# Dynamic analyses of structures with applied rubber

[Doktorsavhandling]

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.

**Nyckelord: **Fractional calculus, Viscoelasticity, Series expansion, Optimization, Finite

Denna post skapades 2007-01-15. Senast ändrad 2013-09-25.

CPL Pubid: 25620