Numerical tools such as topology optimization (TO) have seen large development in both academic and industrial settings, enabling the optimization of structural objectives and/or attributes, subject to a wide range of constraints, pertinent to the engineering and design problems of automotive and aerospace industries. Classical TO methods assume the use of a single material (SMTO), however, a recent and important advancement in this field is that of multi-material topology optimization (MMTO), capable of simultaneous material existence and selection optimization. This is of heightened importance in the aforementioned industries, where many costly engineering materials can be used, but their selection is delegated to engineer experience. Consideration of modal characteristics (i.e., natural frequencies) in MMTO efforts have seen marginal development in recent years, yet is vital to both industries, who’s products are each subject to uncontrolled environments and vibratory motion. Where frequency has been considered in MMTO, mathematical frameworks require the usage of model attributes that are not extractable from commercial finite element analysis (FEA) solvers, leading to reduced computational efficiency. This paper presents an advancement of the frequency-constrained MMTO sensitivities previously utilized in SMTO, enabling the use of commercial solvers, thus inheriting computational improvements. A derivation of sensitivities, a detailed discussion, and analysis of two case studies have been included, so as to provide the reader with a sound understanding of the nature of the constraint sensitivities, and how they may be able to intuit results.
