To determine the optimal parameters of the dynamic vibration absorber (DVA), a complete multi-parameter model of the dynamics of machines and structures is required. A model with two degrees of freedom is unacceptable for a sufficiently precise calculation with sufficient accuracy of the oscillations of the design, and thus for an adequate description of its dynamic characteristics. Therefore, in practice, it is necessary to investigate the design using a complex model. In particular, the methods for determining the concentration of mass and stiffness can be used on the basis of a refined theoretical calculation. A number of numerical schemes (NS) are known for complex vibro-loaded structures, in which developed methods of decomposition and synthesis of NS based on new methods of modal synthesis. Also developed is a complex NS of discrete-continuum type, which provides an opportunity in the adaptive mode to calculate stresses not only in the continuum elements, but also in the places of their greatest concentration - in the compounds.
In this paper, an efficient numerical approach based on the theoretical-experimental method is proposed to maximize the minimal damping of modes in a prescribed frequency range for general viscous tuned-mass systems. Methods of decomposition and numerical synthesis are considered on the basis of the adaptive schemes. The influence of dynamic vibration absorbers and basic design elastic and damping properties is under discussion. A technique is developed to give the optimal DVA’s for the elimination of excessive vibration in sinusoidal and impact forced tall buildings system. One task of this work is to analyze parameters identification of the dynamic vibration absorber and the basic structure. The discrete-continue models of machines dynamics of some elongated element with multi mass DVA’s are offered. A technique is developed to give the optimal DVA’s for the elimination of excessive vibration in harmonic stochastic and impact loaded systems. The questions of robustness at optimization of DVA are considered. Different types of control management for semi-active DVA’s are applied. Examples of DVA’s practical implementation are presented.
[1] M. Constantinou, T. Soong, and G. Dargush, “Passive Energy Dissipation Systems for Structural Design and Retrofit,” Multidisciplinary Center for Earthquake Engineering Research, 1998.
[2] C. Truesdell, A First Course in Rational Continuum Mechanics. New York: Academic Press, 1977.
[3] H. Ashley, “On passive damping mechanisms in large space structures,” Journal of Spacecraft and Rockets, vol. 21, no. 5, pp. 448-455, 1984. https://doi.org/10.2514/3.25679
[4] G. S. Pisarenko, A. P. Yakovlev, and V. V. Matveev, Vibropogloshchaiushchie svoistva konstruktcionnykh materialov [Vibration absorption properties of structural materials]. Kyiv, Ukraine: Naukova Dumka Publ., 1971. [in Russian].
[5] V. G. Karnaukhov, and I. F. Kirichok, Sviazannye zadachi teorii viazko-uprugikh plastin i obolochek [Related problems of the theory of visco-elastic plates and shells]. Kyiv, Ukraine: Naukova Dumka Publ., 1986. [in Russian].
[6] E. E. Ungar, and E. M. Kerwin, “Loss factors of viscoelastic systems in terms of energy concepts”, The Journal of the Acoustical Society of America, vol. 34, no. 7, pp. 954-957, 1962. https://doi.org/10.1121/1.1918227
[7] S. H. Crandall, “The role of damping in vibration theory”, Journal of Sound and Vibration, vol. 11, no. 1, pp. 3-18, 1970. https://doi.org/10.1016/S0022-460X(70)80105-5
[8] S. H. Crandall, “The hysteretic damping model in vibration theory”, Journal of Mechanical Engineering Science, no. 205, pp. 23-28, 1991.
[9] R. H. Scanlan, “Linear damping models and causality in vibrations”, Journal of Sound and Vibration, vol. 13, no. 4, pp. 499-503, 1970. https://doi.org/10.1016/S0022-460X(70)80054-2
[10] D. E. Newland, Mechanical Vibration Analysis and Computation. New York: Longman, Harlow and John Wiley, 1989.
[11] O. C. Zienkiewicz, and R. L. Taylor, The Finite Element Method. London, UK: McGraw-Hill, 1989.
[12] F. Brezzi, and M. Fortin, Mixed and Hybrid Finite Element Methods. New York: Springer-Verlag, 1991. https://doi.org/10.1007/978-1-4612-3172-1
[13] K. J. Bathe, Finite Element Procedures. Watertown, MA: Prentice Hall, Pearson Education, Inc., 1996.
[14] C. L. Dym, and I. H. Shames, Energy and Finite Element Methods in Structural Mechanics. New York: Hemisphere, 1985.
[15] J. N. Reddy, An Introduction to the Finite Element Method. New York: McGraw-Hill, 2006.
[16] S. Snowdon, Vibration and Shock in Damped Mechanical Systems. New York: Wiley, 1968.
[17] D. Braess, Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics. Cambridge, UK: Cambridge University Press, 2007. https://doi.org/10.1017/CBO9780511618635
[18] J. P. Boyd, Chebyshev and Fourier Spectral Methods. New York: Dover Publications, 2001.
[19] G. S. Payette, “Spectral/hp finite element models for fluids and structures,” ProQuest Dissertations and Theses, SAND2012-7615, 2012.
[20] Kazuto Seto, “Active vibration control in machinery,” Journal of the Acoustical Society of Japan, vol. 12, issue 6, pp. 263-272, 1991. https://doi.org/10.1250/ast.12.263
[21] M. J. Balas, “Feedback Control of Flexible Systems,” IEEE Trans. Automat. Contr., pp. 673- 679, 1978. https://doi.org/10.1109/TAC.1978.1101798
[22] C. Moutinho, “Testing a simple control law to reduce broadband frequency harmonic vibrations using semi-active tuned mass dampers,” Smart Mater. Struct., vol. 24, 055007, 2005.
[23] D. J. Mead, Passive vibration control. Chichester: John Wiley & Sons, 2000.
[24] A. D. Nashif, D. I. G. Jones, and J. P. Henderson, Passive vibration control. New York: John Wiley and Sons, 1985.
[25] J. B. Hunt, Dynamic Vibration Absorbers. London, UK: Mechanical Engineering Publications, 1979.
[26] J. Sun, M. Jolly and M. Norris, “Adaptive and Active Tuned Vibration Absorbers – A Survey,” Journal of Vibration and Acoustics, vol. 117 (B), pp. 234-242, 1995.
[27] N. Carpineto, W. Lacarbonara, and F. Vestroni, “Mitigation of Pedestrian-induced Vibrations in Suspension Footbridges via Multiple Tuned Mass Dampers,” Journal of Vibration and Control, vol. 16, no. 5, pp. 749-776, 2010. https://doi.org/10.1177/1077546309350188
[28] I. Kourakis, “Structural systems and tuned mass dampers of super-tall buildings: case study of Taipei 101,” Thesis (M. Eng.), Dept. of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA, 2007.
[29] D. E. Newland, “Vibration of the London Millennium Bridge: cause and cure,” International Journal of Acoustics and Vibrations, vol. 8, no. 1, pp. 9-14, 2003. https://doi.org/10.20855/ijav.2003.8.1124
[30] P. Nawrotzki, “Tuned-mass systems for the dynamic upgrade,” in Proceedings of Eleventh East Asia-Pacific Conference on Structural Engineering and Construction (EASEC-11), Taiwan, 2008, pp. 1-9.
[31] K. Y. Sanliturk, and H. T. Belek, “Tuned-mass systems for the dynamic upgrade,” in Proceedings of the 8th International Congress on Sound and Vibration, Hong Kong, 2001, pp. 2259-2264.
[32] H. Frahm, “Device for damping vibration of bodies,” U.S. Patent 989958, Apr. 18, 1911.
[33] P.Watts, “On a method of reducing the rolling of ships at sea,” The Royal Institution of Naval Architects, vol. 24, pp. 165-190, 1883.
[34] J. B. Hunt, and J. C. Hissen, “The broadband dynamic vibration absorber,” Journal of Sound and Vibration, vol. 83, no. 4, pp. 573-578, 1982. https://doi.org/10.1016/S0022-460X(82)80108-9
[35] J. Ormondroyd, J. P. den Hartog, “The theory of the dynamic vibration absorber,” Transactions of the American Society of Mechanical Engineers, vol. 50, A9-A22, 1928.
[36] J. P. den Hartog, Mechanical Vibrations. New York: Dover Publications, 1985.
[37] S. Timoshenko, Vibration problems in engineering. New York: Van Nostrand Company, 1955.
[38] B. G. Korenev, and L. M. Reznikov, Dynamic Vibration Absorbers: Theory and Technical Applications. Chichester, UK: J.Wiley & Sons, 1993.
[39] J. Sun, M. Jolly and M. Norris, “Adaptive and Active Tuned Vibration Absorbers – A Survey,” Journal of Vibration and Acoustics, vol. 117 (B), pp. 234-242, 1995.
[40] R. E. D. Bishop, and D. B. Welbourn, “The problem of the dynamic vibration absorber,” Engineering, pp. 174-769, 1952.
[41] G. B. Warburton, “On the theory of the acceleration damper,” J. Appl. Mech., vol. 24, pp. 322-324, 1957.
[42] J. C. Snowdon, “Platelike Dynamic Vibration Absorbers,” Journal of Engineering for Industry, vol. 97, issue 1, pp. 88-93, 1975. https://doi.org/10.1115/1.3438595
[43] T. Aida, T. Aso, K. Nakamoto, and K. Kawazoe, “Vibration control of shallow shell structures using shell-type dynamic vibration absorber,” Journal of Sound and Vibration, vol. 218, issue 2, pp. 245-267, 1998. https://doi.org/10.1006/jsvi.1998.1829
[44] M. Z. Kolovsky, Nonlinear Dynamics of Active and Passive Systems of Vibration Protection. Berlin, Germany: Springer Verlag, 1999. https://doi.org/10.1007/978-3-540-49143-9
[45] H. Kauderer, Nichtlineare Mechanik. Berlin, Germany: Springer Verlag, 1958. [in German]. https://doi.org/10.1007/978-3-642-92733-1
[46] L. A. Pipes, “Analysis of a nonlinear dynamic vibration absorber,” J. Appl. Mech., vol. 20, pp. 515-518, 1953.
[47] R. E. Roberson, “Synthesis of a nonlinear vibration absorber,” J. Franklin Inst., vol. 254, pp. 105-120, 1952. https://doi.org/10.1016/0016-0032(52)90457-2
[48] R. A. Ibrahim, “Recent advances in nonlinear passive vibration isolators,” Journal of Sound and Vibration, vol. 314, issue 3-5, pp. 371-452, 2008. https://doi.org/10.1016/j.jsv.2008.01.014
[49] J. Park, S. Wang, and M. J. Crocker, “Mass loaded resonance of a single unit impact damper caused by impacts and the resulting kinetic energy influx,” Journal of Sound and Vibration, vol. 323, issue 3-5, pp. 495-1090, 2009. https://doi.org/10.1016/j.jsv.2009.01.044
[50] M. Saeki, “Analytical study of multi-particle damping,” Journal of Sound and Vibration, vol. 281, issue 3-5, pp. 1133-1144, 2005. https://doi.org/10.1016/j.jsv.2004.02.034
[51] K. S. Marhadi, and V. K. Kinra, “Particle impact damping: effect of mass ratio, material, and shape,” Journal of Sound and Vibration, vol. 283, issue 1-2, pp. 433-448, 2005. https://doi.org/10.1016/j.jsv.2004.04.013
[52] B. M. Shah, et al., “Construction and characterization of a particle-based thrust damping system,” Journal of Sound and Vibration, vol. 326, issue 3-5, pp. 489-502, 2009. https://doi.org/10.1016/j.jsv.2009.06.007
[53] B. Diveyev, I. Vikovych, I. Dorosh, and I. Kernytskyy, “Different type vibration absorbers design for beam-like structures,” in Proceedings of the 19th International Congress on Sound and Vibration, Vilnius, Lithuania, 2012, pp. 1499-1507.
[54] H. Cherchyk, B. Diveyev, V. Martyn, and R. Sava, “Parameters identification of particle vibration absorber for rotating machines,” in Proceedings of the 21st International Congress on Sound and Vibration, Beijing, China, 2014, pp. 5:4233-4240.
[55] B. Diveyev, I. Vikovych, V. Martyn, and I. Dorosh, “Optimization of the impact and particle vibration absorbers,” in Proceedings of the 22nd International Congress on Sound and Vibration, Florence, Italy, 2015, Code 121474.
[56] O. S. Lanets, Vysokoefektyvni mizhrezonansni vibratsiini mashyny z elektromahnitnym pryvodom (Teoretychni osnovy ta praktyka stvorennia) [High-performance inter-resonant vibrating machines with electromagnetic drive (Theoretical Foundations and Creation Practices)]. Lviv, Ukraine: Lviv Polytechnic Publishing House, 2008. [in Ukrainian].
[57] F. Casciati, G. Magonette, and F. Marazzi, Technology of Semiactive Devices and Applications in Vibration Mitigation. New York: Wiley, 2006. https://doi.org/10.1002/0470022914
[58] F. Weber, and H. Distl, “Real-time controlled tuned mass dampers for Wolgograd Bridge,” Beton-Und Stahlbetonbau, vol. 108, pp. 362-372, 2013. https://doi.org/10.1002/best.201300013
[59] C. Seiler, O. Fisher, and P. Huber, “Semi-active MR dampers in TMD's for vibration control of footbridges – part 2: numerical analysis and practical realization,” in Proceedings of the International Conference on the Design and Dynamic Behaviour of Footbridges, Paris, France, November 20-22, 2002.
[60] M. Setareh, et al., “Semiactive tuned mass damper for floor vibration control,” Journal of Structural Engineering, vol. 133, issue 2, pp. 242-250, 2007. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:2(242)
[61] S. Nagarajaiah, “Adaptive passive, semiactive, smart tuned mass dampers: identification and control using empirical mode decomposition, Hilbert transform, and short-term Fourier transform,” Structural Control and Health Monitoring, vol. 16, issue 7-8, pp. 800-841, 2009. https://doi.org/10.1002/stc.349
[62] B. Spencer, and S. Nagarajaiah, “State of the art of structural control,” Journal of Structural Engineering, vol. 129, issue 7, pp. 845-856, 2003. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:7(845)
[63] B T. Pinkaew, and Y. Fujino, “Effectiveness of semi-active tuned mass dampers under harmonic excitation,” Engineering Structures, vol. 23, issue 7, pp. 850-856, 2001. https://doi.org/10.1016/S0141-0296(00)00091-2
[64] P. L. Walsh, and J. S. Lamancusa, “A variable stiffness vibration absorber for minimization of transient vibrations,” Journal of Sound and Vibration, vol. 158, issue 2, pp. 195-211, 1992. https://doi.org/10.1016/0022-460X(92)90045-Y
[65] H. Hu, and D. Jin, “A semi-active vibration control strategy based on piecewise linear vibration absorbers,” Journal of Vibration Engineering, vol. 10, issue 2, pp. 125-130, 1997.
[66] X. Qian, and H. Hu, “A semi-active vibration absorber with an adjustable clearance and its realization,” Journal of Vibration Engineering, vol. 14, issue 4, pp. 378-381, 2001.
[67] J. H. Koo, and M. Ahmadian, “In search of suitable control methods for semi-active tuned vibration absorbers,” Journal of Vibration and Control, vol. 10, issue 2, pp. 163-174, 2004. https://doi.org/10.1177/1077546304032020
[68] F. Allen, and R. Karjalainen, “Using genetic algorithms to find technical trading rules,” Journal of financial economics, vol. 51, pp. 245-271, 1999. https://doi.org/10.1016/S0304-405X(98)00052-X
[69] M W. Y. Fowlkes, and C. M. Creveling, Engineering methods for robust product design: using Taguchi methods in technology and product development. Reading, MA: Addison-Wesley Publishing Company, 1995.
[70] C. Zang, M. I. Friswell, and J. E. Mottershead, “A review of robust optimal design and its application in dynamics,” Computers and Structures, vol. 83, pp. 315-326, 2005. https://doi.org/10.1016/j.compstruc.2004.10.007
[71] C. Moutinho, “Testing a simple control law to reduce broadband frequency harmonic vibrations using semi-active tuned mass dampers,” Smart Materials and Structures, vol. 24, no. 5, 055007, 2015. https://doi.org/10.1088/0964-1726/24/5/055007
[72] Y. Shena, and M. Ahmadian, “Nonlinear dynamical analysis on four semi-active dynamic vibration absorbers with time delay,” Shock and Vibration, vol. 20, pp. 649-663, 2013. https://doi.org/10.1155/2013/345710
[73] B. Diveyev, et al., “Dynamichnyi hasnyk kolyvan” [“Dynamic Vibration Absorber”], UA Patent 114978, March 25, 2017. [in Ukrainian].
[74] B. Diveyev, et al., “Dynamichnyi hasnyk kolyvan” [“Dynamic Vibration Absorber”], UA Patent 121562, December 11, 2017. [in Ukrainian].
[75] A. Herbst, and P. Wolf, “Spray deposit distribution from agricultural boom sprayers in dynamic conditions,” in Proceedings of the 25th International Conference on Noise and Vibration Engineering, Leuven, Belgium, 2000, pp. 1599-1605.
[76] D. Ooms, F. Lebeau, R. Ruter, and M. F. Destain, “Measurements of the horizontal sprayer boom movements by sensor data fusion,” Computers and Electronics in Agriculture, vol. 33, issue 2, pp. 139-162, 2002. https://doi.org/10.1016/S0168-1699(02)00006-6
[77] B. Diveyev, et al., “Modern methods for optimum designing of technological machines,” in Proceedings of the VI Konferrencja naukowo-praktyczna “Energia w nauce i technice”, Bialostock, Poland, 2007, pp. 13-20
[78] B. Diveyev, I. Vikovych, “Application of complex methods for optimum designing mobile vehicles,” in Proceedings of the XXIII Symp. Drgania w ukladach fizycznch, Poznan-Bedlewo, Poland, 2008, pp. 64-67.
[79] B. Diveyev, I. Vikovych, I. Dorosh, and I. Kernytskyy, “Different type vibration absorbers design for beam-like structures,” in Proceedings of the 19th International Congress on Sound and Vibration, Vilnius, Lithuania, 2012, pp. 1499-1507.
[80] B. Diveyev, I. Vikovych, V. Martyn, and I. Dorosh, “Optimization of the impact and particle vibration absorbers,” in Proceedings of the 22nd International Congress on Sound and Vibration, Florence, Italy, 2015, Code 121474.