Model reduction and substructuring for computing responses of structures containing frequency-dependent viscoelastic materials

It is well known that adding viscoelastic materials (VEM) in a vibrating structure reduces its resonance amplitudes through dissipation of a part of its vibration energy into heat. This is the basement of many passives damping treatments, such as constrained viscoelastic layers. They have been widely implemented in the automotive industry and have proven to be effective. Nevertheless, in order to design smart passive damping systems, there is still a need for finite element models capable of predicting the frequency response of structures containing VEM. We address in this paper the problem of local frequency-dependent VEM treatment in the finite element vibration analysis of large automotive structures. For reducing the prohibitive direct response's computing time, we propose to use Component Mode Synthesis where the elastic and viscoelastic components are reduced using a modified MacNeal method. The components are then coupled using an approach that eliminates the junction degrees of freedom. The small size of the complex reduced system allows to compute quickly the frequency responses of the damped structure.