Multiscale optimisation of resonant frequencies for lattice-based additive manufactured structures

This paper introduces a novel methodology for the optimisation of resonant frequencies in three-dimensional lattice structures. The method uses a multiscale approach in which the homogenised material properties of the lattice unit cell are defined by the spatially varying lattice parameters. Material properties derived from precomputed simulations of the small scale lattice are projected onto response surfaces, thereby describing the large-scale metamaterial properties as polynomial functions of the small-scale parameters. Resonant frequencies and mode shapes are obtained through the eigenvalue analysis of the large-scale finite element model which provides the basis for deriving the frequency sensitivities. Frequency tailoring is achieved by imposing constraints on the resonant frequency for a compliance minimisation optimisation. A sorting method based on the Modal Assurance Criterion allows for specific mode shapes to be optimised whilst simultaneously reducing the impact of localised modes on the optimisation. Three cases of frequency constraints are investigated and compared with an unconstrained optimisation to demonstrate the algorithms applicability. The results show that the optimisation is capable of handling strict frequency constraints and with the use of the modal tracking can even alter the original ordering of the resonant mode shapes. Frequency tailoring allows for improved functionality of compliance-minimised aerospace components by avoiding resonant frequencies and hence dynamic stresses.

Automated summary

This paper introduces a novel methodology for optimizing resonant frequencies in three-dimensional lattice structures using a multiscale approach. Material properties derived from precomputed simulations of the small scale lattice are projected onto response surfaces to describe large-scale metamaterial properties as polynomial functions of the small-scale parameters. Resonant frequencies and mode shapes are obtained through eigenvalue analysis of the large-scale finite element model, with frequency tailoring achieved by imposing constraints on the resonant frequency for compliance minimization optimization. Through a sorting method based on the Modal Assurance Criterion, specific mode shapes can be optimized while reducing the impact of localized modes on the optimization. Three cases of frequency constraints are investigated and compared with an unconstrained optimization to demonstrate the algorithm's applicability, showing that strict frequency constraints can be handled and original ordering of resonant mode shapes can be altered with the use of modal tracking.