两相材料结构低噪声设计理论与优化方法研究
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摘要
结构振动声辐射是噪声的主要来源,随着人们对生存环境噪声问题关注度的增加,结构振动噪声控制技术越来越受到重视。经过数十年的相关研究,传统的噪声控制技术已经发展到一个成熟阶段,继续发展的空间已经非常小,因此需要更有效的设计方法来解决结构噪声辐射控制问题。两相材料结构正逐渐成为减振降噪领域一个新的研究方向,研究两相材料结构低噪声设计理论和优化方法,将结构声辐射问题融入到产品设计中,使振动结构成为一个弱辐射体,成为解决结构低频噪声问题的根本方法。
本文分析了国内外结构声辐射理论与优化设计方法的研究现状,将结构动力学、声学和优化等学科融为一体,从噪声源的角度出发,将结构声辐射作为一项指标融入到产品设计阶段,对两相材料结构低噪声设计理论与优化方法进行了深入的研究。建立了基于格林函数的外部声辐射问题的预测模型,对多频激励下结构声辐射理论进行了研究,提出了两相材料结构各向正交惩罚材料密度法(SIMP)插值模型,建立了关于结构辐射声功率的声学设计灵敏度分析模型,提出了基于拓扑优化方法的结构低噪声设计方法,最后对所提出方法的有效性进行了试验验证。
本文主要在以下几个方面进行了相关的研究：
对外部声辐射问题在三维空间的Helmholtz边界积分方程做了基本回顾,提出了采用非等参单元变换解决积分方程奇异性问题,给出了角点系数的数值计算方法,同时针对解的非唯一性问题采用CHIEF方法做出了相应处理,最后应用高斯积分方法,给出了Helmholtz边界积分方程的数值计算方法。
提出了声阻抗矩阵的概念,对多频激励下结构声辐射理论以及声学灵敏度分析进行了研究。建立了关于辐射声功率的声学设计灵敏度分析模型,并将其表示为结构动力学灵敏度和阻抗矩阵灵敏度两部分,以简支薄板为例通过数值算例详细分析了结构辐射声功率关于激励频率、薄板厚度等设计变量的声学设计灵敏度,给出了结构声学设计灵敏度的变化趋势,为产品的低噪声设计提供优化方向和量化依据。
对两相材料插值理论和算法进行了研究,在单相材料结构SIMP插值模型的基础上,提出了两相材料结构SIMP插值模型,推导了基于两相材料结构SIMP插值理论的优化准则算法,并以此为基础,建立了两相材料结构单约束问题的拓扑优化模型,分析讨论了不同优化参数对最终拓扑优化结果的影响,数值结果表明,通过合理选择各个优化参数能够得到理想的拓扑优化结果。
提出了基于拓扑优化理论的两相材料结构低噪声设计方法,以结构单元的体积密度为设计变量,以结构表面辐射声功率最小为设计目标,建立了两相材料结构声辐射问题的拓扑优化模型,数值结果表明优化结果具有弱辐射特性,中低频段的降噪效果尤为明显。
对本文所提出的结构低噪声设计方法进行试验研究,通过与数值计算结果的对比,验证了本文所提出的两相材料结构低噪声设计理论和优化方法的有效性,同时展示了该方法在实际中的可行性。
Structure noise is one of the main noise sources. With more and more concerned about the living environment noise, noise and vibration control technology attracts more attention. After decades of research, traditional noise control technology has been developed to a mature stage and has little development space. So it is necessary to develop a more effective noise control technology. A bi-material structure is becoming a new research direction in noise and vibration reduction field. A bi-material low noise design theory and method will be the fundamental method to solve the problem of structure noise.
This paper analyzes the domestic and international development on sound radiation theory and optimization design methods. The method links the disciplines of structural dynamics, acoustics and optimization into a unified methodology. The structural sound radiation is taken into the product design stage as a design index. A bi-material low noise design theory and method has been researched in-depth.
The external sound radiation prediction model based on the green function is established. Theory of acoustic radiation under multi-frequency excitation has been studied, and an acoustic design sensitivity analysis method and Two-materials SIMP (the Solid Isotropic Material with Penalization) material interpolation model are given. Using topology optimization method, a bi-material low noise design theory and method is presented. The proposed theory and optimization method about bi-material structure low noise design is validated by testing method.
This paper studied the following particular aspects:
A detailed derivation of external sound radiation boundary element method based on the second Green equation is presented. The numerical method for calculating corners' coefficient is presented, facilitating numerical computation. Non-isoparametrical element transformation is given to deal with function singular integration. Gauss numerical integration method for solving the equations is given, while CHIEF method is simultaneously implemented to deal with the nonuniqueness of Helmholtz integral equation.
Acoustic impedance matrix is introduced for studying the sound radiation theory under multi-frequency excitation and acoustic sensitivity analysis. The model of acoustic sensitivity subjected to the sound power is established. The sound radiation can be translated to the analysis of structure dynamic sensitivity and impedance matrix sensitivity. Taking a simple supported plate as a example, the trend of the acoustic sensitivity is given. It provides direction for structure low noise design.
Bi-matrial interpolation theory, algorithm and model based on SIMP are given. Then topological optimization model of continuous structure with single constraint for minimal compliance is presented. Discussion is given for the topological optimization result using different optimization parameters. The numerical results shows, ideal topological results can be obtained through properly selecting individual optimization parameters.
A study of low noise design method about bi-material structure based on the topology optimization theory is given. The element volume density and minimization of sound power are taken as design variable and design objective function respectively. Numerical results show that the optimization result possess low radiation property. The structural low noise design method proposed in this chapter provides a set of product design method for acoustic designers.
Experimental study of the proposed method is given and compared with numerical results. The proposed theory and optimization method about bi-material structure low noise design is validated.
本文分析了国内外结构声辐射理论与优化设计方法的研究现状,将结构动力学、声学和优化等学科融为一体,从噪声源的角度出发,将结构声辐射作为一项指标融入到产品设计阶段,对两相材料结构低噪声设计理论与优化方法进行了深入的研究。建立了基于格林函数的外部声辐射问题的预测模型,对多频激励下结构声辐射理论进行了研究,提出了两相材料结构各向正交惩罚材料密度法(SIMP)插值模型,建立了关于结构辐射声功率的声学设计灵敏度分析模型,提出了基于拓扑优化方法的结构低噪声设计方法,最后对所提出方法的有效性进行了试验验证。
本文主要在以下几个方面进行了相关的研究：
对外部声辐射问题在三维空间的Helmholtz边界积分方程做了基本回顾,提出了采用非等参单元变换解决积分方程奇异性问题,给出了角点系数的数值计算方法,同时针对解的非唯一性问题采用CHIEF方法做出了相应处理,最后应用高斯积分方法,给出了Helmholtz边界积分方程的数值计算方法。
提出了声阻抗矩阵的概念,对多频激励下结构声辐射理论以及声学灵敏度分析进行了研究。建立了关于辐射声功率的声学设计灵敏度分析模型,并将其表示为结构动力学灵敏度和阻抗矩阵灵敏度两部分,以简支薄板为例通过数值算例详细分析了结构辐射声功率关于激励频率、薄板厚度等设计变量的声学设计灵敏度,给出了结构声学设计灵敏度的变化趋势,为产品的低噪声设计提供优化方向和量化依据。
对两相材料插值理论和算法进行了研究,在单相材料结构SIMP插值模型的基础上,提出了两相材料结构SIMP插值模型,推导了基于两相材料结构SIMP插值理论的优化准则算法,并以此为基础,建立了两相材料结构单约束问题的拓扑优化模型,分析讨论了不同优化参数对最终拓扑优化结果的影响,数值结果表明,通过合理选择各个优化参数能够得到理想的拓扑优化结果。
提出了基于拓扑优化理论的两相材料结构低噪声设计方法,以结构单元的体积密度为设计变量,以结构表面辐射声功率最小为设计目标,建立了两相材料结构声辐射问题的拓扑优化模型,数值结果表明优化结果具有弱辐射特性,中低频段的降噪效果尤为明显。
对本文所提出的结构低噪声设计方法进行试验研究,通过与数值计算结果的对比,验证了本文所提出的两相材料结构低噪声设计理论和优化方法的有效性,同时展示了该方法在实际中的可行性。
Structure noise is one of the main noise sources. With more and more concerned about the living environment noise, noise and vibration control technology attracts more attention. After decades of research, traditional noise control technology has been developed to a mature stage and has little development space. So it is necessary to develop a more effective noise control technology. A bi-material structure is becoming a new research direction in noise and vibration reduction field. A bi-material low noise design theory and method will be the fundamental method to solve the problem of structure noise.
This paper analyzes the domestic and international development on sound radiation theory and optimization design methods. The method links the disciplines of structural dynamics, acoustics and optimization into a unified methodology. The structural sound radiation is taken into the product design stage as a design index. A bi-material low noise design theory and method has been researched in-depth.
The external sound radiation prediction model based on the green function is established. Theory of acoustic radiation under multi-frequency excitation has been studied, and an acoustic design sensitivity analysis method and Two-materials SIMP (the Solid Isotropic Material with Penalization) material interpolation model are given. Using topology optimization method, a bi-material low noise design theory and method is presented. The proposed theory and optimization method about bi-material structure low noise design is validated by testing method.
This paper studied the following particular aspects:
A detailed derivation of external sound radiation boundary element method based on the second Green equation is presented. The numerical method for calculating corners' coefficient is presented, facilitating numerical computation. Non-isoparametrical element transformation is given to deal with function singular integration. Gauss numerical integration method for solving the equations is given, while CHIEF method is simultaneously implemented to deal with the nonuniqueness of Helmholtz integral equation.
Acoustic impedance matrix is introduced for studying the sound radiation theory under multi-frequency excitation and acoustic sensitivity analysis. The model of acoustic sensitivity subjected to the sound power is established. The sound radiation can be translated to the analysis of structure dynamic sensitivity and impedance matrix sensitivity. Taking a simple supported plate as a example, the trend of the acoustic sensitivity is given. It provides direction for structure low noise design.
Bi-matrial interpolation theory, algorithm and model based on SIMP are given. Then topological optimization model of continuous structure with single constraint for minimal compliance is presented. Discussion is given for the topological optimization result using different optimization parameters. The numerical results shows, ideal topological results can be obtained through properly selecting individual optimization parameters.
A study of low noise design method about bi-material structure based on the topology optimization theory is given. The element volume density and minimization of sound power are taken as design variable and design objective function respectively. Numerical results show that the optimization result possess low radiation property. The structural low noise design method proposed in this chapter provides a set of product design method for acoustic designers.
Experimental study of the proposed method is given and compared with numerical results. The proposed theory and optimization method about bi-material structure low noise design is validated.
引文
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