6. Choice and optimal layout of structures

As we stated in chapter , the simplest way to take damping into account when modeling a complex structure is to use the loss factor η. This is especially true when finite elements are used to model the system and calculate the dynamic behavior of the structure [3]. In this case, indeed, by using the factor η for material modeling, we arrive at an estimate of the overall damping of the structure, for each natural frequency of the complete structure.

If we want to calculate the damping of the s-th vibration mode, η _s , for a structure composed of N elements each with damping η ^e , we show that this can be approximated by :