Topology optimization design of Chladni patterns for vibration mode manipulability

Classical Chladni patterns (CPs) are visual representations of eigenvectors, which have a wide range of applications in vibration analysis, instrument design, particle manipulation and separation. Homogeneous structures often exhibit highly regular CPs, which limits their applicability. Application-oriented CPs are highly desired and can be achieved by inverse designs using topology optimization. This study presents an optimization method for designing prescribed CPs using density-based topological optimization. The optimization problem is formulated to minimize the error between the eigenvectors and the targeted CPs. Numerical results demonstrate that the proposed method can generate design configurations for a targeted CP. Moreover, it also can create novel structural configurations for the simultaneous control of several CPs. The presented method enables the precise customized design of CPs, which further provides more options for application-oriented requirements.