Structural Design Optimization of Vibration Isolating Structures

The design of high performance instruments often involves the attenuation of poorly damped resonant modes. These resonant modes are a limiting factor to the performance of these instruments. Current design approaches typically start from a baseline design and introduce stiffening or damping reinforce- ments to tune and/or damp these modes. However, the influence on the structural damping of these reinforcements is difficult to predict and often results in trial and error-based design approaches for the design of damping reinforcements. A common solution is to introduce viscoelastic material in baseline designs to increase structural damping. These materials dissipate energy when subjected to deformation and should therefore be located at positions which undergo large deformations during vibration. Typically, the viscoelastic material is placed in conventional (un)constrained layer damping configurations. However, to achieve optimized damping characteristics both the location as well as the geometry of viscoelastic material should be optimized. In this thesis, a multi-material topology optimization routine is presented as a systematic method- ology to develop structures with optimal damping characteristics. The proposed method applies a multi-material, parametric level set-based approach to simultaneously distribute structural and vis- coelastic material within the design domain. The developed optimization routine allows for the design of freeform, viscoelastic dampers without the limitation to conventional (un)constrained layer damp- ing configurations and is thereby able to achieve improved damping characteristics. The structural loss factor is applied as a performance measure to compare the damping between different viscoelastically damped structures and as objective function during the optimization. The viscoelastic material behavior is represented by a complex-valued material modulus, which results in a complex-valued eigenvalue problem. The formulation of the structural loss factor is modified to account for the complex-valued eigensolutions, resulting in accurate assessment of the structural loss factor for designs containing viscoelastic material with high material loss factors. The optimization routine maximizes the structural loss factor for single or multiple selected eigen- modes. An adjoint sensitivity analysis is performed to provide an exact expression for the structural loss factor sensitivity. Based on this sensitivity information, the optimization routine is able to de- velop structures with optimized loss factors for the specified eigenmodes. The method is also able to generate damping solutions for existing designs containing badly damped resonant modes.Precision and Microsystems EngineeringMechanical, Maritime and Materials Engineerin