The design of high performance instruments often involves the attenuation of poorly damped resonant modes. Current design practices typically rely on informed trial and error based modifications to improve dynamic performance. In this article, a multi-material topology optimization approach is presented as a systematic methodology to develop structures with optimal damping characteristics. The proposed method applies a multi-material, parametric, level set-based topology optimization to simultaneously distribute structural and viscoelastic material to optimize damping characteristics. The viscoelastic behavior is represented by a complex-valued material modulus resulting in a complex-valued eigenvalue problem. The structural loss factor is used as objective function during the optimization and is calculated using the complex-valued eigenmodes. An adjoint sensitivity analysis is presented that provides an analytical expression for the corresponding sensitivities. Multiple numerical examples are treated to illustrate the effectiveness of the approach and the influence of different viscoelastic material models on the optimized designs is studied. The optimization routine is able to generate designs for a number of eigenmodes and to attenuate a resonant mode of an existing structure.

The design of high performance instruments often involves the attenuation of poorly damped resonant modes. Current design methods typically rely on informed trial and error based modifications to improve dynamic performance. In this contribution, we present a multi-material topology optimization as an alternative, systematic methodology to design structures with optimized damping characteristics. A parametric, level set-based topology optimization is employed to simultaneously distribute structural and viscoelastic material to optimize the structure’s damping characteristics. To model the viscoelastic behavior a complex-valued material modulus is applied. The structural loss factor is determined from the complex-valued eigensolutions and its value is maximized during the optimization. We demonstrate the performance of the optimization by maximizing the damping of a cantilever beam.