Multi-material topology optimization of viscoelastically damped structures using a parametric level set method

Journal article (2017)

Authors

M. van der Kolk Computational Design and Mechanics - Mechanical, Maritime and Materials Engineering
G.J. van der Veen Computational Design and Mechanics - Mechanical, Maritime and Materials Engineering
Matthijs Langelaar Computational Design and Mechanics - Mechanical, Maritime and Materials Engineering
Research Group
Computational Design and Mechanics (Mechanical, Maritime and Materials Engineering) (TU Delft)
Modal analysis Topology optimization Level set method Multi-material optimization Loss factor Constrained layer damping Viscoelastic damping
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Published Date

2017

Language

English

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Faculty

Mechanical, Maritime and Materials Engineering

Department

Precision and Microsystems Engineering

Research Group

Computational Design and Mechanics

Abstract

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.