Abstract

The objective of this paper is to investigate how higher damping is achieved by energy dissipation as high-frequency vibration due to the addition of impact mass. In an impact damper system, collision between primary and impact masses cause an exchange of momentum resulting in dissipation of energy. A numerical model is developed to study the dynamic behavior of an impact damper system using a multi-degree-of-freedom (MDOF) system with augmented Lagrangian multiplier contact algorithm. Mathematical modeling and numerical simulations are carried out using ansysfea package. Studies are carried out for various mass ratios subjecting the system to low-frequency high amplitude excitation. Time responses obtained from numerical simulations at fundamental mode when the system is excited in the vicinity of its fundamental frequency are validated by comparing with experimental results. Magnification factor evaluated from numerical simulation results is comparable with those obtained from experimental data. The transient response obtained from numerical simulations is used to study the behavior of first three modes of the system excited in vicinity of its fundamental frequency. It is inferred that dissipation of energy is a main reason for achieving higher damping for an impact damper system in addition to being transformed to heat, sound, and/or those required to deform a body.

References

1.
Park
,
J.
,
Wang
,
S.
, and
Crocker
,
M. J.
,
2009
, “
Mass Loaded Resonance of a Single Unit Impact Damper Caused by Impacts and the Resulting Kinetic Energy Influx
,”
J. Sound Vib.
,
323
(
3–5
), pp.
877
895
.10.1016/j.jsv.2009.01.044
2.
Ema
,
S.
, and
Marui
,
E.
,
1994
, “
A Fundamental Study on Impact Dampers
,”
J. Mach. Tools Manuf.
,
34
(
3
), pp.
407
421
.10.1016/0890-6955(94)90009-4
3.
Kushida
,
Y.
,
Umehara
,
H.
,
Hara
,
S.
, and
Yamada
,
K.
,
2018
, “
Momentum Exchange Impact Damper Design Methodology for Object-Wall-Collision Problems
,”
J. Vib. Control
,
24
(
14
), pp.
3206
3218
.10.1177/1077546317703202
4.
Du
,
Y. C.
, and
Zhang
,
M. M.
,
2012
, “
The Effect of Damper Components on the Performance of Impact Damping
,”
Appl. Mech. Mater.
,
217–219
, pp.
2644
2648
.10.4028/www.scientific.net/AMM.217-219.2644
5.
Saeki
,
M.
,
2002
, “
Impact Damping With Granular Materials in a Horizontally Vibrating System
,”
J. Sound Vib.
,
251
(
1
), pp.
153
161
.10.1006/jsvi.2001.3985
6.
Li
,
K.
, and
Darby
,
A. P.
,
2006
, “
Experiments on the Effect of an Impact Damper on a Multiple-Degree-of-Freedom System
,”
J. Vib. Control
,
12
(
5
), pp.
445
464
. pp10.1177/1077546306063504
7.
Saeki
,
M.
,
2005
, “
Analytical Study of Multi-Particle Damping
,”
J. Sound Vib.
,
281
(
3–5
), pp.
1133
1144
.10.1016/j.jsv.2004.02.034
8.
Cempel
,
C.
,
1974
, “
The Multi-Unit Impact Damper: Equivalent Continuous Force Approach
,”
J. Sound Vib.
,
34
(
2
), pp.
199
209
.10.1016/S0022-460X(74)80304-4
9.
Singh
,
S.
,
Mukherjee
,
S.
, and
Sanghi
,
S.
,
2008
, “
Study of a Self-Impacting Double Pendulum
,”
J. Sound Vib.
,
318
(
4–5
), pp.
1180
1196
.10.1016/j.jsv.2008.05.001
10.
Lee
,
K.
,
2011
, “
A Short Note for Numerical Analysis of Dynamic Contact Considering Impact and a Very Stiff Spring-Damper Constraint on the Contact Point
,”
Multibody Syst. Dyn.
,
26
(
4
), pp.
425
439
.10.1007/s11044-011-9257-8
11.
Du
,
Y.
,
Wang
,
S.
, and
Zhang
,
J.
,
2010
, “
Energy Dissipation in Collision of Two Balls Covered by Fine Particles
,”
Int. J. Impact Eng.
,
37
(
3
), pp.
309
316
.10.1016/j.ijimpeng.2009.06.011
12.
Du
,
Y.
, and
Wang
,
S.
,
2010
, “
Modeling the Fine Particle Impact Damper
,”
Int. J. Mech. Sci.
,
52
(
7
), pp.
1015
1022
.10.1016/j.ijmecsci.2010.04.004
13.
Wong
,
C. X.
,
Daniel
,
M. C.
, and
Rongong
,
J. A.
,
2009
, “
Energy Dissipation Prediction of Particle Dampers
,”
J. Sound Vib.
,
319
(
1–2
), pp.
91
118
.10.1016/j.jsv.2008.06.027
14.
Mao
,
K.
,
Wang
,
M. Y.
,
Xu
,
Z.
, and
Chen
,
T.
,
2004
, “
DEM Simulation of Particle Damping
,”
Powder Technol.
,
142
(
2–3
), pp.
154
165
. pp10.1016/j.powtec.2004.04.031
15.
Ramachandran, S., and Lesieutre, G.,
,
2005
, “
Dynamics and Performance of a Vertical Impact Damper
,”
AIAA
Paper No. 2005-2326.10.2514/6.2005-2326
16.
Muscia
,
R.
,
1991
, “
A Theoretical Experimental Method Based on Modal Analysis for Estimating the Damping Capacity of Vibrating Structures
,”
Mech. Sys. Signal Process.
,
5
(
6
), pp.
475
499
.10.1016/0888-3270(91)90048-A
17.
Vinayaravi
,
R.
,
Kumaresan
,
D.
,
Jayaraj
,
K.
,
Asraff
,
A. K.
, and
Muthukumar
,
R.
,
2013
, “
Experimental Investigation and Theoretical Modelling of an Impact Damper
,”
J. Sound Vib.
,
332
(
5
), pp.
1324
1334
.10.1016/j.jsv.2012.10.032
18.
Hestenes
,
M. R.
,
1969
, “
Multiplier and Gradient Methods
,”
J. Optim. Theory Appl.
,
4
(
5
), pp.
303
320
.10.1007/BF00927673
19.
Powell
,
M. J. D.
,
1969
, “
A Method for Nonlinear Constraints in Minimization Problems
,”
Optimization
, ed.
R.
Fletcher
,
Academic Press
,
New York
, pp.
283
298
.
20.
Simo
,
J. C.
, and
Laursen
,
T. A.
,
1992
, “
An Augmented Lagrangian Treatment of Contact Problems Involving Friction
,”
Comput. Struct
,
42
(
1
), pp.
97
116
.10.1016/0045-7949(92)90540-G
21.
Hughes
,
T. J. R.
,
Taylor
,
R. L.
,
Sackman
,
J. L.
,
Curnier
,
A.
, and
Kanoknukulchai
,
W.
,
1976
, “
A Finite Element Method for a Class of Contact-Impact Problems
,”
Comput. Meth. appl. Mech. Eng.
,
8
(
3
), pp.
249
276
.10.1016/0045-7825(76)90018-9
22.
Wriggers
,
P.
,
Vu Van
,
T.
, and
Stein
,
E.
,
1990
, “
Finite Element Formulation of Large Deformation Impact-Contact Problems With Friction
,”
Comput. Struct.
,
37
(
3
), pp.
319
331
.10.1016/0045-7949(90)90324-U
23.
Laursen
,
T. A.
, and
Chawla
,
V.
,
1997
, “
Design of Energy Conserving Algorithms for Frictionless Dynamic Contact Problems
,”
Int. J. Numer. Methods Eng.
,
40
(
5
), pp.
863
886
.10.1002/(SICI)1097-0207(19970315)40:5<863::AID-NME92>3.0.CO;2-V
24.
Armero
,
F.
, and
Pet Cz
,
E.
,
1998
, “
Formulation and Analysis of Conserving Algorithms for Dynamic Contact/Impact Problems
,”
Comput. Methods Appl. Mech. Eng.
,
158
(
3–4
), pp.
269
300
.10.1016/S0045-7825(97)00256-9
25.
Bergan
,
P. G.
, and
Mollestad
,
E.
,
1985
, “
An Automatic Time-Stepping Algorithm for Dynamic Problems
,”
Comput. Methods Appl. Mech. Eng.
,
49
(
3
), pp.
299
318
.10.1016/0045-7825(85)90127-6
26.
Newmark
,
N. M.
,
1959
, “
A Method of Computation for Structural Dynamics
,”
ASCE J. Eng. Mech. Div.
,
85
(
3
), pp.
67
94
.10.1061/JMCEA3.0000098
27.
Moorthy
,
R. J. K.
,
Kakodkar
,
A.
,
Srirangarajan
,
H. R.
, and
Suryanarayan
,
S.
,
1993
, “
An Assessment of the Newmark Method for Solving Chaotic Vibrations of Impacting Oscillators
,”
Comput. Struct.
,
49
(
4
), pp.
597
603
.10.1016/0045-7949(93)90064-K
You do not currently have access to this content.