Vibration Responses for SDOF System: II – Coulomb and Structural Damping
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Abstract
The principal objective of this paper is to deal with the vibration analysis of single degree of freedom system with Coulomb damping and structural damping. Closed-form expressions in terms of vibration amplitude or magnification factor and phase angle are derived. Due to the difficulty and complexity in determining the damping value in practical systems, concepts of equivalent viscous damping coefficient are introduced and explained that how to treat and receive this coefficient properly. Important observations are found and clearly discussed herein.
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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Copyright @2021 Engineering Transactions
Faculty of Engineering and Technology
Mahanakorn University of Technology
References
P. Posayanant, W. Wongwanishwatana, P. Premthamkorn and Y. Sompornjaroensuk, “Vibration responses for SDOF system: I – Free and forced vibrations with and without damping,” Eng. Trans. MUT, 2025, paper submitted for publication. (in Thai)
W.T. Thomson, Theory of Vibration with Applications, 4th Edition, Chapman & Hall, London, 1993.
S.S. Rao, Mechanical Vibrations, 3rd Edition, Addison-Wesley Publishing Company, Inc., Massachusetts, 1995.
D.J. Inman, Engineering Vibration, 2nd Edition, Prentice-Hall, Inc., New Jersey, 2001.
W.J. Bottega, Engineering Vibrations, Taylor & Francis Group, LLC., Boca Raton, 2006.
S. Raynor and E. Frank, “Method of computation of damped resonance frequencies for a system of equal masses, equal spring constants, and equal viscous-damping coefficients,” J. Acoust. Soc. Am., vol. 39, no.2, pp. 269-271, 1966.
A.E. Anuta, “The modal equations with viscous damping,” Comput. Struct., vol. 41, no. 4, pp. 621-627, 1991.
M.I. Friswell and A.W. Lees, “Resonance frequencies of viscously damped structures,” J. Sound Vib., vol. 217, no. 5, pp. 950-959, 1998.
M. Gurgoze and N.A. Hizal, “Viscously damped mechanical systems subject to several constraint equations,” J. Sound Vib., vol. 229, no. 5, pp. 1264-1268, 2000.
M. Gurgoze, “Receptance matrices of viscously damped systems subject to several constraint equations,” J. Sound Vib., vol. 230, no. 5, pp. 1185-1190, 2000.
M. Gurgoze, “Viscously damped linear systems subjected to damping modifications,” J. Sound Vib., vol. 245, no. 2, pp. 353-362, 2001.
M. Gurgoze, “Non-proportionally damped systems subjected to damping modification by several viscous dampers,” J. Sound Vib., vol. 271, pp. 441-452, 2004.
M. Gurgoze, “On various eigenvalue problem formulations for viscously damped linear mechanical systems,” Int. J. Mech. Eng. Educ., vol. 33, no. 3, pp. 235-243, 2005.
J.P. Den Hartog, “Forced vibrations with combined viscous and Coulomb damping,” Lond. Edinb. Dubl. Phil. Mag., vol. 9, no. 59, pp. 801-817, 1930.
G.C.K. Yeh, “Forced vibrations of a two-degree-of-freedom system with combined Coulomb and viscous damping,” J. Acoust. Soc. Am., vol. 39, no.1, pp. 14-24, 1966.
P.-C. Chen and W.W. Soroka, “Correlation technique for transient response of a hysteretically-damped dynamic system to stationary random excitation,” J. Sound Vib., vol. 22, no. 1, pp. 75-79, 1972.
S.F. Masri, “Forced vibration of the damped bilinear hysteretic oscillator,” J. Acoust. Soc. Am., vol. 57, no.1, pp. 106-112, 1975.
L.Y. Chen, J.T. Chen, C.H. Chen and H.-K. Hong, “Free vibration of a SDOF system with hysteretic damping,” Mech. Res. Commun., vol. 21, no. 6, pp. 599-604, 1994.
L. Meirovitch, Principles and Techniques of Vibrations, Prentice-Hall, Inc., New Jersey, 1997.
E. Kreyszig, Advanced Engineering Mathematics, 9th Edition, John Wiley & Sons, Inc., Singapore, 2006.
J.J. Tuma, Engineering Mathematics Handbook, 2nd, Enlarged and Revised Edition, McGraw-Hill Book Company, New York, 1979.
S.S. Rao, Vibration of Continuous System, John Wiley & Sons, Inc., New Jersey, 2007.
A.W. Leissa and M.s. Qatu, Vibrations of Continuous Systems, McGraw-Hill Companies, Inc., New York, 2011.
