This paper lies within the framework of the so-called redesign problem of structures subjected to dynamic constraints. A hybrid synthesis algorithm is developed, combining the truncated modal basis of the initial system and the spatial or material co-ordinates of an added component, which is modelled with shell-type finite elements parameterized with respect to a shape factor. Based upon a quadratic inverse formulation, the proposed technique shows several advantages in comparison to other synthesis methods, such as a refined sensitivity strategy, a powerful modal synthesis approach and a simplified optimization phase. Numerical examples are provided illustrating the capabilities of the novel procedure.

1.
Stetson
,
K. A.
, and
Palma
,
G. E.
,
1976
, “
Inversion of First-Order Perturbation Theory and Its Application to Structural Design
,”
AIAA J.
,
14
(
4
), pp.
454
460
.
2.
Sandstro¨m, R. E., 1981, “Inverse Perturbation Methods for Vibration Analysis,” Optimization of Distributed Parameter Structures, E. J. Haug and J. Cea, eds., Alphen aan de Rijn, The Netherlands, 2, pp. 1539–1552.
3.
Sandstro¨m
,
R. E.
, and
Anderson
,
W. J.
,
1982
, “
Modal Perturbation Methods for Marine Structures
,”
SNAME Trans.
,
90
, pp.
41
54
.
4.
Kim
,
K.-O.
, and
Anderson
,
W. J.
,
1984
, “
Generalized Dynamic Reduction in Finite Element Dynamic Optimization
,”
AIAA J.
,
22
(
11
), pp.
1616
1617
.
5.
Hoff
,
C. J.
,
Bernitsas
,
M. M.
,
Sandstro¨m
,
R. E.
, and
Anderson
,
W. J.
,
1984
, “
Inverse Perturbation Method for Structural Redesign With Frequency and Mode Shape Constraints
,”
AIAA J.
,
22
(
9
), pp.
1304
1309
.
6.
Bernitsas
,
M. M.
, and
Kang
,
B.
,
1991
, “
Admissible Large Perturbations in Structural Redesign
,”
AIAA J.
,
29
(
1
), pp.
104
113
.
7.
Alzahabi
,
B.
, and
Bernitsas
,
M. M.
,
2001
, “
Redesign of Cylindrical Shells by Large Admissible Perturbations
,”
J. Ship Res.
,
45
(
3
), pp.
177
186
.
8.
Schorderet, A., 1997, “Synthe`se modale et proble`me inverse en dynamique des structures,” Ph.D. Thesis 1698, Ecole polytechnique fe´de´rale de Lausanne, Lausanne.
9.
Gmu¨r
,
Th.
,
1990
, “
A Subspace Forward Iteration Method for Solving the Quadratic Eigenproblem Associated With the FDE Formulation
,”
Int. J. Numer. Methods Eng.
,
29
(
5
), pp.
935
951
.
10.
Gmu¨r, Th., and Schorderet, A., 1996, “MAFE—A Code for Modal Analysis by Finite Elements (Including Substructuring),” Users’ manual, Ecole polytechnique fe´de´rale de Lausanne, Lausanne.
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