Dynamic analyses of structures with applied rubber
The aim with the present thesis has been to develop efficient, practical and accurate
methods in order to model rubber in dynamic analyses, with emphasis on passive constrained
layer damping materials. A fractional order viscoelastic constitutive model is
mapped onto experimental data from a measurement standard using a vibrating beam
technique. Within the standard, Euler-Bernoulli formulation is used for the dynamic
behavior of the covering layers in the sandwich structure. Here, a 6th order differential
equation for the dynamic analysis of the deflection of a three-layer sandwich beam with
a viscoelastic middle layer was developed where transverse shear deformation as well
as rotational inertia effects of the covering layers were taken into account.
In order to model constrained layer damping with a thin viscoelastic material sandwiched
between two metal layers, a novel interface finite element was developed. The
element directly couples together two shell elements. The formulation of the element
uses a power series expansion of the internal displacement fields in the thickness direction.
Thereby, higher order variations in the thickness direction can be captured if
the element is formulated so that more nodes are used in the in-plane directions. The
accuracy of the element is verified by comparisons with measurements on sample specimens
with well defined boundary conditions and with the results from a commercial
finite element code.
In aircraft applications, using rubber in connection with other materials or when
the fixing of rubber components includes a certain amount of dry friction, nonlinear
effects can not be excluded which will give rise to superharmonic tones in the acoustic
response in the aircraft cabin. In order to analyse such effects, an analysis tool based
on a harmonic balance method was developed were the displacement fields and component
characteristics were expressed as series expansions and it was found that the
superharmonic response could be considerable.
Finally, an optimization procedure for shape and position of attached constrained
layer damping material (ADM) is developed. In the optimization procedure developed,
a modified gradient method is used in the finite element context to add small pieces
of ADM patches to an existing finite element mesh in order to maximize the benefit of
the attached material.