Many vibration isolators can be modeled with a discontinuity in the stiffness and damping coefficients. The sudden change in the values of the coefficients can be represented as a piecewise linear or nonlinear function. Soft suspensions are best for isolation; however, a nonlinear hardening suspension is required to minimize relative displacement at high amplitudes. Often, the physical design limits the relative displacement. Taking advantage of nonlinearity in the suspension is not enough in limiting the relative displacement at very high amplitude. Therefore, a secondary suspension must be involved to limit very high relative displacements. In this investigation, the averaging method was applied to the differential equation generated from the model to find the frequency response. A sensitivity analysis was performed to find regions of instability in the frequency response

Volume Subject Area:
Design Engineering
Keywords:
Piecewise Nonlinear System, Vibration Isolation, Frequency Response Analysis
Topics:
Damping, Design, Differential equations, Displacement, Frequency response, Hardening, Nonlinear systems, Nonlinear vibration, Sensitivity analysis, Stability, Stiffness, Vibration isolation, Vibration isolators
1.
Babitsky V.I. & Krupenin, V. L. (2001). Vibration of strongley nonlinear discontinuous systems. New York: Springer.
2.
Chatterjee
S.
,
Mallik
A. K.
and
Ghosh
A.
 (
1996
): “
Periodic Response of Piecewise Non-linear Oscillators under Harmonic Excitation
,”
Journal of Sound and Vibration
, vol.
191
(
1
), pp.
129
–
144
.
3.
Chicurel-Uziel
E.
 (
2001
): “
Exact, Single Equation Closed-form Solution of Vibrating Systems with Piecewise Linear Springs
,”
Journal of Sound and Vibration
,
245
(
2
),
285
–
301
.
4.
Murdock J. A. (1998). Qualitative Theory of Nonlinear Resonance by Averaging and Dynamical Systems Methods. in Dynamics Reported, (Vol. 1). (Kirchgraber, U. & Walter, H. O., eds.), New York: Wiley.
5.
Murdock J.A. (1999). Perturbations Theory and Methods. Philadelphia: Society for Industrial and Applied Mathematics.
6.
Nakhaie Jazar
G.
&
Golnaraghi
F.
 (
2002
).
Engine mounts for automotive applications: a survey
.
The Shock and Vibration Digest
,
34
(
5
),
363
–
379
.
7.
Narimani A., and Golnaraghi M. F, Nakhaie Jazar G, (2003): “Optimizing Piecewise Linear Isolator for Steady State Vibration,” 2003 ASME-IMECE Symposium on Dynamic Response of Advanced Materials and Structures, Washington D. C., USA, November.
8.
Narimani A., Nakhaie Jazar G., and Golnaraghi M. F, (2002): “Vibration Analysis of a Piecewise Linear System,” Fourteenth U.S. National Congress of Theoretical and Applied Mechanics, Blacksburg, Virginia, USA, June 23–28.
9.
Narimani
A.
,
Nakhaie Jazar
G
, and
Golnaraghi
M. F.
, (
2004
a): “
Frequency Response of a Piecewise Linear Vibration Isolator
,”
Journal of Vibration and Control
,
10
(
12
),
1775
–
1894
.
10.
Narimani
A.
,
Nakhaie Jazar
G
, and
Golnaraghi
M. F
, (
2004
b)
Sensitivity Analysis of Frequency Response of a Piecewise Linear System in Frequency Island
,
Journal of Vibration and Control
,
10
(
2
),
175
–
198
.
11.
Natsiavas
S.
 (
1998
): “
Stability of Piecewise Linear Oscillators with viscous and dry friction damping
,”
Journal of Sound and Vibration
,
217
(
3
),
507
–
522
.
12.
Natsiavas
S.
 (
1990
).
On the dynamics of oscillators with bi-linear damping and stiffness
.
International Journal of Non-Linear Mechanics
,
25
(
5
),
535
–
554
.
13.
Nayfeh A.H. and Mook D.T. (1979): “Nonlinear Oscillations,” Wiley-Interscience Publications, Wiley Classics Library edition.
14.
Stahl P., and Nakhaie Jazar G, (2005): “Frequency Response Analysis of Piecewise Nonlinear Vibration Isolator,” 20th ASME Biennial Conference on Mechanical Vibration and Noise, Long Beach, CA, USA, September 24–28.
15.
Zill, GD. & Cullen, M.R. (1992). Advanced Engineering Mathematics. Boston: PWS-Kent.
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