

    Google Scholar 

  72. Hambric, S.A., Jarrett, A.W., Lee, G.F., Fedderly, J.J.: Inferring viscoelastic dynamic material properties from finite element and experimental studies of beams with constrained layer damping. J. Vib. Acoust. 129(2), 158–168 (2007)

    Article  Google Scholar 

  73. Harari, I.: A survey of finite element methods for time-harmonic acoustics. Comput. Methods Appl. Mech. Eng. 195(13–16), 1594–1607 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  74. Harris, C.M., Piersol, A.G. (eds.): Harris’ Shock and Vibration Handbook, 5th edn. McGraw-Hill, New York (2002)

    Google Scholar 

  75. Hattori, N., Iida, T.: Idling noise from circular saws made of metals with different damping capacities. J. Wood Sci. 45(5), 392–395 (1999)

    Article  Google Scholar 

  76. Hattori, N., Kondo, S., Ando, K., Kitayarna, S., Mornose, K.: Suppression of the whistling noise in circular saws using commercially-available damping metal. Holz Roh Werkst. 59(5), 394–398 (2001)

    Article  Google Scholar 

  77. Herrin, D.W., Wu, T.W., Seybert, A.F.: Boundary element modeling. In: Crocker, M.J. (ed.) Handbook of Noise and Vibration Control, pp. 116–127. Wiley, Hoboken (2007)

    Chapter  Google Scholar 

  78. Heyliger, P., Pei, K.C., Saravanos, D.: Layerwise mechanics and finite element model for laminated piezoelectric shells. AIAA J. 34(11), 2353–2360 (1996)

    Article  MATH  Google Scholar 

  79. Ihlenburg, F.: Finite Element Analysis of Acoustic Scattering. Springer, New York (1998)

    Book  MATH  Google Scholar 

  80. Jeung, Y.S., Shen, I.Y.: Development of isoparametric, degenerate constrained layer element for plate and shell structures. AIAA J. 39(10), 1997 (2001)

    Article  Google Scholar 

  81. Johnson, A.R.: Modeling viscoelastic materials using internal variables. Shock Vib. Dig. 31(2), 91–100 (1999)

    Article  Google Scholar 

  82. Johnson, C.D., Kienholz, D.A.: Finite element prediction of damping in structures with constrained viscoelastic layers. AIAA J. 20(9), 1284–1290 (1982)

    Article  Google Scholar 

  83. Johnson, C.D., Kienholz, D.A., Rogers, L.C.: Finite element prediction of damping in beams with constrained viscoelastic layers. Shock Vib. Bull. 51(1), 71–81 (1980)

    Google Scholar 

  84. Jones, D.I.G.: Handbook of Viscoelastic Vibration Damping. Wiley, Chichester (2001)

    Google Scholar 

  85. Junger, M.C., Feit, D.: Sound, Structures and Their Interaction, 2nd edn. MIT Press, Cambridge (1986)

    Google Scholar 

  86. Kelly, W.J., Stevens, K.K.: Application of perturbation techniques to the modal analysis of a shaft with added viscoelastic damping. In: 7th International Modal Analysis Conference (IMAC VII). Society of Experimental Mechanics, Las Vegas, NV, US (1989)

    Google Scholar 

  87. Kergourlay, G., Balmès, E., Legal, G.: A characterization of frequency-temperature-prestress effects in viscoelastic films. J. Sound Vib. 297(1–2), 391–407 (2006)

    Article  Google Scholar 

  88. Killian, J.W., Lu, Y.P.: A finite element modeling approximation for damping material used in constrained damped structures. J. Sound Vib. 97(2), 352–354 (1984)

    Article  Google Scholar 

  89. Kim, H.R., Renshaw, A.A.: Asymmetric, speed dependent tensioning of circular rotating disks. J. Sound Vib. 218(1), 65–80 (1998)

    Article  Google Scholar 

  90. Kirkhope, J., Wilson, G.J.: Vibration and stress analysis of thin rotating-disks using annular finite-elements. J. Sound Vib. 44(4), 461–474 (1976)

    Article  MATH  Google Scholar 

  91. Kosmatka, J.B., Liguore, S.L.: Review of methods for analyzing constrained-layer damped structures. J. Aerospace Eng. 6(3), 268–283 (1993)

    Article  Google Scholar 

  92. Lakes, R.S., Wineman, A.: On Poisson’s ratio in linearly viscoelastic solids. J. Elast. 85(1), 45–63 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  93. Lamb, H., Southwell, R.V.: The vibrations of a spinning disk. Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci. 99(699), 272–280 (1921)

    Article  Google Scholar 

  94. Lee, C.H., Choi, H.S.: Adhesive sheet for noise and shock absorption, and saw blade making use of it, and manufacturing methods therefor (2003). US Patent 6526959, March 4, 2003

    Google Scholar 

  95. Lee, M.R., Singh, R.: Analytical formulations for annular disk sound radiation using structural modes. J. Acoust. Soc. Am. 95(6), 3311–3323 (1994)

    Article  Google Scholar 

  96. Lehmann, B.F., Hutton, S.G.: Self-excitation in guided circular saws. J. Vib. Acoust. Stress Reliab. Des. 110(3), 338–344 (1988)

    Article  Google Scholar 

  97. Lepoittevin, G., Kress, G.: Optimization of segmented constrained layer damping with mathematical programming using strain energy analysis and modal data. Mater. Des. 31(1), 14–24 (2010)

    Article  Google Scholar 

  98. Lesieutre, G.A., Bianchini, E.: Time domain modeling of linear viscoelasticity using anelastic displacement fields. J. Vib. Acoust. 117(4), 424–430 (1995)

    Article  Google Scholar 

  99. Lesieutre, G.A., Bianchini, E., Maiani, A.: Finite element modeling of one-dimensional viscoelastic structures using anelastic displacement fields. J. Guid. Control Dyn. 19(3), 520–527 (1996)

    Article  MATH  Google Scholar 

  100. Liénard, P.: Etude d’une méthode de measure du frottement intérieur de revêtements plastiques travaillant en flexion. Rech. Aéronaut. 20(1), 11–22 (1951)

    Google Scholar 

  101. Liguore, S.L., Kosmatka, J.B.: Evaluation of analytical methods to predict constrained layer damping behaviour. In: 6th International Modal Analysis Conference (IMAC VI), Kissimmee, FL, pp. 421–427 (1988)

    Google Scholar 

  102. Lin, R.M., Lim, M.K.: Complex eigensensitivity-based characterization of structures with viscoelastic damping. J. Acoust. Soc. Am. 100(5), 3182–3191 (1996)

    Article  Google Scholar 

  103. Liu, Y.: Fast Multipole Boundary Element Method: Theory and Applications in Engineering. Cambridge University Press, Cambridge (2009)

    Book  Google Scholar 

  104. Lu, Y.P., Everstine, G.C.: More on finite-element modeling of damped composite systems. J. Sound Vib. 69(2), 199–205 (1980)

    Article  Google Scholar 

  105. Lu, Y.P., Killian, J.W., Everstine, G.C.: Vibrations of three layered damped sandwich plate composites. J. Sound Vib. 64(1), 63–71 (1979)

    Article  Google Scholar 

  106. Lumsdaine, A., Scott, R.A.: Shape optimization of unconstrained viscoelastic layers using continuum finite elements. J. Sound Vib. 216(1), 29–52 (1998)

    Article  Google Scholar 

  107. Macé, M.: Damping of beam vibrations by means of a thin constrained viscoelastic layer: evaluation of a new theory. J. Sound Vib. 172(5), 557–591 (1994)

    Article  Google Scholar 

  108. MacNeal, R.H.: Finite Elements: Their Design and Performance. Marcel Dekker, New York (1994)

    Google Scholar 

  109. Marui, E., Ema, S., Miyachi, R.: An experimental investigation of circular-saw vibration via a thin-plate model. Int. J. Mach. Tools Manuf. 34(7), 893–905 (1994)

    Article  Google Scholar 

  110. Maue, J., Hertwig, R.: Low-noise circular saw blades. In: Société Francaise d’Acoustique, Deutsche Gesellschaft für Akustik (eds.) Proceedings of the Joint Congress CFA/DAGA’04, Strassbourg, pp. 805–806 (2004)

    Google Scholar 

  111. McTavish, D.J., Hughes, P.C.: Modeling of linear viscoelastic space structures. J. Vib. Acoust. 115(1), 103–110 (1993)

    Article  Google Scholar 

  112. Mead, D.J.: The effect of a damping compound on jet-efflux excited vibration. Aircraft Eng. 32(1), 64–72 (1960)

    Google Scholar 

  113. Mead, D.J.: Passive Vibration Control. Wiley, Chichester (1998)

    Google Scholar 

  114. Mead, D.J.: Structural damping and damped vibration. Applied Mechanics Reviews 55(6) (2002)

    Google Scholar 

  115. Mead, D.J., Markus, S.: Loss factors and resonant frequencies of encastre damped sandwich beams. J. Sound Vib. 12(1), 99 (1970)

    Article  MATH  Google Scholar 

  116. Morand, H.J.P., Ohayon, R.: Fluid Structure Interaction: Applied Numerical Methods. Wiley, Chichester (1995)

    Google Scholar 

  117. Moreira, R., Rodrigues, J.D.: Constrained damping layer treatments: finite element modeling. J. Vib. Control 10(4), 575–595 (2004)

    Article  MATH  Google Scholar 

  118. Moreira, R.A.S., Rodrigues, J.D.: Multilayer damping treatments: modeling and experimental assessment. J. Sandw. Struct. Mater. 12(2), 181–198 (2010)

    Article  Google Scholar 

  119. Moreira, R.A.S., Rodrigues, J.D., Ferreira, A.J.M.: A generalized layerwise finite element for multi-layer damping treatments. Comput. Mech. 37(5), 426–444 (2006)

    Article  MATH  Google Scholar 

  120. Mote, C.D., Schajer, G.S., Holøyen, S.: Circular-saw vibration control by induction of thermal membrane stresses. J. Eng. Ind. 103(1), 81–89 (1981)

    Article  Google Scholar 

  121. Myklestad, N.O.: The concept of complex damping. J. Appl. Mech. 19(3), 284–286 (1952)

    Google Scholar 

  122. Nallainathan, L., Liu, X.L., Chiu, W.K., Jones, R.: Modelling orthotropic viscoelastic behaviour of composite laminates using a coincident element method. Polymers and Polymer Compos. 11(8), 669–677 (2003)

    Google Scholar 

  123. Nashif, A., Jones, D., Henderson, J.: Vibration Damping. Wiley, New York (1985)

    Google Scholar 

  124. Nielsen, K.S., Stewart, J.S.: Woodworking machinery noise. In: Crocker, M.J. (ed.) Handbook of Noise and Vibration Control, pp. 975–986. Wiley, Hoboken (2007)

    Chapter  Google Scholar 

  125. Nigh, G.L., Olson, M.D.: Finite-element analysis of rotating-disks. J. Sound Vib. 77(1), 61–78 (1981)

    Article  MATH  Google Scholar 

  126. Nishio, S., Marui, E.: Effects of slots on the lateral vibration of a circular saw blade. Int. J. Mach. Tools Manuf. 36(7), 771–787 (1996)

    Article  Google Scholar 

  127. Noise Abatement for Circular Saws. Occupational Safety & Health Service, Department of Labour, Wellington, New Zeland (1989)

    Google Scholar 

  128. Nolle, A.W.: Methods for measuring dynamic mechanical properties of rubber-like materials. J. Appl. Phys. 19(8), 753–774 (1948)

    Article  Google Scholar 

  129. Norton, M.P., Karczub, D.G.: Fundamentals of Noise and Vibration Analysis for Engineers, 2nd edn. Cambridge University Press, Cambridge (2003)

    Book  Google Scholar 

  130. Oberst, H.: Ueber die dämpfung der biegeschwingungen dünner blech durch fest haftende beläge. Acust. 2(4), 181–194 (1952)

    Google Scholar 

  131. Ohayon, R., Soize, C.: Structural Acoustics and Vibration: Mechanical Models, Variational Formulations and Discretization. Academic Press, San Diego (1998)

    Google Scholar 

  132. Olson, L., Vandini, T.: Eigenproblems from finite-element analysis of fluid structure interactions. Comput. Struct. 33(3), 679–687 (1989)

    Article  MATH  Google Scholar 

  133. Park, C.H., Baz, A.: Vibration control of bending modes of plates using active constrained layer damping. J. Sound Vib. 227(4), 711–734 (1999)

    Article  Google Scholar 

  134. Park, C.H., Baz, A.: Vibration damping and control using active constrained layer damping: a survey. Shock Vib. Dig. 31(5), 355–364 (1999)

    Article  Google Scholar 

  135. Park, C.H., Baz, A.: Comparison between finite element formulations of active constrained layer damping using classical and layer-wise laminate theory. Finite Elem. Anal. Des. 37, 35–56 (2001)

    Article  MATH  Google Scholar 

  136. Pierce, A.D.: Acoustics: An Introduction to its Physical Principles and Applications. Acoustical Society of America, Woodbury (1989)

    Google Scholar 

  137. Plouin, A.S., Balmès, E.: Pseudo-modal representations of large models with viscoelastic behavior. In: 16th International Modal Analysis Conference (IMAC XVI), vol. 2, pp. 1440–1446. Society for Experimental Mechanics, Santa Barbara (1998)

    Google Scholar 

  138. Plouin, A.S., Balmès, E.: A test validated model of plates with constrained viscoelastic materials. In: 17th International Modal Analysis Conference (IMAC XVII), vol. 1, pp. 194–200. Society for Experimental Mechanics, Kissimmee (1999)

    Google Scholar 

  139. Plouin, A.S., Balmès, E.: Steel/viscoelastic/steel sandwich shells computational methods and experimental validations. In: 18th International Modal Analysis Conference (IMAC XVIII), vol. 1, pp. 384–390. Society for Experimental Mechanics, San Antonio (2000)

    Google Scholar 

  140. Pohl, M., Rose, M.: Vibration and noise reduction of a circular saw blade with applied piezoceramic patches and semi-active shunt networks. In: Adaptronic Congress, Berlin, June 19–20, 2009

    Google Scholar 

  141. Pritz, T.: Measurement methods of complex Poisson’s ratio of viscoelastic materials. Appl. Acoust. 60(3), 279–292 (2000)

    Article  Google Scholar 

  142. Putra, A., Thompson, D.J.: Sound radiation from rectangular baffled and unbaffled plates. Appl. Acoust. 71(12), 1113–1125 (2010)

    Article  Google Scholar 

  143. Ray, M.C., Baz, A.: Optimization of energy dissipation of active constrained layer damping treatments of plates. J. Sound Vib. 208(3), 391–406 (1997)

    Article  Google Scholar 

  144. Reddy, J.N.: Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, 2nd edn. CRC Press, Boca Raton (2004)

    Google Scholar 

  145. Riande, E., Calleja, R.D., Prolongo, M.G., Masegosa, R.M., Salom, C.: Polymer Viscoelasticity: Stress and Strain in Practice. Marcel Dekker, New York (2000)

    Google Scholar 

  146. Ro, J., El-Ali, A., Baz, A.: Control of sound radiation from a fluid-loaded plate using active constrained layer damping. In: Ferguson, N.S., Wolfe, H.F., Mei, C. (eds.) Proceedings of the Sixth International Conference on Recent Advances in Structural Dynamics, Southampton, pp. 1252–1273 (1997)

    Google Scholar 

  147. Robert, G.: Commercial software. In: Ewins, D.J., Rao, S.S., Braun, S.G. (eds.) Encyclopedia of Vibration, pp. 243–256. Academic Press, Oxford (2001)

    Chapter  Google Scholar 

  148. Ross, D., Ungar, E.E., Kerwin Jr., E.M.: Damping of plate flexural vibrations by means of viscoelastic laminae. In: Structural Damping, pp. 49–88. ASME Publication, New York (1959)

    Google Scholar 

  149. Sandberg, G., Wernberg, P., Davidsson, P.: Fundamentals of fluid-structure interaction. In: Sandberg, G., Ohayon, R. (eds.) Computational Aspects of Structural Acoustics and Vibration, pp. 23–101. Springer, Udine (2009)

    Chapter  Google Scholar 

  150. Saravanos, D.A.: Integrated damping mechanics for thick composite laminates and plates. J. Appl. Mech. 61(2), 375–385 (1994)

    Article  MATH  Google Scholar 

  151. Schajer, G.S.: Understanding saw tensioning. Holz Roh Werkst. 42(11), 425–430 (1984)

    Article  Google Scholar 

  152. Schajer, G.S.: Why are guided circular saws more stable than unguided saws. Holz Roh Werkst. 44(12), 465–469 (1986)

    Article  Google Scholar 

  153. Schajer, G.S., Mote, C.D.: Analysis of optimal roll tensioning for circular-saw stability. Wood Fiber Sci. 16(3), 323–338 (1984)

    Google Scholar 

  154. Schmidt, A., Gaul, L.: Finite element formulation of viscoelastic constitutive equations using fractional time derivatives. Nonlinear Dyn. 29(1–4), 37–55 (2002)

    Article  MATH  Google Scholar 

  155. Seubert, S.L., Anderson, T.J., Smelser, R.E.: Passive damping of spinning disks. J. Vib. Control 6(5), 715–725 (2000)

    Article  Google Scholar 

  156. Shen, I.Y.: Bending-vibration control of composite and isotropic plates through intelligent constrained-layer treatments. Smart Mater. Struct. 3(1), 59–70 (1994)

    Article  Google Scholar 

  157. Silva, L.A.: Internal variable and temperature modeling behavior of viscoelastic structures—a control analysis. Ph.D. thesis, Virginia Tech, VA, USA (2003)

    Google Scholar 

  158. Singh, R.: Case-history: the effect of radial slots on the noise of idling circular saws. Noise Control Eng. J. 31(3), 167–172 (1988)

    Article  Google Scholar 

  159. Sinha, S.K.: Determination of natural frequencies of a thick spinning annular disk using a numerical Rayleigh-Ritz’s trial function. J. Acoust. Soc. Am. 81(2), 357–369 (1987)

    Article  Google Scholar 

  160. Slanik, M.L., Nemes, J.A., Potvin, M.J., Piedboeuf, J.C.: Time domain finite element simulations of damped multilayered beams using a Prony series representation. Mech. Time-Depend. Mater. 4(3), 211–230 (2000)

    Article  Google Scholar 

  161. Slater, J.C., Belvin, W.K., Inman, D.J.: Survey of modern methods for modeling frequency dependent damping in finite element models. In: 11th International Modal Analysis Conference (IMAC XI), vol. 1923, pp. 1508–1512. Society for Experimental Mechanics, Kissimmee (1993)

    Google Scholar 

  162. Slocum, G.F., Gray, L.R.: Circular saw blade (1991). US Patent 5038653, August 13, 1991

    Google Scholar 

  163. Sneva, I.: Circular saw having vibration damping means (1951). US Patent 2563559, August 7, 1951

    Google Scholar 

  164. Snowdon, J.C.: Vibration and Shock in Damped Mechanical Systems. Wiley, New York (1968)

    Google Scholar 

  165. Song, D., Huang, C., Liu, Z.S.: Vibration modeling and software tools. In: de Silva, C.W. (ed.) Computer Techniques in Vibration. CRC Press, Boca Raton (2007)

    Google Scholar 

  166. Soni, M.L., Bogner, F.K.: Finite-element vibration analysis of damped structures. AIAA J. 20(5), 700–707 (1982)

    Article  Google Scholar 

  167. Southwell, R.V.: On the free transverse vibrations of a uniform circular disc clamped at its centre, and on the effects of rotation. Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci. 101(709), 133–153 (1922)

    Article  Google Scholar 

  168. Stakhiev, Y.M.: Research on circular saws vibration in Russia: from theory and experiment to the needs of industry. Holz Roh Werkst. 56(2), 131–137 (1998)

    Article  Google Scholar 

  169. Stakhiev, Y.M.: Research on circular saw disc problems: several of results. Holz Roh Werkst. 61(1), 13–22 (2003)

    Article  Google Scholar 

  170. Stanway, R., Rongong, J.A., Sims, N.D.: Active constrained-layer damping: a state-of-the-art review. Proc. Inst. Mech. Eng. I. J. Syst. Control Eng. 217(6), 437–456 (2003)

    Google Scholar 

  171. Stewart, J.S.: Circular saw blade (1980). US Patent 4232580, November 11, 1980

    Google Scholar 

  172. Sun, C.T., Lu, Y.P.: Vibration Damping of Structural Elements. Prentice Hall, Englewood Cliffs (1995)

    MATH  Google Scholar 

  173. Sundstrom, E.W.: Saw blade (1974). US Patent 3854364, December 17, 1974

    Google Scholar 

  174. Suzuki, K., Kageyama, K., Kimpara, I., Hotta, S., Ozawa, T., Ozaki, T.: Vibration and damping prediction of laminates with constrained viscoelastic layers—numerical analysis by a multilayer higher-order-deformable finite element and experimental observations. Mech. Adv. Mater. Struct. 10(1), 43–75 (2003)

    Article  Google Scholar 

  175. Thompson, L.L.: A review of finite-element methods for time-harmonic acoustics. J. Acoust. Soc. Am. 119(3), 1315–1330 (2006)

    Article  Google Scholar 

  176. Tian, J.F., Hutton, S.G.: Cutting-induced vibration in circular saws. J. Sound Vib. 242(5), 907–922 (2001)

    Article  Google Scholar 

  177. Trindade, M.A.: Reduced-order finite element models of viscoelastically damped beams through internal variables projection. J. Vib. Acoust. 128(4), 501–508 (2006)

    Article  Google Scholar 

  178. Trindade, M.A., Benjeddou, A.: Hybrid active-passive damping treatments using viscoelastic and piezoelectric materials: review and assessment. J. Vib. Control 8(6), 699–745 (2002)

    Article  MATH  Google Scholar 

  179. Trindade, M.A., Benjeddou, A., Ohayon, R.: Modeling of frequency-dependent viscoelastic materials for active-passive vibration damping. J. Vib. Acoust. 122(2), 169–174 (2000)

    Article  Google Scholar 

  180. Trindade, M.A., Benjeddou, A., Ohayon, R.: Finite element modelling of hybrid active-passive vibration damping of multilayer piezoelectric sandwich beams—part 1: formulation. Int. J. Numer. Methods Eng. 51(7), 835–854 (2001)

    Article  MATH  Google Scholar 

  181. Trindade, M.A., Benjeddou, A., Ohayon, R.: Finite element modelling of hybrid active-passive vibration damping of multilayer piezoelectric sandwich beams—part 2: system analysis. Int. J. Numer. Methods Eng. 51(7), 855–864 (2001)

    Article  Google Scholar 

  182. Trochidis, A.: Vibration damping of circular saws. Acust. 69(6), 270–275 (1989)

    Google Scholar 

  183. Tschoegl, N.W.: The Phenomenological Theory of Linear Viscoelastic Behaviour: An Introduction. Springer, Berlin (1989)

    Book  MATH  Google Scholar 

  184. Tschoegl, N.W., Knauss, W.G., Emri, I.: Poisson’s ratio in linear viscoelasticity—a critical review. Mech. Time-Depend. Mater. 6(1), 3–51 (2002)

    Article  Google Scholar 

  185. Tsunoda, K.: Vibration-damped rotatable cutting disk (1974). US Patent 3799025, March 26, 1974

    Google Scholar 

  186. Vasques, C.M.A.: Vibration control of adaptive structures: Modeling, simulation and implementation of viscoelastic and piezoelectric damping technologies. Ph.D. thesis, Faculdade de Engenharia, Universidade do Porto, Porto, Portugal (2008)

    Google Scholar 

  187. Vasques, C.M.A., Dias Rodrigues, J.: Shells with hybrid active-passive damping treatments: modeling and vibration control. In: 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, vol. 11, pp. 7529–7579. American Institute of Aeronautics and Astronautics, Newport (2006)

    Google Scholar 

  188. Vasques, C.M.A., Mace, B.R., Gardonio, P., Dias Rodrigues, J.: Analytical formulation and finite element modelling of beams with arbitrary active constrained layer damping treatments. Technical Memorandum No. 934, Institute of Sound and Vibration Research, Southampton, UK (2004)

    Google Scholar 

  189. Vasques, C.M.A., Mace, B.R., Gardonio, P., Rodrigues, J.D.: Arbitrary active constrained layer damping treatments on beams: finite element modelling and experimental validation. Comput. Struct. 84(22–23), 1384–1401 (2006)

    Article  Google Scholar 

  190. Vasques, C.M.A., Moreira, R.A.S., Dias Rodrigues, J.: Viscoelastic damping technologies—part I: modeling and finite element implementation. J. Adv. Res. Mech. Eng. 1(2), 76–95 (2010)

    Google Scholar 

  191. Vasques, C.M.A., Moreira, R.A.S., Dias Rodrigues, J.: Viscoelastic damping technologies—part II: experimental identification procedure and validation. J. Adv. Res. Mech. Eng. 1(2), 96–110 (2010)

    Google Scholar 

  192. Wallace, C.E.: Radiation-resistance of a rectangular panel. J. Acoust. Soc. Am. 51(3), 946–952 (1972)

    Article  Google Scholar 

  193. Wang, H.J., Chen, L.W.: Axisymmetric vibration and damping analysis of rotating annular plates with constrained damping layer treatments. J. Sound Vib. 271(1–2), 25–45 (2004)

    Article  Google Scholar 

  194. Wang, G., Wereley, N.M.: Frequency response of beams with passively constrained damping layers and piezo-actuators. In: Davis, L.P. (ed.) Smart Structures and Materials 1998: Passive Damping and Isolation, Bellingham, WA, US. SPIE, vol. 3327, pp. 44–60 (1998)

    Chapter  Google Scholar 

  195. Wang, G., Wereley, N.M.: Spectral finite element analysis of sandwich beams with passive constrained layer damping. J. Vib. Acoust. 124(3), 376–386 (2002)

    Article  Google Scholar 

  196. Wang, X.G., Xi, F.J., Daming, L., Zhong, Q.: Estimation and control of vibrations of circular saws. In: Proceedings of the IEEE International Conference on Control Applications, vol. 1, pp. 514–520 (1999)

    Google Scholar 

  197. Wikner, K.G., Josefsson, F.P.: Laminated saw blade (1976). US Patent 3990338, November 9, 1976

    Google Scholar 

  198. Yao, T., Duan, G.L., Cai, J.: Review of vibration characteristics and noise reduction technique of circular saws. Zhendong yu Chongji/J. Vib. Shock 27(6), 162–166 (2008)

    Google Scholar 

  199. Yellin, J.: An analytical and experimental analysis for a one-dimensional passive stand-off layer dampind treatment. Ph.D. thesis, Mechanical Engineering Department, University of Washington, Washington, US (2004)

    Google Scholar 

  200. Yellin, J.M., Shen, I.Y., Reinhall, P.G., Huang, P.Y.H.: An analytical and experimental analysis for a one-dimensional passive stand-off layer damping treatment. J. Vib. Acoust. Trans. ASME 122(4), 440–447 (2000)

    Article  Google Scholar 

  201. Yellin, J.M., Shen, I.Y., Reinhall, P.G.: Experimental and finite element analysis of stand-off layer damping treatments for beams. In: Wang, K.W. (ed.) Proceedings of the SPIE, San Diego, CA, US, vol. 5760, pp. 89–99 (2005)

    Google Scholar 

  202. Yiu, Y.C.: Finite element analysis of structures with classical viscoelastic materials. In: 34th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, La Jolla, CA, US, vol. 4, pp. 2110–2119 (1993)

    Google Scholar 

  203. Yu, R.C., Mote, C.D.: Vibration of circular saws containing slots. Holz Roh Werkst. 45(4), 155–160 (1987)

    Article  Google Scholar 

  204. Yu, S.C., Huang, S.C.: Vibration suppression of a CLD treated plate subject to a harmonic traveling load. J. Chin. Inst. Chem. Eng. 25(6), 627–638 (2002)

    Article  MathSciNet  Google Scholar 

  205. Zhang, S.H., Chen, H.L.: A study on the damping characteristics of laminated composites with integral viscoelastic layers. Compos. Struct. 74(1), 63–69 (2006)

    Article  Google Scholar 

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The joint funding scheme provided by the European Social Fund and from Portuguese funds from MCTES through POPH/QREN/Tipologia 4.2 are gratefully acknowledged.

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  2. Department of Engineering, University of Porto, Rua Dr Roberto Frias s/n, Porto, 4200-465, Portugal

    J. Dias Rodrigues

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Vasques, C.M.A., Cardoso, L.C. (2011). Viscoelastic Damping Technologies: Finite Element Modeling and Application to Circular Saw Blades. In: Vasques, C., Dias Rodrigues, J. (eds) Vibration and Structural Acoustics Analysis. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1703-9_9

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