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In this paper, a multi-scale modeling approach is proposed to determine the undamped natural frequencies of lattice structures (LSs) and the related mode shapes. At the macroscopic scale, the LS is modeled as an equivalent homogenized medium whose elastic properties are determined through the strain energy-based homogenization technique. The accuracy of the finite element (FE) model of the homogenized continuum (denoted  as low-fidelity FE model ) in predicting the undamped natural frequencies and the associated modes is assessed by comparing them to those provided by a high-fidelity FE model of the real architecture of the LS (wherein all the geometrical features of the LS are explicitly modeled). In this context, the influence of the number of representative volume elements (RVEs) to be considered at the macroscopic scale on the relative error on the natural frequencies, resulting from both FE models of the LS, is investigated. Moreover, the influence of the geometrical imperfections induced by the additive manufacturing technology on the accuracy of the low-fidelity FE model is also investigated. These analyses are carried out for different topologies of LS taken from the literature. Results highlight that the accuracy of the low-fidelity FE model in predicting the undamped natural frequencies and their related mode shapes mainly depends upon the LS RVE topology and on the number of RVEs considered at the macroscopic scale.

On the accuracy of a homogenized continuum model of lattice structures in modal analyses