DAMPING BEHAVIOR OF COMPOSITES AN EVOLUTIONARY APPROACH FINDING MATHEMATICAL RELATIONSHIPS

jinksimaginaryAI and Robotics

Nov 7, 2013 (3 years and 7 months ago)

165 views

Mechanics of Nano, Micro and Macro Composite Structures

Politecnico di Torino, 18
-
20 June 2012


A. J. M. Ferreira, E. Carrera (Editors)

http://paginas.fe.up.pt/~icnmmcs/

DAMPING BEHAVIOR OF
COMPOSITES


A
N

EVOLUTIONARY
APPROACH FIN
DING MATHEMATICAL RE
LATIONSHIPS

Lars Ulke
-
Winter
,
Matthias Klaerner, Lothar Kroll


Institute of Lightweight Structures

Chemnitz University of Technology

09107 Chemnitz
,
Germany

e
-
mail:
lars.ulke
-
winter@mb.tu
-
chemnitz.de
, web page: http://www.
strukturleichtbau.net

Key words:

Damping,
Composite structures,
Optimisation, GEP, genetic
algorithms


1

DAMPING OF THERMOPLA
STIC FRP

Thermoplastic fibre reinforced composites are characterised by
orthotropic material
parameters in stiffness, strength and damping

as well as simultaneous advantages in mass
production and recycling applicability.
Moreover, thermoplastic frp have a significant higher
material damping than thermoset materials
and thus a

huge design space of the material
parameters influenced by

the matrix material, the fibres, the textile processing, the fibre
volume content as well as the lay up.
This enables

targeted modifications of the structural
dynamic behaviour and sound emission
of composite structures.

Especially modern very stiff and lightweight constructions tend to higher sound radiation
and thus NVH efforts in an early concept phase. This vibro
-
acoustic engineering of
lightweight structures using dynamic FEM or BEM simulation
s necessitates viscous damping
parameters as w
ell as the perception of the nonlin
ear dependency.
The damping ratio has been
determined using free vibrations of cantilever beams with various fibre orientations. The
experimental results have been used to exa
mine the parameters of the ADAMS/BACON
damping model. This model is based on the three basic deformation modes: longitudinal and
transversal tension/compression as well as longitudinal shear and thus considers the
anisotropic characteristics of fibre reinf
orced composites

[1
-
3
]
. The model had been
developed and tested for unidirectional reinforced materials originally and was applied for
woven thermoplastic frps with reasonable results.

2

TWO STAGE OPTIMISATI
ON STRATEGY

A

new

two stage
evolutiona
ry optimisation strategy
is used to determine functions
describing the dependencies of the damping ratio, e.g. related to the fibre orientation. Both
functions, of the ADAMS/BACON model and of the evolutionary optimisation, are compared
with the experiment
al results.

The
new
evolutionary optimi
s
ation approach is inspired by
the
Gene Expression Programming Algorithm (GEP)

[
4
] co
ding

mathematical expression
s

by a
genetic representation [
5
].

Unfortunately
,

this algorithm leads to long and unhandy
mathematical
terms. Therefore a further development
helps

find
ing

shorter forms
according
to
a
two
loop

optimisation
approach.

In the

outer loop the right mathematical structure

is
determined

and
within
the inner loop
all

corresponding
free coefficients

are evaluated
.

Lars Ulke
-
Winter, Matthias Klaerner, Lothar Kroll


2

3

AN EXAMPLE: DEPENDEN
CY OF THE FIBRE ANGL
E

The new evolutionary optimisation strategy determines functions to describe the
dependencies of the damping ratio.
Therefore, common thermoplastic frps with plain woven
glass fibres, a wrap
-
to
-
werf

ration of 2:2 and Polyamid
-
Matrix are investigated. The
measurement results show a significant dependency of the fibre angle (see figure 1).

This dependency can be described by the ADAMS/BACON model (compare section 1)
necessitating all elastic parameters

of a single layer

and depending on three damping
coefficients: longitudinal, transversal and shear damping.

In contrast, the evolutionary
strategy achieves quite reasonable results in finding a function type only with these
measurement results.


Figure
1
: Damping ratio

of thermoplastic frp with woven reinforcements: measurement results
,

optimised
function

type

and ADAMS
-
BACON description

REFERENCES

[1]

Adams RD and Bacon DGC. Effect of fibre orientation and laminate geometry on the
dynamic
properties of CFRP. J Compos Mater 1973; 7: 402

428.

[2]

Adams RD and Maheri MR. Dynamic flexural properties of anisotropic fibrous composite beams.
Compos Sci Technol 1994; 50: 497

514.

[3]

Maheri

MR and Adams RD. Modal vibration damping of anisotropic FRP laminates using the
Rayleigh
-
Ritz energy minimization scheme. J Sound Vib 2003; 259(1): 17

29.

[4]

Ferreira, C., Automatically Defined Functions in Gene Expression Programming. In N. Nedjah,
L. de M.

Mourelle, A. Abraham, eds., Genetic Systems Programming: Theory and Experiences,
Studies in Computational Intelligence, Vol. 13, pp. 21
-
56, Springer
-
Verlag, 2006.

[5]

J.H. Holland, Adaptation in Natural and Artificial Systems: An Introductory Analysis with
Ap
plications to Biology, Control and Artificial Intelligence. Ann Arbor, MI: University of
Michigan Press, 1975.