Extending Den Hartog's vibration absorber technique to multi-degree-of-freedom systems

Journal of Vibration and Acoustics

Volumn 127, Issue 4, 2005, Pages 341-350

  Ozer, Mehmet Bulent ^a   Royston, Thomas J ^a  

^a University of Illinois at Chicago   (United States)

Author keywords

Den Hartog method; Dynamic vibration absorber; Invariant points; Multi degree of freedom systems; Sherman Morrison formula; Tuned mass damper

Indexed keywords

DAMPING; DEGREES OF FREEDOM (MECHANICS); MATHEMATICAL MODELS; OPTIMIZATION; VIBRATION CONTROL;

DEN HARTOG METHOD; DYNAMIC VIBRATION ABSORBER; INVARIANT POINTS; MULTI DEGREE OF FREEDOM SYSTEMS; SHERMAN-MORRISON FORMULA; TUNED MASS DAMPER;

VIBRATIONS (MECHANICAL);

EID: 24644519979     PISSN: 10489002     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.1924642     Document Type: Article

References (30)

1. Frahm, H, 1909, "Device for Damping Vibrations of Bodies," U.S. Patent No. 989958.
2. Ormondroyd, J., and Den Hartog, J. P., 1928, "Theory of the Dynamic Vibration Absorber," Trans. ASME, 50, pp. 9-22.
3. Den Hartog, J. P., 1934, Mechanical Vibrations, McGraw Hill, NY, Chap. 3 (eprint by Dover Publications).
4. Pennestri, E., 1998, "An Application of Chebyshev's Min-Max Criterion to the Optimal Design of a Damped Dynamic Vibration Absorber," J. Sound Vib., 217, pp. 757-765.
5. Thompson, A. G., 1980, "Auxilary Mass Throw in a Tuned and Damped Vibration Absorber," J. Sound Vib., 70, pp. 481-486.
6. Thompson, A. G., 1981, "Optimum Tuning and Damping of a Dynamic Vibration Absorber Applied to a Force Excited and Damped Primary System," J. Sound Vib., 77, pp. 403-415.
7. 2 Optimization of Dynamic Vibration Absorbers Attached to Damped Linear Systems," ASME J. Vibr. Acoust., 124, pp. 284-295.
8. Randall, S. E., Halsted, D. M., and Taylor, D. L., 1981, "Optimum Vibration Absorbers for Linear Damped Systems," ASME J. Mech. Des., 103, pp. 908-913.
9. Soom, A., and Lee, M., 1983, "Optimal Design of Linear and Nonlinear Vibration Absorbers for Damped Systems," ASME J. Vib., Acoust., Stress, Reliab. Des., 105, pp. 112-119.
10. Jordanov, I. N., and Cheshankov, I. B., 1988, "Optimal Design of Linear and Nonlinear Dynamic Vibration Absorbers," J. Sound Vib., 123, pp. 157-170.
11. Jordanov, I. N., and Cheshankov, I. B., 1989, "Optimal Design of Linear and Nonlinear Dynamic Vibration Absorbers reply," J. Sound Vib., 132, pp. 157-159.
12. Hadi, M. N. S., and Arfiadi, Y., 1998, "Optimum Design of Absorber for MDOF Structures," J. Struct. Eng., 124, pp. 1272-1280.
13. Singh, M. P., and Moreschi, L. M., 2002, "Optimal Placement of Dampers for Passive Response Control," Earthquake Eng. Struct. Dyn., 31, pp. 955-976.
14. Rana, R., and Soong, T. T., 1998, "Parametric Study and Simplified Design of Tuned Mass Dampers," Eng. Struct., 20, pp. 193-204.
15. Sadek, F., Mohraz, B., Taylor, A. W., and Chang R. M., 1997, "A Method of Estimating the Parameters of Tuned Mass Dampers for Seismic Applications," Earthquake Eng. Struct. Dyn., 26, pp. 617-635.
16. Lin, C.-C., Wang, J.-F., and Ueng J.-M., 2001, "Vibration Control Identification of Seismically Excited m.d.o.f Structure-PTMD Systems," J. Sound Vib., 240, pp. 87-115.
17. Xu, Y. L., and Kwok, K. C. S., 1994, "Semianalytical Method for Parametric Study of Tuned Mass Dampers," J. Struct. Eng., 120, pp. 747-764.
18. 1 Optimally Tuned Passive Isolators and Absorbers," ASME J. Dyn. Syst., Meas., Control, 120, pp. 282-287.
19. 2 Approach for Optimally Tuning Passive Vibration Absorbers to Flexible Structures," J. Guid. Control Dyn., 17, pp. 636-638.
20. Eskinat, E., and Ozturk, L., 1997, "Vibration Absorbers as Controllers," 4th European Control Conference Brussels, Belgium.
21. Vakakis, A. F., and Palpetis, S. A., 1986, "The Effect of a Viscously Damped Dynamic Absorber on a Linear Multi Degree of Freedom System," J. Sound Vib., 105, pp. 49-60.
22. Kitis, L., Wang, B. P., and Pilkey, W. D., 1983, "Vibration Reduction Over a Frequency Range," J. Sound Vib., 89, pp. 559-569.
23. Ozer, M. B., and Royston, T. J., 2005, "Application of Sherman-Mordson Matrix Inversion Formula to Damped Vibration Absorbers Attached to Multi Degree of Freedom Systems," I. Sound Vib., 283(3-5), pp. 1235-1249.
24. Lewis, F. M., 1955, "The Extended Theory Of the Viscous Vibration Damper," ASME J. Appl. Mech., 22, pp. 377-382.
25. Plunkett, R., 1958, "The Calculation of Optimum Concentrated Damping for Continuous Systems," ASME J. Appl. Mech., 25, pp. 219-224.
26. Sherman, J., and Morrison, W. J., 1949, "Adjustment of an Inverse Matrix corresponding to changes in the elements of a given column or a given row of the Original Matrix." Ann. Math. Stat., 20, p. 621.
27. Hager, W. W., 1989, "Updating the Inverse of a Matrix," SIAM Rev., 31, pp. 221-239.
28. Ozer M. B., and Royston, T. J., 2003, "Optimal Passive Structural Sound Radiation Control Using Shunted Nonlinear Piezoelectric Materials," J. Acoust. Soc. Am., 114, pp. 1934-1946.
29. Hong, K. L., and Kim, J., 1996, "New Analysis Method for General Acoustic-Structural Coupled Systems," J. Sound Vib., 192, pp. 465-480.
30. Yang, B., 1993, "Exact Receptances of Nonproportionally Damped Dynamic-Systems," ASME J. Vibr. Acoust., 115, pp. 47-52.