Material microstructure topology optimization of piezoelectric composite beam under initial disturbance for vibration suppression

This study proposes a material microstructure topology optimization model for a piezoelectric composite beam subject to initial disturbance. The optimization model is built through the Solid Isotropic Material with Penalization interpolation subject to the material volume fraction on the microlevel. And the objective function is to minimize the time integral about local structural response. By introducing the Lyapunov second equation, this time integral is simplified and does not need any numerical integration technique. It can also be used to measure the global vibration response instead of short time gap. Besides, different objectives such as a regional structural response can also be obtained by only changing the weight matrix form. And the sensitivity of the objective function with respect to the design variables are also deduced by solving the Lyapunov equation. A bidirectional evolutionary structural optimization algorithm is used to acquire the optimal results. Four numerical examples including multiphase material microstructure topology optimization verify the developed method that can effectively suppress local structural vibration level and obtain lighter structure.