TOPOLOGY OPTIMIZATION OF PIEZO-EMBEDDED COMPLIANT MECHANISM CONSIDERING FUNTAMENTAL FREQUENCY CONSTRAINTS

With the widespread application of piezoelectric compliant mechanisms in high-frequency vibration environments such as aerospace engineering and precision machining, there is an urgent need to develop a topology optimization method for designing piezoelectric compliant mechanisms with large strokes and high-frequency responses. Current topology optimization methods for compliant mechanisms primarily focus on improving the output stroke while neglecting their dynamic characteristics. In this paper, a topology optimization method for piezo-embedded compliant mechanisms is proposed, which considers both output stroke and dynamic characteristics. First of all, to more accurately describe the interaction between the piezoelectric actuator and the compliant mechanism, the piezoelectric actuator is directly coupled into the analysis model by establishing a mechanical-electrical coupling optimization analysis model for the piezo-embedded compliant mechanism. Secondly, based on the density-based method, a topology optimization method of piezo-embedded compliant mechanisms, considering the fundamental frequency constraint, is established with the aim of maximizing the output stroke of the mechanism. The p-norm approximation function is adopted to alleviate the non-differentiability issue arising from repeated eigenvalues and mode switching during the iterative process. Furthermore, using the adjoint method and chain derivation method, the sensitivities of the objective function and constraints with respect to design variables are derived. Finally, several numerical examples are provided to verify the effectiveness of the proposed optimization method and to demonstrate the influence of fundamental frequency constraints on the optimized results. Numerical results show that the proposed method can achieve a stable iterative process, fast convergence, and effectively provide a high output stroke design while satisfying fundamental frequency constraints. Compared to the optimized results that solely maximize output displacement, the configurations of the optimized designs obtained through the proposed method are notably different. As the fundamental frequency constraint increases, the fundamental frequency of the optimized designs correspondingly rises, while the output displacement decreases.