声学—结构灵敏度及结构—声学优化设计研究
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摘要
声学-结构灵敏度是振动声学指标对结构参数的变化率，该值对结构降噪有重要意义，是设计低噪声结构的重要内容之一；基于声学-结构灵敏度的结构-声学优化可设计出最优的低噪声结构，是结构声学设计追求的目标之一。结构降噪设计是车辆、航空、航海及一般工业中的重要设计内容之一，可改善乘坐的舒适性及产品的竞争力，声学-结构灵敏度和结构声学优化设计可为相关工程中的结构降噪提供定量和最优的设计方法。本文研究的目的是基于声学-结构灵敏度，开发一种有效的、通用的结构-声学优化设计方法。
本文论述了结构-声学仿真的有限元法、边界元法原理，比较了有限元法与边界元法的优缺点，概述了有限元法、边界元法在结构-声学仿真中的应用，讨论了声学-结构灵敏度及结构-声学优化设计的研究历史与现状。基于结构-声学仿真的有限元法和边界元法推导了响应声压、声功率对结构参数的灵敏度，基于敏度信息建立了结构声学优化的数学模型，用可行方向法对结构声学指标进行了优化设计研究，给出了研究算例。
论文完成的主要工作有：基于有限元法，分析推导了振动响应位移和响应速度对壳厚度的灵敏度，通过实例分析了位移灵敏度和速度灵敏度的关系。速度灵敏度是声学-结构灵敏度计算中所必需的，也是结构振动优化的先决条件；基于有限元直接法计算结构振动响应及响应速度对壳厚度的灵敏度，基于边界元法计算了结构声学响应及响应声压、声功率对振动速度的灵敏度，联合两个灵敏度计算了声学指标对结构参数的灵敏度；追求声学指标最小化，建立了减小结构振动速度的优化设计数学模型，对振动结构进行了振动速度最小化设计研究。通过对结构优化前和优化后的边界元声学分析，定量分析了振动优化后的降噪效果；基于结构-声场耦合系统的有限元法，分析推导了结构-声场耦合系统特征值灵敏度的计算方法；基于结构-声场耦合系统的有限元法，分析推导了结构-声场耦合系统声学响应的计算方法，用模态叠加法分析推导了响应声压对结构参数的灵敏度；基于结构-声场耦合系统的有限元法，建立了结构-声学优化的数学模型；基于响应声压对结构参数的灵敏度信息，用可行方向法对响应声压、结构重量分别进行了单目标优化设计研究和多目标优化设计研究；分别用有限元法、边界元法分析推导了内场、外场声学频率响应函数的计算方法，基于随机振动的基本理论，分析推导了随机载荷激励下结构随机声场的计算方法，用可行方向法对响应声压谱密度进行了优化设计研究。
上述工作得出以下结论：1．结构振动位移敏度与振动速度敏度的关系与振动位移和振动速度的关系一致，即从幅值上看后者是前者的ω倍；2．声学-结构灵敏度随激励频率的增大而增大，在结构系统模态频率处出现峰值，可根据灵敏度信息直接修改结构以降低噪声，也可用于对结构进行声学优化设计研究；3．结构-声学优化可在结构重量相对不变的
Acoustic-structure sensitivity is a change rate of response acoustic pressure with respect to structure design parameters, it has the vital significant to the structure noise reduction, and it is one in the design contents of quiet structure; structure-acoustic optimization based on Acoustic-structure sensitivity may design the most superior low noise structure, and it is one of goals of structure-acoustics design. The acoustic design for vehicle, ship, plane and ordinary industry is very important to improve the carborne acoustic comfort and to enhance competitiveness for the products in market, the Acoustic-structure sensitivity and the structure-acoustic optimization can provide a ration and optimum design method for the vibration structure. The objective of this fundamental study is to develop effective ,general method for the noise reduction of vibration structure .
This paper discusses the fundamental theory of FEM and BEM for structure-acoustic numerical simulation, compares advantage and disadvantage for FEM and BEM, summarizes their application in structure-acoustic simulation, debates the research history and actuality for Acoustic-structure sensitivity and structure-acoustic optimization. The acoustic-structure sensitivity formulation basing on FEM and BEM is deduced and implemented, the mathmatical model of structure-acoustic sizing design optimization is established and achieved basing on acoustic- structure sensitivity by used of the the feasible direction method.
The main work in the thesis is as follows: Based on the FEM, the numerical analysis of Dynamics displacement Response, velocity Response and its Sensitivity is deduced and implemented for the plate vibration. The velocity Sensitivity of structure vibration with respect to structure parameters is essential to calculate the acoustic- structure sensitivity; The velocity sensitivity of vibration structure with respect to structure parameter, the response pressure and response acoustic power with respect to the normal velocity is carried out by using of FEM and BEM, respectively, and then these sensitivity were combined to obtain a acoustic- structure sensitivity; For purpose of minimizing structure noise, the mathematical model of the sizing design optimization for minimizing the vibrating velocity is established and performed. The acoustic radiation of structure vibration bas been studied by use of the BEM before optimization and after optimization, the results were compared for the former and the latter; Based on the FEM of the coupled acoustic-structure system, the sensitivity of eigenvalue is deduced and performed; Based on the FEM of the coupled acoustic-structure system, the acoustic response feature is deduced and performed, the modal superpose method of the acoustic-structure sensitivity is put forward and performed; Based on the FEM of the coupled acoustic-structure system, the mathematical model of the sizing design optimization for minimizing acoustic response, structure weight and the multi-object optimization is established and performed basing on acoustic-structure sensitivity by used of the feasible direction method; The acoustic transfer function simulated by a unit force is deduced and performed by used of FEM and BEM, respectively, and then acoustic response feature of the structure random vibration simulated by a
本文论述了结构-声学仿真的有限元法、边界元法原理，比较了有限元法与边界元法的优缺点，概述了有限元法、边界元法在结构-声学仿真中的应用，讨论了声学-结构灵敏度及结构-声学优化设计的研究历史与现状。基于结构-声学仿真的有限元法和边界元法推导了响应声压、声功率对结构参数的灵敏度，基于敏度信息建立了结构声学优化的数学模型，用可行方向法对结构声学指标进行了优化设计研究，给出了研究算例。
论文完成的主要工作有：基于有限元法，分析推导了振动响应位移和响应速度对壳厚度的灵敏度，通过实例分析了位移灵敏度和速度灵敏度的关系。速度灵敏度是声学-结构灵敏度计算中所必需的，也是结构振动优化的先决条件；基于有限元直接法计算结构振动响应及响应速度对壳厚度的灵敏度，基于边界元法计算了结构声学响应及响应声压、声功率对振动速度的灵敏度，联合两个灵敏度计算了声学指标对结构参数的灵敏度；追求声学指标最小化，建立了减小结构振动速度的优化设计数学模型，对振动结构进行了振动速度最小化设计研究。通过对结构优化前和优化后的边界元声学分析，定量分析了振动优化后的降噪效果；基于结构-声场耦合系统的有限元法，分析推导了结构-声场耦合系统特征值灵敏度的计算方法；基于结构-声场耦合系统的有限元法，分析推导了结构-声场耦合系统声学响应的计算方法，用模态叠加法分析推导了响应声压对结构参数的灵敏度；基于结构-声场耦合系统的有限元法，建立了结构-声学优化的数学模型；基于响应声压对结构参数的灵敏度信息，用可行方向法对响应声压、结构重量分别进行了单目标优化设计研究和多目标优化设计研究；分别用有限元法、边界元法分析推导了内场、外场声学频率响应函数的计算方法，基于随机振动的基本理论，分析推导了随机载荷激励下结构随机声场的计算方法，用可行方向法对响应声压谱密度进行了优化设计研究。
上述工作得出以下结论：1．结构振动位移敏度与振动速度敏度的关系与振动位移和振动速度的关系一致，即从幅值上看后者是前者的ω倍；2．声学-结构灵敏度随激励频率的增大而增大，在结构系统模态频率处出现峰值，可根据灵敏度信息直接修改结构以降低噪声，也可用于对结构进行声学优化设计研究；3．结构-声学优化可在结构重量相对不变的
Acoustic-structure sensitivity is a change rate of response acoustic pressure with respect to structure design parameters, it has the vital significant to the structure noise reduction, and it is one in the design contents of quiet structure; structure-acoustic optimization based on Acoustic-structure sensitivity may design the most superior low noise structure, and it is one of goals of structure-acoustics design. The acoustic design for vehicle, ship, plane and ordinary industry is very important to improve the carborne acoustic comfort and to enhance competitiveness for the products in market, the Acoustic-structure sensitivity and the structure-acoustic optimization can provide a ration and optimum design method for the vibration structure. The objective of this fundamental study is to develop effective ,general method for the noise reduction of vibration structure .
This paper discusses the fundamental theory of FEM and BEM for structure-acoustic numerical simulation, compares advantage and disadvantage for FEM and BEM, summarizes their application in structure-acoustic simulation, debates the research history and actuality for Acoustic-structure sensitivity and structure-acoustic optimization. The acoustic-structure sensitivity formulation basing on FEM and BEM is deduced and implemented, the mathmatical model of structure-acoustic sizing design optimization is established and achieved basing on acoustic- structure sensitivity by used of the the feasible direction method.
The main work in the thesis is as follows: Based on the FEM, the numerical analysis of Dynamics displacement Response, velocity Response and its Sensitivity is deduced and implemented for the plate vibration. The velocity Sensitivity of structure vibration with respect to structure parameters is essential to calculate the acoustic- structure sensitivity; The velocity sensitivity of vibration structure with respect to structure parameter, the response pressure and response acoustic power with respect to the normal velocity is carried out by using of FEM and BEM, respectively, and then these sensitivity were combined to obtain a acoustic- structure sensitivity; For purpose of minimizing structure noise, the mathematical model of the sizing design optimization for minimizing the vibrating velocity is established and performed. The acoustic radiation of structure vibration bas been studied by use of the BEM before optimization and after optimization, the results were compared for the former and the latter; Based on the FEM of the coupled acoustic-structure system, the sensitivity of eigenvalue is deduced and performed; Based on the FEM of the coupled acoustic-structure system, the acoustic response feature is deduced and performed, the modal superpose method of the acoustic-structure sensitivity is put forward and performed; Based on the FEM of the coupled acoustic-structure system, the mathematical model of the sizing design optimization for minimizing acoustic response, structure weight and the multi-object optimization is established and performed basing on acoustic-structure sensitivity by used of the feasible direction method; The acoustic transfer function simulated by a unit force is deduced and performed by used of FEM and BEM, respectively, and then acoustic response feature of the structure random vibration simulated by a
引文
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