Abstract
This work is focused on the topology optimization of structures that are subjected to harmonic force excitation with prescribed frequency and amplitude. As an important objective of such a design problem, the natural resonance frequency of the structure is driven far away from the prescribed excitation frequency for the purpose of avoiding resonance and reducing the vibration level. Therefore when the excitation frequency is higher than the natural resonance frequency of the structure, the natural resonance frequency will decrease, then the optimum topology configuration will be distorted with large amount of gray elements. A MAC (Modal Assurance Criteria) based excitation frequency increasing method is proposed to obtain a desired configuration. MAC is adopted here to track the natural resonance frequency which can provide the baseline reference for the current excitation frequency during the optimum iterative procedure. Then the excitation frequency increases progressively up to its originally prescribed value. By means of numerical examples, the proposed formulation can generate effective topology configurations which can avoid resonance.
Highlights
Topology optimization has been recognized as an effective approach to figure out the structure layout during the conceptual design phase since the original idea of homogenization-based design method was proposed [1]
Correlative researches in the field were mainly focused on two types of problems: one is topology optimization related to dynamic characteristics, the other is related to dynamic responses
Natural frequencies and mode shapes are two major optimization objects in topology optimization related to dynamic characteristics
Summary
Topology optimization has been recognized as an effective approach to figure out the structure layout during the conceptual design phase since the original idea of homogenization-based design method was proposed [1]. Olhoff and Du [15] minimized the dynamic compliance of structure subject to harmonic loads, optimization results show that when the natural resonance frequency of the initial structure is less than the given excitation frequency, the natural resonance frequency will decrease and the static compliance of the structure will increase very quickly. He started out the design with a small value of excitation frequency and sequentially increased the value up to its prescribed value. The limit value of the natural resonance frequency can be estimated to distinguish low-frequency and high-frequency
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