Dynamic topology optimization of plate for vibration suppression

Abstract

Structural vibration control has always received considerable attentions for the unpleasant motions and environmental noise pollutions. Engineers and researchers have been looking for the more suitable and efficient methods to reduce structural vibration. Topology optimization method, as one design tool which could provide designers a design space with substantially more freedoms than size and shape optimization, has the potential to solve the long-standing problems. Stemming from this idea, the aim of this project is to apply topology optimization method to structural attenuation design.

In this thesis, the optimal distribution of damping material on vibrating structures by using topology optimization method has been investigated. Four topology optimization models for bi-material plate, free damping layer plate and constrained damping layer plate are established respectively to achieve structure vibration suppression design. In the bi-material case, both the sensitivity expressions for power flow response and dynamic compliance are derived. The comparison of these two objective functions illustrates minimization of power flow response also has great effect on the vibration suppression. In free damping layer plate topology optimization case, by comparing the optimal topology pattern with the steady-state responses of the structure, a rapid strategy to obtain a feasible damping material layout is proposed. Also in this research, an interface finite element is introduced to build the viscoelastic layer of constrained damping layer which reduces the computation cost of optimization procedure in constrained damping layer plate topology optimization case. One conclusion can be drawn that a better performance of vibration suppression can be achieved by increasing the thickness of viscoelastic layer or constrained layer. But with the increase of thickness of the constrained layer, the vibration amplitude decrease continuously while the same phenomenon is not that obvious for viscoelastic layer. The relationship between the constrained damping patch distribution and mode shape of the structure is also discovered in this case. In addition, a convenient implementation framework written by Python is developed for implement topology optimization method in Abaqus. Further extensions such as new topology optimization model, new objective functions and different optimizers could be easily built.

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Identifiers

ORCID for Yeping Xiong: orcid.org/0000-0002-0135-8464

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