A novel interval dynamic topology optimization methodology of piezoelectric structures under reliable active control

In this paper, considering the influence of uncertainties in piezoelectric intelligent structures with active vibration control law, a robust topology optimization method to reduce the sensitivity of structural dynamic flexibility to uncertainty factors for piezoelectric intelligent structures is proposed. The effect of active control can be equivalent to the damping. Considering the influence of uncertainty, the structural dynamic response of the system will be within the interval range. Due to the monotonicity of the steady-state displacement response on uncertain parameters and the monotonicity of dynamic flexibility on uncertain parameters are both difficult to determine, a more accurate upper and lower limit is obtained using the collocation method. With the constraints of reliability and volume, the robustness index is defined based on the dynamic flexibility of the structure and defined as the objective function to establish the robust topology optimization model. In terms of optimization solution, the reliability index is transformed into the constraint translation distance. The sensitivity of constraint functions and objective functions to design variables is derived by employing the chain derivative method and the adjoint vector method. Finally, two examples are used to verify the effectiveness of the proposed method.