Non-linear energy sinks (NES) are often used to mitigate the dynamic response of structures, but its large-scale use and design have been limited by their inherent non-linearities. Assuming that loads are random in nature, the stochastic analysis of non-linear systems may be done through computational intensive techniques as Monte Carlo simulations (MCS). Alternatively, the Stochastic Linearisation (SL) technique has proven to be an effective tool. Since, in general, controlled systems are non-classically damped and most of SL algorithms operate recursively, the computational burden required is still large for those problem that make intensive use of SL technique, like passive control optimal design procedures. In this study, a procedure to speed up the Stochastic Linearisation technique by avoiding numerical evaluations of response statistics is proposed and an application have been carried out on a well-known case study related to the vibrations mitigation of an aircraft wing. The ability of the proposed procedure to effectively reduce the computational effort and to reliably design the optimal passive control device is showed.

1.
J. B.
Roberts
and
P. D.
Spanos
,
Random vibration and statistical linearization
(
Dover
,
Mineola, NY, USA
,
2003
).
2.
T. S.
Atalik
and
S.
Utku
,
Earthquake Engineering and Structural Dynamics
4
,
411
420
(
1976
).
3.
I.
Elishakoff
,
Shock and Vibration Digest
32
,
179
188
(
2000
).
4.
V.
Artale
,
G.
Navarra
,
A.
Ricciardello
, and
G.
Barone
,
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering
3
(
2017
), .
5.
E. H.
Vanmarcke
,
Journal of the Engineering Mehanics Division
98
,
425
446
(
1972
).
6.
M.
Di Paola
and
G.
Muscolino
,
Journal of Sound and Vibration
110
,
233
245
(
1986
).
7.
E. H.
Vanmarcke
,
Journal of Applied Mechanics
42
, p.
215
(
1975
).
8.
A.
Der Kiureghian
,
Journal of the Engineering Mechanics Division
106
,
1195
1213
.
9.
G.
Barone
,
F. Lo
Iacono
,
G.
Navarra
, and
A.
Palmeri
, “
A novel analytic model of power spectral density function coherent with earthquake response spectra
,” in
Proceedings of the 1st UNCECOMP International Conference
(Athens,
2015
), pp.
394
406
.
10.
G.
Barone
,
F. Lo
Iacono
,
G.
Navarra
, and
A.
Palmeri
,
Soil Dynamics and Earthquake Engineering
in press (
2019
), .
11.
M.
Di Paola
and
G.
Muscolino
,
Journal of Sound and Vibration
124
,
479
488
(
1988
).
12.
T.
Igusa
,
A.
Der Kiureghian
, and
J. L.
Sackman
,
Earthquake Engineering & Structural Dynamics
12
,
121
136
(
1984
).
13.
G.
Navarra
,
F. Lo
Iacono
,
M.
Oliva
, and
D.
Cascone
, “
Speeding up the Stochastic Linearisation for systems controlled by non-linear passive devices
,” in
Proceedings of the XXIV Conference of The Italian Association of Theoretical and Applied Mechanics
(
2019
).
14.
O.
Gendelman
,
L. I.
Manevitch
,
A. F.
Vakakis
, and
R.
M'Closkey
,
Journal of Applied Mechanics
68
, p.
34
(
2001
).
15.
F.
Nucera
,
F. Lo
Iacono
,
D. M.
McFarland
,
L. A.
Bergman
, and
A. F.
Vakakis
,
Journal of Sound and Vibration
313
,
57
76
(
2008
).
16.
M.
Oliva
,
G.
Barone
, and
G.
Navarra
,
Engineering Structures
145
,
135
152
(
2017
).
17.
S. A.
Hubbard
,
D. M.
McFarland
,
L. A.
Bergman
, and
A. F.
Vakakis
,
Journal of Aircraft
47
,
1918
1931
(
2010
).
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