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DINAME 2017
XVII International Symposium on Dynamic Problems of Mechanics
A COMPONENT MODE SYNTHESIS APPROACH FOR DYNAMIC ANALYSIS OF ELASTOMER DAMPING DEVICES
Submission Author:
Jean-François Deü , France , France
Co-Authors:
Jean-François Deü
Presenter: Jean-François Deü
doi://10.26678/ABCM.DINAME2017.DIN17-0179
Abstract
Due to their capacities to dissipate energy, elastomers are highly used in damping devices like silent blocs or joints. A typical example of this use is found in the spatial industry: during takeoff and flight, launchers are subject to a significant amount of vibrations from either the propulsion engine or the acoustical environment. Shocks may also occur during the pyrotechnic separation of the different floors of the launcher. All these vibration sources may damage the satellite or any other sensitive equipment onboard, and a common solution is to use viscoelastic damping devices to dissipate a part of the mechanical energy. The design of theses damping devices is usually done by using finite element codes. The computational cost of the associated models may become prohibitive for example during an optimization process. Many solutions already exist to reduce the numerical model of linear undamped structures, but only a few give access to reduced order models with damping behavior, especially when it comes from viscoelasticity which may be seen as a strong form of damping. Two types of solutions for the reduction of viscoelastic models can be found in the literature. The first one consists in the replacement of the damping device model by an equivalent rheological model which can be identified through a series of experimental measurements on the damper. The main problem with this approach is that the behavior of the rheological model may not fit the real behavior of the damper in all directions, and more importantly necessitate experimental identification for each new device and consequently can’t be used for optimization purpose. The second one, which is chosen in this work, is to use a FE model of the damper and to achieve the reduction using a substructuring based for example of the Craig-Bampton method [1]. The original Craig-Bampton method uses a combination of static and dynamic modes to reduce the finite element model of a sub-structure to a smaller finite element model called super-element. Here we propose a modified Craig-Bampton method taking into account the frequency dependence of the mechanical properties. This approach, based upon the work of Rouleau [2], consists in choosing a modal projection basis well adapted to highly damped structures. Moreover, the super-element is obtained by considering that the device’s interfaces are much more rigid than the rubber core. To make use of this difference, a kinematical constraint is employed to enforce rigid body motion of the sub-structure interfaces [3]. The combination of all these techniques leads to a twelve dofs super element (three rotations and three translations per face) replacing the initial full model. As an application, the dynamic response of a structure supported by four hourglass shaped rubber devices under harmonic loads is analyzed to show the efficiency of the proposed approach. [1] R.R. Craig and M.C.C. Bampton. Coupling of substructures for dynamic analysis. AIAA Journal, vol. 6, issue 7, pp.1313-1319, 1968. [2] L. Rouleau, J.-F. Deü, A. Legay. Review of reduction methods based on modal projection for highly damped structures. 11th World Congress on Computational Mechanics, WCCM XI, Barcelona, Spain, July 20-25, 2014. [3] J.-F. Deü, B. Morin, A. Legay, L. Rouleau. Predictive numerical models for non-linear dynamic behavior of elastomer damping devices. 13th U.S. National Congress on Computational Mechanics, USNCCM 13, San Diego, California, USA, July 27-30, 2015.
Keywords
damping, viscoelasticity, substructuring approach, reduced order model
