薄板结构低噪声仿生拓扑优化方法

摘要/Abstract

摘要： 针对薄板结构的低噪声设计问题，以结构声辐射功率最小化为优化目标，借鉴植物脉序分枝结构的构型特征，提出了薄板结构加强筋布局的仿生拓扑优化方法。以结构应变能最小和释放局部最大剪应力作为加强筋主脉和次脉的生长准则，以广义Murray准则作为加强筋脉序的分歧准则，构造了具有脉序分级特征的加强筋自适应生长算法。以固支薄板结构的横向弯曲振动及声辐射问题为典型算例，对比分析了仿脉序分布加筋板结构的声辐射功率和振动功率流的分布特性。数值结果表明，与相同体积约束下的正交加筋布局方式相比，仿脉序分布加筋方法使薄板结构具有更优的声振特性，进而验证了薄板结构加强筋仿生布局降噪方法的有效性与可靠性。

关键词: 仿生设计, 加强筋布局, 拓扑优化, 薄板结构, 低噪声

Abstract: Aimed at minimizing the acoustic radiation power of thin plates for noise reduction, a bionic approach of topology optimization was presented to address stiffeners layout of thin plates by co-opting the characteristic configuration of botanic venation branched structures. A primary vein growth of stiffeners was governed by minimal strain energy while a secondary vein growth of ones by releasing maximal shear stress. At each junctions, leaf veins were adjusted according to the general Murray criterion. Consequently an adaptive growth algorithm of stiffeners was established featured with hierarchical structure like leaf vein. Exemplifying the transverse bending vibration and resulting acoustic radiation for clamped thin plates, the acoustic radiation power and the distribution of vibrational power flow were analysed respectively for thin plates with stiffeners layout imitating botanic venation. The numerical results show that the stiffeners layout method to imitating botanic venation is superior to the orthogonal stiffeners layout method in vibro-acoustic characteristics subjected to the same volume constraints for stiffeners. Therefore the bionic layout method of stiffeners to noise reduction is valid or feasible for thin plates.

Key words: bionic design, stiffer layout, topology optimization, thin plate structure, low noise

中图分类号:

TB532

滕晓艳, 江旭东, 史冬岩. 薄板结构低噪声仿生拓扑优化方法[J]. 中国机械工程.

Teng Xiaoyan, Jiang Xudong, Shi Dongyan. A Bionic Approach of Topology Optimization to Low Noise for Thin Plates[J]. China Mechanical Engineering.

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