Optimization and realization of distributed vibration absorbers

Nowadays a lot of structures, like ships, aircrafts, wind turbines and engines are designed as light weight structures. They are susceptible to disturbances caused by vibrations and other mostly unwanted excitations. Hence the performance, lifetime and system behavior of the structures are negatively influenced. It is useful to equip systems with tuned vibration absorbers (TVA) to overcome these disadvantages. Attaching multiple distributed TVAs over the whole structure it is favorable to consider the interactions between them when deciding on adequate positions and designing parameters for these devices. An optimization of the positioning and the design parameters is necessary which take the dynamic behavior of the structure in combination with the effects of the TVAs into account. In this contribution optimization procedures are presented that perform the discrete positioning and the continuous parameter optimization for a number of vibration absorbers fixed to a truss structure. As an abstraction of complex light weight structures a 3D truss structure is considered and the designed optimization process is exemplarily shown. In a predefined frequency range of interest (between 130-170 Hz) four modes are present, the first bending mode, the phase shifted bending mode, the first torsional mode and one truss structure specific rhombic mode. For these modes four passive devices are applied to the structure. At first the positioning of the devices is carried out, as the optimal actuator placement is of great significance for the effectiveness of the vibration absorbers. The optimization problem is formed with controllability measures, which are maximized. This leads to an optimization problem with binary and continuous variables and linear matrix inequalities. In a second step, the parameters of the tuned vibration absorbers are optimized. The parameter optimization problem for the coupling of the structure and the vibration absorbers is formulated as a structured controller design problem. For this problem an approach is suggested, which maximizes the minimum damping ratio of the modes in a specified frequency range.