基于混合模型的中频振动声学分析
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摘要
本文的研究工作由国家自然基金项目“薄壁结构—声耦合问题的中频计算方法研究”(项目编号：10872075)资助。本文采用基于波动的方法以及混合法,对三维结构声耦合问题、无限域中的声辐射以及组合结构振动声学问题进行了理论推导和数值模拟,并对组合结构振动分析进行了相关试验研究。系统地建立了复杂结构振动分析以及耦合结构声学问题的低中频分析模型,并对中频分析相关理论进行了探讨。研究内容包括如下几个方面：基于波动法的多域结构声耦合模型和无限域内结构声耦合模型,基于混合法的声、结构声耦合模型和组合结构模型,以及组合结构振动试验研究。分析考虑了实际工程需求,可为实际薄壁结构振动分析以及结构声学分析提供可靠实用的计算方法。
提出了中频和混合模型的完整定义,讨论了中频分析方法的要求、中频动力学独特行为以及中频振动声预报中出现的不确定性,为中频振动声预报提供了理论基础和研究思路。
推导了基于波动的方法在复杂结构声耦合中的通用建模步骤,提出了一组新的基于阻抗的连续性条件,新的连续性条件引入人工阻尼到数值模型中,增强了数值算法的稳定性,阻抗耦合因子采用特征声阻抗,得到了较好的效果。并将该方法应用到声腔问题以及薄板和声腔耦合的问题中。结果表明该方法具有自由度少、收敛性快等特点,为中频段的振动声学分析提供了有效方法。
采用类似有限元处理无限域的方法,利用人工截断曲面将求解域分割成有界域和无界域,有界域再分割成凸形子域,在截断曲面内外分别定义可以表示声压场的波函数,提出了圆形截面下的波函数。利用波函数的特点,给出障板的隐式处理方法。通过连续性边界条件在人工截面上将内外子域联系起来,构造出可以求解的系统模型。最后将该方法应用到了声传输、声辐射和声散射等无限域结构声学问题中。算例验证了该方法的高计算效率。
讨论了混合模型在结构声耦合分析中的应用。基于波动的方法的不足之处是高计算效率只针对中度复杂的几何模型。为了利用两者的优势：有限元法的广泛应用和基于波动的方法的高收敛特性,提出了混合预报法。基本原理是将有限元模型中较大且几何简单的部分采用基于波动的方法代替。得到的耦合模型仍具有较少的自由度,耦合方式为直接耦合。给出了混合法的建模程序。并针对声腔以及薄板和声腔的耦合问题进行了数值算例。利用有限元法的细分,可以得到更高精度的结果或者在相同计算资源下获得更高的计算频率范围。利用有限元法的模态叠加,可以进一步减少计算量,提高计算效率。
讨论了混合模型在组合结构振动分析中的应用。通过连续性条件将两种非一致性近似场耦合起来,耦合方法为直接耦合,连续性条件直接作为子域的边界条件。针对实际工程中常出现的框架—面板结构建立了混合分析模型,对刚性比较大的框架结构采用传统的有限元分析而对薄板这类弹性结构采用基于波动的方法分析,如果采用纯有限元分析,则大量的计算资源都消耗在对薄板的建模上。算例分析表明：由于框架所需单元数目比较少,那么有限元部分对混合模型精度的影响也比较小,混合模型的精度主要由基于波动的方法来控制；收敛性和频响函数预报分析显示了混合模型比有限元法具有更高的计算效率,使得混合法可以用于中频振动分析。
进行了组合结构振动试验研究。设计了薄板、折弯板、组合结构试验模型。采用混合法对结构进行了分析,并与试验进行了对比,证实了本文计算模型的有效性。并对振动分析中出现的不确定性也作了探讨。
本文针对实际工程中常用的薄壁结构和组合结构的振动声学问题进行了研究,提出了基于波动法和基于混合模型的理论分析方法,并对结构振动分析进行了试验验证。经过进一步的完善和发展,可望形成复杂结构振动声学系统的分析计算方法。
The work of this thesis was supported by National Natural Science Foundation of China "Computation and analysis of structural-acoustic coupled problems in the medium frequency range for thin wall structures"(No.10872075).Based on wave based method and hybrid method, theoretical analysis and numerical simulation for three-dimensional structural acoustic analysis, sound radiation analysis in unbounded domain and buid-up structures are investigated respectively, and the experiment analysis of vibration for built-up structures is studied. The low and mid frequency models for complex structural vibration systems and coupled structural-acoustic systems are introduced, the theory about mid frequency analysis has investigated. Research include following sections:wave based modeling for multi-domain structural acoustic; wave based modeling for sound radiation in unbounded domains; hybrid method modeling for acoustic、structural acoustic and built-up structures; experiments of vibration analysis for built-up structures. Taking into account the requirements for practical engineering, provide a reliable calculating method for vibration analysis or structural acoustic analysis of practical thin-wall structures.
Proposing complete definition for mid-frequency analysis and hybrid model. Discussing the requirements for mid-frequency method、exhibition for mid-frequency unique dynamics behavior and uncertainty for mid-frequency analysis. Provides a theoretical basis and research ideas for mid-frequency vibro-acoustic analysis.
A new set of continuity conditions for multi-domain wave based modeling is introduced. The impedance coupling approach introduces artificial damping into the numerical model, which has a beneficial effect on the method's efficiency as compared to the conventional pressure and velocity coupling approach.A generally applicable selection criterium for the impedance coupling factor is proposed. The characteristic impedance of the considered fluid gives the best results. By applied the proposed method, the cavity model and thin plate and cavity coupled model are buit. It shows that the proposed method is more efficient than the element based method and better convergence properties.
Wave based method applies similar methodologies as for the FE schemes for tackling problems in unbounded domains. After an initial truncation and partitioning into a number of bounded convex subdomains and one unbounded subdomain, separated by a truncation curve, novel wave function sets are defined. These wave function sets are able to represent the acoustic pressure field within the unbounded subdomain, exterior to the truncation surface. Wave function sets for circular truncation curves are defined and validated. The wave function sets defined for the unbounded subdomains allow the introduction of rigid baffle planes implicitly in the wave function definitions. Selection of appropriate wave functions within subdomains and enforcement of continuity conditions over the truncation surface between the bounded and unbounded region, yields a WB model which can be solved for the associated wave function contribution factors. Application of the proposed approach to various validation examples illustrates an enhanced computational efficiency as compared with element-based methods.
The applicability of the WBM is limited since the high computational efficiency only appears for moderate geometrical complexity. In order to take advantage of the wide application range of the FEM and the high convergence rate of the WBM, the coupling between both prediction tools is proposed. The basic idea is to replace parts of the finite element model with simple geometrical shapes by much smaller wave models. The resulting hybrid model has fewer degrees of freedom (DOF's). The hybrid modeling concept is demonstrated for structural-acoustic systems. Results show that because of the finite element method part existing in hybrid model, therefore hybrid model also has numerical pollution. The use of modal reduction techniques for the structural part results in a significant gain in CPU time.
Considering the hybrid model concept for vibration analysis of buit-up structures.The coupling between the non-conforming approximation fields is created by enforcing continuity conditions. In this case the continuity conditions are enforced directly to the subdomains as boundary conditions. For a pure FE model, the main portion of the computational load is spent in modelling the plate domains. In the hybrid approach the plates can be modelled very efficiently by the WBM, leaving only the stiff frame to be modelled by the FEM.The number of FE dofs required to accurately model the stiff frame is relatively small. Consequently, the accuracy of the hybrid model is mainly determined by the accuracy of the WB models. The convergence analysis and predicted frequency response functions show that the newly developped hybrid method has an enhanced computational efficiency over the FEM.
The vibration analysis of built-up structures is studied by experiment. The models of thin plate, bending plate, built-up structures are designed. Calculation model confirmed the validity of proposed method in this paper. The uncertainty in mid frequency vibration analysis is also discussed.
The vibration analysis of thin wall structures and built-up structures used in practical engineering is studied. The theory analysis models of wave based method and hybrid model are proposed.The vibration analysis of structures is also studied by experiment. Afte improving and developing, provide a reliable computation and analysis method of complex structural-acoustic systems.
提出了中频和混合模型的完整定义,讨论了中频分析方法的要求、中频动力学独特行为以及中频振动声预报中出现的不确定性,为中频振动声预报提供了理论基础和研究思路。
推导了基于波动的方法在复杂结构声耦合中的通用建模步骤,提出了一组新的基于阻抗的连续性条件,新的连续性条件引入人工阻尼到数值模型中,增强了数值算法的稳定性,阻抗耦合因子采用特征声阻抗,得到了较好的效果。并将该方法应用到声腔问题以及薄板和声腔耦合的问题中。结果表明该方法具有自由度少、收敛性快等特点,为中频段的振动声学分析提供了有效方法。
采用类似有限元处理无限域的方法,利用人工截断曲面将求解域分割成有界域和无界域,有界域再分割成凸形子域,在截断曲面内外分别定义可以表示声压场的波函数,提出了圆形截面下的波函数。利用波函数的特点,给出障板的隐式处理方法。通过连续性边界条件在人工截面上将内外子域联系起来,构造出可以求解的系统模型。最后将该方法应用到了声传输、声辐射和声散射等无限域结构声学问题中。算例验证了该方法的高计算效率。
讨论了混合模型在结构声耦合分析中的应用。基于波动的方法的不足之处是高计算效率只针对中度复杂的几何模型。为了利用两者的优势：有限元法的广泛应用和基于波动的方法的高收敛特性,提出了混合预报法。基本原理是将有限元模型中较大且几何简单的部分采用基于波动的方法代替。得到的耦合模型仍具有较少的自由度,耦合方式为直接耦合。给出了混合法的建模程序。并针对声腔以及薄板和声腔的耦合问题进行了数值算例。利用有限元法的细分,可以得到更高精度的结果或者在相同计算资源下获得更高的计算频率范围。利用有限元法的模态叠加,可以进一步减少计算量,提高计算效率。
讨论了混合模型在组合结构振动分析中的应用。通过连续性条件将两种非一致性近似场耦合起来,耦合方法为直接耦合,连续性条件直接作为子域的边界条件。针对实际工程中常出现的框架—面板结构建立了混合分析模型,对刚性比较大的框架结构采用传统的有限元分析而对薄板这类弹性结构采用基于波动的方法分析,如果采用纯有限元分析,则大量的计算资源都消耗在对薄板的建模上。算例分析表明：由于框架所需单元数目比较少,那么有限元部分对混合模型精度的影响也比较小,混合模型的精度主要由基于波动的方法来控制；收敛性和频响函数预报分析显示了混合模型比有限元法具有更高的计算效率,使得混合法可以用于中频振动分析。
进行了组合结构振动试验研究。设计了薄板、折弯板、组合结构试验模型。采用混合法对结构进行了分析,并与试验进行了对比,证实了本文计算模型的有效性。并对振动分析中出现的不确定性也作了探讨。
本文针对实际工程中常用的薄壁结构和组合结构的振动声学问题进行了研究,提出了基于波动法和基于混合模型的理论分析方法,并对结构振动分析进行了试验验证。经过进一步的完善和发展,可望形成复杂结构振动声学系统的分析计算方法。
The work of this thesis was supported by National Natural Science Foundation of China "Computation and analysis of structural-acoustic coupled problems in the medium frequency range for thin wall structures"(No.10872075).Based on wave based method and hybrid method, theoretical analysis and numerical simulation for three-dimensional structural acoustic analysis, sound radiation analysis in unbounded domain and buid-up structures are investigated respectively, and the experiment analysis of vibration for built-up structures is studied. The low and mid frequency models for complex structural vibration systems and coupled structural-acoustic systems are introduced, the theory about mid frequency analysis has investigated. Research include following sections:wave based modeling for multi-domain structural acoustic; wave based modeling for sound radiation in unbounded domains; hybrid method modeling for acoustic、structural acoustic and built-up structures; experiments of vibration analysis for built-up structures. Taking into account the requirements for practical engineering, provide a reliable calculating method for vibration analysis or structural acoustic analysis of practical thin-wall structures.
Proposing complete definition for mid-frequency analysis and hybrid model. Discussing the requirements for mid-frequency method、exhibition for mid-frequency unique dynamics behavior and uncertainty for mid-frequency analysis. Provides a theoretical basis and research ideas for mid-frequency vibro-acoustic analysis.
A new set of continuity conditions for multi-domain wave based modeling is introduced. The impedance coupling approach introduces artificial damping into the numerical model, which has a beneficial effect on the method's efficiency as compared to the conventional pressure and velocity coupling approach.A generally applicable selection criterium for the impedance coupling factor is proposed. The characteristic impedance of the considered fluid gives the best results. By applied the proposed method, the cavity model and thin plate and cavity coupled model are buit. It shows that the proposed method is more efficient than the element based method and better convergence properties.
Wave based method applies similar methodologies as for the FE schemes for tackling problems in unbounded domains. After an initial truncation and partitioning into a number of bounded convex subdomains and one unbounded subdomain, separated by a truncation curve, novel wave function sets are defined. These wave function sets are able to represent the acoustic pressure field within the unbounded subdomain, exterior to the truncation surface. Wave function sets for circular truncation curves are defined and validated. The wave function sets defined for the unbounded subdomains allow the introduction of rigid baffle planes implicitly in the wave function definitions. Selection of appropriate wave functions within subdomains and enforcement of continuity conditions over the truncation surface between the bounded and unbounded region, yields a WB model which can be solved for the associated wave function contribution factors. Application of the proposed approach to various validation examples illustrates an enhanced computational efficiency as compared with element-based methods.
The applicability of the WBM is limited since the high computational efficiency only appears for moderate geometrical complexity. In order to take advantage of the wide application range of the FEM and the high convergence rate of the WBM, the coupling between both prediction tools is proposed. The basic idea is to replace parts of the finite element model with simple geometrical shapes by much smaller wave models. The resulting hybrid model has fewer degrees of freedom (DOF's). The hybrid modeling concept is demonstrated for structural-acoustic systems. Results show that because of the finite element method part existing in hybrid model, therefore hybrid model also has numerical pollution. The use of modal reduction techniques for the structural part results in a significant gain in CPU time.
Considering the hybrid model concept for vibration analysis of buit-up structures.The coupling between the non-conforming approximation fields is created by enforcing continuity conditions. In this case the continuity conditions are enforced directly to the subdomains as boundary conditions. For a pure FE model, the main portion of the computational load is spent in modelling the plate domains. In the hybrid approach the plates can be modelled very efficiently by the WBM, leaving only the stiff frame to be modelled by the FEM.The number of FE dofs required to accurately model the stiff frame is relatively small. Consequently, the accuracy of the hybrid model is mainly determined by the accuracy of the WB models. The convergence analysis and predicted frequency response functions show that the newly developped hybrid method has an enhanced computational efficiency over the FEM.
The vibration analysis of built-up structures is studied by experiment. The models of thin plate, bending plate, built-up structures are designed. Calculation model confirmed the validity of proposed method in this paper. The uncertainty in mid frequency vibration analysis is also discussed.
The vibration analysis of thin wall structures and built-up structures used in practical engineering is studied. The theory analysis models of wave based method and hybrid model are proposed.The vibration analysis of structures is also studied by experiment. Afte improving and developing, provide a reliable computation and analysis method of complex structural-acoustic systems.
引文
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