Structural topology optimization of vibrating structures with specified eigenfrequencies and eigenmode shapes

In vibration optimization problems, eigenfrequencies are usually maximized in the optimization since resonance phenomena in a mechanical structure must be avoided, and maximizing eigenfrequencies can provide a high probability of dynamic stability. However, vibrating mechanical structures can provide additional useful dynamic functions or performance if desired eigenfrequencies and eigenmode shapes in the structures can be implemented. In this research, we propose a new topology optimization method for designing vibrating structures that targets desired eigenfrequencies and eigenmode shapes. Several numerical examples are presented to confirm that the method presented here can provide optimized vibrating structures applicable to the design of mechanical resonators and actuators.