This paper addresses the phenomenon of the destabilizing effect of slight damping on asymmetric linear systems. Previous works had showed that the destabilizing effect, regarded for a long time as a “paradox,” depends upon the ratio of the damping coefficients. This work extends those results to n-dof systems. In fact, conditions for a general asymmetric n-dof slightly damped system to be stable are obtained. Also, a useful sufficient condition is carried out. This practical design tool gives optimum damping ratios and takes into consideration the parameter uncertainties as well. The solution is based on the eigenvalue sensitivity analysis. Moreover, a formal physical explanation of the destabilizing effect of damping is given. Eventually, the theory is validated by means of a simple example.

Issue Section:
Technical Papers
Keywords:
damping, eigenvalues and eigenfunctions, vibrations
Topics:
Damping, Eigenvalues
1.
Gasparetto
,
A.
,
1998
, “
A System Theory Approach to Mode Coupling Chatter in Machining
,”
ASME J. Dyn. Syst., Meas., Control
,
120
, pp.
545
–
547
.
2.
Inman
,
D. J.
,
1983
, “
Dynamics of Asymmetric Nonconservative Systems
,”
ASME J. Appl. Mech.
,
50
, pp.
199
–
203
.
3.
Kounadis
,
A. N.
,
1992
, “
On the Paradox of the Destabilizing Effect of Damping in Non-Conservative Systems
,”
Int. J. Non-Linear Mech.
,
27
, pp.
597
–
609
.
4.
Semler
,
C.
,
Alighanbari
,
H.
, and
Pai¨doussis
,
M. P.
,
1998
, “
A Physical Explanation of the Destabilizing Effect of Damping
,”
ASME J. Appl. Mech.
,
65
, pp.
642
–
648
.
5.
Bolotin
,
V. V.
, and
Zhinzher
,
N. I.
,
1969
, “
Effects of Damping on Stability of Elastic Systems Subjected to Non-Conservative Forces
,”
Int. J. Solids Struct.
,
16
, pp.
965
–
989
.
6.
Herrmann
,
G.
, and
Jong
,
I. C.
,
1966
, “
On Nonconservative Stability Problems of Elastic Systems with Slight Damping
,”
ASME J. Appl. Mech.
,
32
, pp.
125
–
133
.
7.
Herrmann
,
G.
, and
Jong
,
I. C.
,
1965
, “
On the Destabilizing Effect of Damping in Nonconservative Elastic Systems
,”
ASME J. Appl. Mech.
,
32
, pp.
592
–
597
.
8.
Nemat-Nasser
,
S.
,
Prasad
,
S. N.
, and
Herrmann
,
G.
,
1966
, “
Destabilizing Effect of Velocity-Dependent Forces in Nonconservative Continuous Systems
,”
AIAA J.
,
4
, pp.
1276
–
1280
.
9.
Adhikari
,
S.
, and
Friswell
,
M. I.
,
2001
, “
Eigenderivative Analysis of Asymmetric Non-conservative Systems
,”
Int. J. Numer. Methods Eng.
,
51
, pp.
709
–
733
.
10.
Wan
,
J. S.
,
1994
, “
Cone Algorithm: An Extension of the Perceptron Algorithm
,”
IEEE Trans. Syst. Man Cybern.
,
24
, pp.
1571
–
1576
.
11.
Murty K., 1976, Linear and Combinatorial Programming, Wiley, New York.
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