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Level set-based isogeometric topology optimization for maximizing fundamental eigenfrequency

Manman XU, Shuting WANG, Xianda XIE

《机械工程前沿（英文）》 2019年第14卷第2期页码 222-234 doi: 10.1007/s11465-019-0534-1

摘要： Maximizing the fundamental eigenfrequency is an efficient means for vibrating structures to avoid resonance and noises. In this study, we develop an isogeometric analysis (IGA)-based level set model for the formulation and solution of topology optimization in cases with maximum eigenfrequency. The proposed method is based on a combination of level set method and IGA technique, which uses the non-uniform rational B-spline (NURBS), description of geometry, to perform analysis. The same NURBS is used for geometry representation, but also for IGA-based dynamic analysis and parameterization of the level set surface, that is, the level set function. The method is applied to topology optimization problems of maximizing the fundamental eigenfrequency for a given amount of material. A modal track method, that monitors a single target eigenmode is employed to prevent the exchange of eigenmode order number in eigenfrequency optimization. The validity and efficiency of the proposed method are illustrated by benchmark examples.

关键词： topology optimization level set method isogeometric analysis eigenfrequency

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Shape and topology optimization for tailoring the ratio between two flexural eigenfrequencies of atomic force microscopy cantilever probe

Qi XIA,Tao ZHOU,Michael Yu WANG,Tielin SHI

《机械工程前沿（英文）》 2014年第9卷第1期页码 50-57 doi: 10.1007/s11465-014-0286-x

摘要：

In an operation mode of atomic force microscopy that uses a higher eigenmode to determine the physical properties of material surface, the ratio between the eigenfrequency of a higher flexural eigenmode and that of the first flexural eigenmode was identified as an important parameter that affects the sensitivity and accessibility. Structure features such as cut-out are often used to tune the ratio of eigenfrequencies and to enhance the performance. However, there lacks a systematic and automatic method for tailoring the ratio. In order to deal with this issue, a shape and topology optimization problem is formulated, where the ratio between two eigenfrequencies is defined as a constraint and the area of the cantilever is maximized. The optimization problem is solved via the level set based method.

关键词： atomic force microscopy cantilever probe eigenfrequency optimization