Abstract
An analytical approach is presented to investigate the optimal problem of non-traditional type of Dynamic vibration absorber (DVA) for damped primary structures subjected to ground motion. Different from the standard configuration, the non-traditional DVA contains a linear viscous damper connecting the absorber mass directly to the ground instead of the main mass. There have been many studies on the design of the non-traditional DVA for undamped primary structures. Those studies have shown that the non-traditional DVA produces better performance than the standard DVA does. When damping is present at the primary system, there are very few works on the non-traditional dynamic vibration absorber. To the best of our knowledge, there is no study on the design of non-traditional DVA for damped structures under ground motion. We propose a simple method to determine the approximate analytical solutions of the nontraditional DVA when the damped primary structure is subjected to ground motion. The main idea of the study is based on the criterion of the equivalent linearization method to replace approximately the original damped structure by an equivalent undamped one. Then the approximate analytical solution of the DVA’s parameters is given by using known results for the undamped structure obtained. Comparisons have been done to validate the effectiveness of the obtained results.
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References
H. Frahm, Device for damped vibration of bodies, U. S. Patent No. 989958, 30 October (1909).
J. Ormondroyd and J. P. Den Hartog, The theory of the dynamic vibration absorber, Transactions of ASME, J. of Applied Mechanics, 50 (7) (1928) 9–22.
E. Hahnkamm, The damping of the foundation vibrations at varying excitation frequency, Master of Architecture, 4 (1932) 192–201 (in German).
J. E. Brock, A note on the damped vibration absorber, Transactions of ASME, J. of Applied Mechanics, 13 (4) (1946) A–284.
J. P. Den Hartog, Mechanical vibrations, McGraw-Hill, New York, USA (1956).
O. Nishihara and T. Asami, Close-form solutions to the exact optimizations of dynamic vibration absorber (minimizations of the maximum amplitude magnification factors), J. of Vibration and Acoustics, 124 (2002) 576–582.
S. H. Crandall and W. D. Mark, Random vibration in mechanical systems, Academic Press, New York, USA (1963).
Y. Iwata, On the construction of the dynamic vibration absorbers, Preparation of the Japan Society of Mechanical Engineering, 820 (8) (1982) 150–152 (in Japanese).
T. Asami et al., Optimum design of dynamic absorbers for a system subjected to random excitation, JSME International J., Series 3, Vibration, Control Engineering, Engineering for Industry, 34 (2) (1991) 218–226.
H. Yamaguchi, Damping of transient vibration by a dynamic absorber, Transactions of the Japan Society of Mechanical Engineering, Series C, 54 (1988) 561–568 (in Japanese).
T. Ioi and K. Ikeda, On the dynamic vibration damped absorber of the vibration system, Bulletin of the Japanese Society of Mechanical Engineering, 21 (1978) 64–71.
S. E. Randall, D. M. Halsted and D. L. Taylor, Optimum vibration absorbers for linear damped systems, ASME J. of Mechanical Design, 103 (1981) 908–913.
A. G. Thompson, Optimum tuning and damping of a dynamic vibration absorber applied to a force excited and damped primary system, J. of Sound and Vibration, 77 (1981) 403–415.
G. B. Warburton, Optimal absorber parameters for various combinations of response and excitation parameters, Earthquake Engineering and Structural Dynamics, 10 (1982) 381–401.
Y. Fujino and M. Abe, Design formulas for tuned mass dampers based on a perturbation technique, Earthquake Engineering and Structural Dynamics, 22 (1993) 833–854.
O. Nishihara and H. Matsuhisa, Design and tuning of vibration control devices via stability criterion, Preparation of the Japan Society of Mechanical Engineering, 97-10-1 (1997) 165–168.
E. Pennestrì, An application of Chebyshev’s min-max criterion to the optimal design of a damped dynamic vibration absorber, J. of Sound and Vibration, 217 (4) (1998) 757–765.
T. Asami, O. Nishihara and A. M. Baz, Analytical solutions to H8 and H2 optimization of dynamic vibration absorbers attached to damped linear systems, J. of Vibration and Acoustics, 124 (2002) 284–295.
A. Ghosh and B. Basu, A closed-form optimal tuning criterion for TMD in damped structures, Structural Control and Health Monitoring, 14 (2007) 681–692.
B. Brown and T. Singh, Minimax design of vibration absorbers for linear damped systems, J. of Sound and Vibration, 330 (11) (2010) 2437–2448.
N. D. Anh and N. X. Nguyen, Extension of equivalent linearization method to design of TMD for linear damped systems, Structural Control and Health Monitoring, 19 (6) (2012) 565–573.
N. D. Anh and N. X. Nguyen, Design of TMD for damped linear structures using the dual criterion of equivalent linearization method, International J. of Mechanical Sciences, 77 (2013) 164–170.
O. F. Tigli, Optimum vibration absorber (tuned mass damper) design for linear damped systems subjected to random loads, J. of Sound and Vibration, 331 (13) (2012) 3035–3049.
M. Z. Ren, A variant design of the dynamic vibration absorber, J. of Sound and Vibration, 245 (4) (2001) 762–770.
K. Liu and J. Liu, The damped dynamic vibration absorbers: revisited and new result, J. of Sound and Vibration, 284 (2005) 1181–1189.
Y. L. Cheung and W. O. Wong, Design of a non-traditional dynamic vibration absorber (L), J. of the Acoustical Society of America, 126 (2) (2009) 564–567.
W. O. Wong and Y. L. Cheung, Optimal design of a damped dynamic vibration absorber for vibration control of structure excited by ground motion, Engineering Structures, 30 (2008) 282–286.
W. O. Wong and Y. L. Cheung, H-infinity optimization of a variant design of the dynamic vibration absorber-Revisited and new results, J. of Sound and Vibration, 330 (2011) 3901–3912.
W. O. Wong and Y. L. Cheung, H2 optimization of a nontraditional dynamic vibration absorber for vibration control of structures under random force excitation, J. of Sound and Vibration, 330 (2011) 1039–1044.
K. Liu and G. Coppola, Optimal design of damped dynamic vibration absorber for damped primary systems, Transactions of the Canadian Society for Mechanical Engineering, 34 (1) (2010) 119–135.
N. Krylov and N. Bogoliubov, Introduction to Nonlinear Mechanics, Princeton U. Press (1943).
T. K. Caughey, Response of Van der Pols oscillator to random excitations, Transactions of ASME, J. of Applied Mechanics, 26 (1) (1956) 345–348.
T. K. Caughey, Random excitation of a system with bilinear hysteresis, Transactions of ASME, J. of Applied Mechanics, 27 (1) (1960) 649–652.
N. D. Anh, Duality in the analysis of responses to nonlinear systems, Vietnam J. of Mechanics, 32 (4) (2010) 263–266.
N. D. Anh, N. N. Hieu and N. N. Linh, A dual criterion of equivalent linearization method for nonlinear systems subjected to random excitation, Acta Mechanica, 223 (3) (2012) 645–654.
N. D. Anh, N. X. Nguyen and L. T. Hoa, Design of threeelement dynamic absorber for damped linear structures, J. of Sound and Vibration, 332 (2013) 4482–4495.
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Recommended by Associate Editor Moon Ki Kim
Nguyen Dong Anh currently works at Institute of Mechanics, Vietnam Academy of Science and Technology, Hanoi, Vietnam. He received his Dr.Sci. in Mathematics and Physics from the Institute of Mathematics, Kiev, Ukraine. His research fields are nonlinear random vibration and structural control.
Nguyen Xuan Nguyen received his M.Sci. in Mechanics from Vietnam National University, Hanoi, Vietnam in 2008. He is currently a lecturer at the Department of Mathematics, Mechanics and Informatics, VNU University of Science, Hanoi, Vietnam. His research interests include structural dynamics and vibration control.
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Anh, N.D., Nguyen, N.X. Research on the design of non-traditional dynamic vibration absorber for damped structures under ground motion. J Mech Sci Technol 30, 593–602 (2016). https://doi.org/10.1007/s12206-016-0113-x
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DOI: https://doi.org/10.1007/s12206-016-0113-x