A Topology Optimization Problem in Control of Structures Using Modal Disparity

Modal disparity and a topology optimization problem seeking to maximize this disparity are introduced, with the goal of developing a new methodology for control of vibration in flexible structures. Modal disparity is generated in a structure by the application of external forces that vary the stiffness of the structure. When the forces are switched on and off and, as a result, the structure is switched between two stiffness states, modal disparity results in vibration energy being transferred from a set of not-controlled modes to a set of controlled modes. This allows the vibration of the structure to be completely attenuated by removing energy only from a small set of controlled modes. A topology optimization problem determines the best locations for application of the external forces. Simulation results are presented to demonstrate control of vibration exploiting modal disparity in two three-dimensional (3D) frame structures.