汽车中频NVH高效高精度计算理论与方法
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摘要
随着人们对汽车的舒适性的要求越来越高,其振动噪声的研究越来越受关注。在汽车的开发中,由于整车开发后期30%的整改问题都与振动噪声相关,不仅延长了开发周期,同时也需要耗费大量的成本,因此各大主机厂都希望通过前期的振动噪声虚拟分析及优化来降低整车开发成本和缩短汽车开发周期。在汽车振动噪声(NVH, Noise Vibration and Harshness)的模拟中,理想的数值计算工具应该适用于人耳所能听到的所有频率范围,如20Hz-20000Hz,然而在实际中,不同的数值方法有不同的频率适用范围,如有限元(FEM)只能用于计算低频的振动噪声问题,而在高频问题计算中,统计能量法最适用。在低频和高频之间,存在着一个中频范围：其频率高于有限元的频率适用范围而低于统计能量法的适用频率范围。由于中频振动噪声问题严重影响了产品的振动噪声性能,目前还没有一种很好的数值方法来对其进行模拟,因此需要开发相应的中频振动噪声数值方法来对其进行研究和计算。
为了更好地计算汽车的中频NVH问题,本论文系统地研究了声学计算的理论与方法,从数值离散模型的原理上寻求中频振动噪声问题的解决方案,从而提出汽车中频NVH计算的有效数值方法。通过研究表明：声学计算的误差是离散系统不能很好的模拟连续介质而造成的,由于有限元的刚度系统偏硬,因而使得声波在其离散模型中传播的速度大于实际的声速,因而在中频计算时产生较大的色散误差。本文一方面通过引入了广义的梯度光滑技术,对构造的一系列光滑域进行声压梯度的光滑操作,有效降低了有限元的系统刚度,大大减小了由于有限元离散模型“过刚”而导致的中频声波传播的色散误差。另一方面通过对离散模型质量系统的理论研究,发现可以对不同数值方法的质量矩阵进行重构,实现质量矩阵元素的分配优化,以及质量矩阵与“过刚”刚度矩阵的最佳匹配,达到降低声学色散误差的目的。通过本文系统的研究,本文形成了基于离散模型的汽车中频NVH计算的通用改进体系,提出了一系列的新型数值算法,其研究的工作和创新性成果主要体现在：
1)研究了汽车声学计算理论、误差产生的本质原因,提出两种基于离散模型的中频NVH分析及改进方法。本文从有限元的伽辽金离散形式出发,首次结合离散系统的刚度矩阵、质量矩阵对特征值的影响,揭示了声学误差产生的本质原因是由于传统伽辽金有限元的离散系统刚度过大,使得离散模型的刚度系统和质量系统失去平衡,从而导致中频NVH计算的色散误差。提出了基于离散模型刚度系统及质量系统的两种中频NVH问题通用改进方法,从物理层面统一了中频NVH分析的传统声学误差及离散模型理论,建立了基于离散模型的中频NVH分析与误差控制方法,为基于离散模型的高效高精度计算方法的提出奠定了理论基础。
2)系统地研究了基于广义梯度光滑的汽车NVH计算理论与方法,通过引入广义的梯度光滑操作,在光滑域形式与离散系统刚度关系的基础上,发现了光滑域形式,离散系统刚度以及声学误差的影响规律,提出了一系列高效高精度的汽车中频NVH分析方法,形成了梯度光滑有限元的汽车中频NVH计算体系。本文构造了声学的光滑伽辽金弱形式,系统的研究了广义梯度光滑有限元的声学色散误差,发现了光滑域形式与声学误差的规律,可以通过构建合适的光滑域,得到接近连续介质系统的离散刚度矩阵,大大降低甚至消除声学色散误差,极大的扩展了汽车NVH计算的频率范围；推导了光滑有限元计算的数值波数结果,发现基于点光滑的有限元(NS-FEM)计算的数值波数总是大于实际的数值波数,与有限元的计算的数值波数具有相反的性质,然而其误差大于有限元的误差,不太适合计算声学问题,在此基础上构建了新型的α-FEM声学计算模型,大大提高了中频声学问题计算的精度；构建了二维基于边的光滑有限元(ES-FEM)声学计算模型,三维基于四面体面的光滑有限元(FS-FEM)动态计算模型,基于四面体边的有限元(ES-T-FEM)动态模型,理论及数值分析研究表明：ES-FEM能够获得很好的声场及梯度解,对扭曲网格不敏感,具有较好的收敛率和效率,计算的结果优于四边形单元的解。FS-FEM能够提高汽车振动噪声计算的精度,然而仍然存在刚度过大的缺陷,ES-T-FEM在计算汽车振动噪声问题时,即使采用线性的四面体单元也能比传统的四面体有限元或者改进的六面体单元得到更好的精度与计算效率,因而非常适用于求解汽车的中频振动噪声问题。
3)首次提出了基于离散模型质量系统的中频NVH分析改进方法,在保持质量守恒的前提下,研究了高斯点位置对质量矩阵元素分布的影响规律,创建了高斯点影响下的质量系统与刚度系统的匹配模型,通过质量矩阵与不同系统刚度矩阵的匹配来降低声学仿真的误差,提出一系列简单而高效高精度的汽车中频NVH问题计算方法。通过采用不同数值方法的刚度矩阵,在质量矩阵中引入积分点的位置参数来合理的匹配该数值方法的刚度,最终通过调节积分点的位置实现对质量矩阵的元素分布进行最佳合理分配,从而来达到提高声学仿真精度的目的。提出了声学质量重构有限元技术(MR-FEM),质量重构光滑有限元技术(MR-SFEM),进一步提高了有限元和光滑有限元计算的精度,同时对ES-FEM质量系统与刚度系统的匹配进行了研究。理论和数值研究表明：在计算时间方面,质量重构有限元(MR-FEM)不增加前处理工作量和计算时间,具有非常高的计算效率；在计算精度上,质量重构有限元技术的误差是传统有限元技术的二分之一,而基于四边形的质量重构光滑有限元(MR-SFEM)的误差是传统光滑有限元的三分之一；基于边的光滑有限元采用一致质量矩阵时比采用集中质量矩阵得到更高一阶的计算精度
4)系统地开展了汽车声固体耦合的数值方法研究,通过采用对于任意复杂的问题域都能自适应剖分的三角形单元和四面体单元,构建了一系列适应于任意复杂汽车结构的声固耦合数值方法。由于本文提出的基于三角形和四面体网格数值方法能够很好的提高声学的计算精度,因此本文构建了适合任意复杂声固耦合模型计算的耦合ES-FEM/FEM,耦合ES-/FS-FEM,耦合ES-FEM,以及耦合ES-FEM/BEM.数值分析表明：基于梯度光滑的有限元系统能够降低声固耦合有限元系统的刚度,提高声固耦合计算的精度,拓展了计算的频率范围,为三角形和四面体在工程的进一步应用打下基础。
5)为了验证上述方法的有效性,本论文在对汽车中频振动噪声分析的梯度光滑有限元及质量重构有限元进行理论研究与数值分析的同时,也开展了汽车关键零部件振动,声学模态以及及噪声传递函数试验,通过试验验证了新型数值方法在处理工程中复杂问题时可以得到较好的精度,为该方法在汽车中频NVH分析及进一步应用打下基础。
本文研究工作受到国家建设高水平大学公派研究生项目,国家博士学术新人奖,国家自然基金(11202074)以及教育部“长江学者和创新团队发展计划”项目(5311050050037)的资助。
With the increasing demand for comfort of automobiles, more and more attentions are paid on the noise and vibration (NV). In the development of the vehile,30%of TIR(Test In Road) problems are associated with NV problems at the late development stage of a vehicle, which will not only extended the development cycle, but also requires a lot of costs. In such a sophisticated design, there is also an increasing trend towards virtual design and prototyping to reduce costs and development time. In the vehicle NV simulation, the ideal tool should be applicable to all the frequency range, which is the audio-frequency range, such as20Hz-20000Hz. In practice, specific methods are applicable in a limited frequency region. Finite Element Analysis (FEA) is a "low frequency" method which is both well developed and well established. At "high frequencies", Statistical Energy Analysis (SEA) is most established. There is however a "mid-frequency" gap in the modeling capabilities:too high for FEA, too low for SEA. This is important, since mid-frequency behavior strongly affects product performance and competitiveness, and there are no effective numerical methods to calculate them, so the numerical methods for the mid-frequency of NV should be studied.
In order to simulate the vehicle NV problems in the mid-frequency range, this paper will systematically study the theory of computational acoustics, and try to seek effective numerical methods from the main reason of the dispersion error of discretized numerical model. Our studies have also revealed that the dispersion error is rooted in the discretized model, which cannot simulate the continuous media well. It is well known that the FEM suffers from the "overly-stiff problem, making the calculated waves propagate with artificially higher speeds than the actual ones in the media, and is leading to the dispersion error. One way to soften the "overly-stiff FEM model is the generalized gradient smoothing operation, which will decrease the dispersion error in the mid-frequency problem. Alternatively, the mass matrix is constructed by re-distribute the entries in the mass matrix to achieve a preferred balance between stiffness and mass of the discretized system, which minimize the dispersion error. This paper has formulated a general improvement of the discretized model to control the error of noise and vibration simulations, and the main research work and innovative achievements in this dissertation are:
1) This work studied the theory and essence of dispersion error for computational acoustics, and proposes two improved numerical models for NVH problems in mid-frequency range. The "over-stiffness" feature of FEM is illustrated from the Galerkin finite element discrete form, combined with eigenvalues caused by the balance between the stiffness and mass matrix of discrete systems, which leading to large dispersion error in mid-frequency NVH problems. A general formulation based on the stiffness and mass system of discrete model are proposed to improve the acoustic simulation, which unifies the acoustic dispersion error and theory of discrete model, establishes the error control method of discrete model, and laid the theoretical foundation for high-precision and high-efficiency computational methods for acoustic problems.
2) Made a systematic study of computational theory and methods of generalized gradient smoothing operation for vehicle NVH in mid-frequency range. By introducing the generalized gradient smoothing operation, the influence of smoothing domain, discrete system stiffness and acoustic dispersion error is founded on the basis of smoothing domain and discrete system stiffness relationship, and a series of high-precision and high-efficiency computational methods are proposed, which forming a system of the gradient smoothing finite element methods for vehicle mid-frequency NVH analysis. This work formulates the smoothed Garlerkin weak form for acoustic problems, studies the dispersion error of generalized gradient smoothed finite element methods (GS-FEM) with various smoothing domains. A "close-to-exact" discrete system can be obtained by constructing a suitable gradient smoothing domain, which will greatly reduce or even eliminate the acoustic dispersion error, and expand the frequency range of vehicle NVH computation; Derived the numerical wave number for the GS-FEM, and found that numerical wave number of NS-FEM is always larger than the actual wave number, which is complementary to the standard FEM, but the dispersion error of NS-FEM is larger than the FEM and unsuitable for acoustic analysis. An alpha finite element method (a-FEM) is then formulated for the acoustic problems, which will lead to accuracy simulation of acoustic problems; The ES-FEM using triangular mesh, and FS-FEM, ES-T-FEM using tetrahedral mesh are also formulated for dynamic and acoustic problems. Numerical studies show that:the ES-FEM gives very accurate results on the acoustic pressure and the gradient of acoustic pressure, not sensitive to the irregular mesh, provides higher convergence rate and efficiency than the traditional FEM using triangular mesh and even better than the FEM using quadrilateral mesh in the mid-frequency. In3D problems, the FS-FEM can provide more accuracy and efficiency results than the FEM, while the FS-FEM also suffer from slight overly-stiff, and can also be improved; The ES-T-FEM can provide very accurate results in dynamic problems and even can provide much better results than the traditional tetrahedral FEM, even better than the MIR method, thus very suitable for solving vehicle NVH problems in the mid-frequency range.
3) Proposed a novel approach for vehicle mid-frequency NVH analysis based on the mass system of discrete model, which is also in accordance with the mass conservation theorem. This work studies the influence of Gaussian locations on mass matrix, and establishes a perfect balance model of stiffness matrix and mass matrix under the influence of Gauss points to reduce the dispersion error, and proposes a series of simple, high-precision and high-efficiency computational methods for vehicle mid-frequency NVH analysis. In these methods, the stiffness of FEM or smoothed finite element methods are directly adopted, and the mass matrix of the discrete systems will be modified by shifting the integration points away from the usual Gaussian locations to re-distribute the entries in the mass matrix, with aim to achieve a preferred balance between stiffness and mass of the discretized system, which minimize the dispersion error. The MR-FEM and MR-SFEM have been proposed for acoustic problems. Theoretical and numerical studies verified that the present MR-FEM method works ideally for acoustic problems:they do not increase the pre-processing and computation time, and thus provide a very high computational efficiency compared with traditional FEM or SFEM; the MR-FEM can provide much more stable and accurate results(as much as four times of accuracy)compared to the standard FEM using triangular mesh and quadrilateral mesh; The ES-FEM using consistence can achieve a higher order of accuracy than the ES-FEM using lump mass matrix; The MR-SFEM can provide much more stable and accurate results(as much as three times of accuracy)compared to the SFEM,
4) Studied the numerical methods systematically for vehicle structural-acoustic problem, and propose a series of numerical methods for complex vehicle model by adopting the triangular mesh and tetrahedral mesh which have good applicability for any complex problem domain. Since the adopted triangular mesh and tetrahedral mesh used in this paper and can provide very accurate results in the mid-frequency acoustic simulation, and the coupled ES-FEM/FEM, coupled ES-/FS-FEM, coupled ES-FEM, as well as the coupling ES-FEM/BEM have been constructed for any complex structural-acoustic problems. Numerical studies have been verified that the gradient smoothing operation can reduce the stiffness of the coupled system, and provide more accurate results than the traditional coupled FEM, which laid the foundation for the further engineering application.
5) In this thesis, we studied the gradient smoothing finite element method and mass re-distribute of FEM for vibration and noise from the theoretical and numerical aspect, we also have extended it to the practical engineering application, such as the compartment of vehicle, the engine chamber, which strongly support the robustness and efficiency of proposed numerical methods. These numerical models are also verified by the test and found that the novel numerical methods can provide much better results than the FEM using same low-order elements, and even close to the accuracy of the finite element using high-order elements, which greatly improved the efficiency of computing and has abroad application in vehicle mid-frequency NVH analysis.
The work of this paper is supported by the State to the construction of the high level of Graduate Students, National Dr. Young Scholar Award, the National Natural Science Foundation (11202074) and program for Changjiang Scholar and Innovative Research Team in University (5311050050037).
为了更好地计算汽车的中频NVH问题,本论文系统地研究了声学计算的理论与方法,从数值离散模型的原理上寻求中频振动噪声问题的解决方案,从而提出汽车中频NVH计算的有效数值方法。通过研究表明：声学计算的误差是离散系统不能很好的模拟连续介质而造成的,由于有限元的刚度系统偏硬,因而使得声波在其离散模型中传播的速度大于实际的声速,因而在中频计算时产生较大的色散误差。本文一方面通过引入了广义的梯度光滑技术,对构造的一系列光滑域进行声压梯度的光滑操作,有效降低了有限元的系统刚度,大大减小了由于有限元离散模型“过刚”而导致的中频声波传播的色散误差。另一方面通过对离散模型质量系统的理论研究,发现可以对不同数值方法的质量矩阵进行重构,实现质量矩阵元素的分配优化,以及质量矩阵与“过刚”刚度矩阵的最佳匹配,达到降低声学色散误差的目的。通过本文系统的研究,本文形成了基于离散模型的汽车中频NVH计算的通用改进体系,提出了一系列的新型数值算法,其研究的工作和创新性成果主要体现在：
1)研究了汽车声学计算理论、误差产生的本质原因,提出两种基于离散模型的中频NVH分析及改进方法。本文从有限元的伽辽金离散形式出发,首次结合离散系统的刚度矩阵、质量矩阵对特征值的影响,揭示了声学误差产生的本质原因是由于传统伽辽金有限元的离散系统刚度过大,使得离散模型的刚度系统和质量系统失去平衡,从而导致中频NVH计算的色散误差。提出了基于离散模型刚度系统及质量系统的两种中频NVH问题通用改进方法,从物理层面统一了中频NVH分析的传统声学误差及离散模型理论,建立了基于离散模型的中频NVH分析与误差控制方法,为基于离散模型的高效高精度计算方法的提出奠定了理论基础。
2)系统地研究了基于广义梯度光滑的汽车NVH计算理论与方法,通过引入广义的梯度光滑操作,在光滑域形式与离散系统刚度关系的基础上,发现了光滑域形式,离散系统刚度以及声学误差的影响规律,提出了一系列高效高精度的汽车中频NVH分析方法,形成了梯度光滑有限元的汽车中频NVH计算体系。本文构造了声学的光滑伽辽金弱形式,系统的研究了广义梯度光滑有限元的声学色散误差,发现了光滑域形式与声学误差的规律,可以通过构建合适的光滑域,得到接近连续介质系统的离散刚度矩阵,大大降低甚至消除声学色散误差,极大的扩展了汽车NVH计算的频率范围；推导了光滑有限元计算的数值波数结果,发现基于点光滑的有限元(NS-FEM)计算的数值波数总是大于实际的数值波数,与有限元的计算的数值波数具有相反的性质,然而其误差大于有限元的误差,不太适合计算声学问题,在此基础上构建了新型的α-FEM声学计算模型,大大提高了中频声学问题计算的精度；构建了二维基于边的光滑有限元(ES-FEM)声学计算模型,三维基于四面体面的光滑有限元(FS-FEM)动态计算模型,基于四面体边的有限元(ES-T-FEM)动态模型,理论及数值分析研究表明：ES-FEM能够获得很好的声场及梯度解,对扭曲网格不敏感,具有较好的收敛率和效率,计算的结果优于四边形单元的解。FS-FEM能够提高汽车振动噪声计算的精度,然而仍然存在刚度过大的缺陷,ES-T-FEM在计算汽车振动噪声问题时,即使采用线性的四面体单元也能比传统的四面体有限元或者改进的六面体单元得到更好的精度与计算效率,因而非常适用于求解汽车的中频振动噪声问题。
3)首次提出了基于离散模型质量系统的中频NVH分析改进方法,在保持质量守恒的前提下,研究了高斯点位置对质量矩阵元素分布的影响规律,创建了高斯点影响下的质量系统与刚度系统的匹配模型,通过质量矩阵与不同系统刚度矩阵的匹配来降低声学仿真的误差,提出一系列简单而高效高精度的汽车中频NVH问题计算方法。通过采用不同数值方法的刚度矩阵,在质量矩阵中引入积分点的位置参数来合理的匹配该数值方法的刚度,最终通过调节积分点的位置实现对质量矩阵的元素分布进行最佳合理分配,从而来达到提高声学仿真精度的目的。提出了声学质量重构有限元技术(MR-FEM),质量重构光滑有限元技术(MR-SFEM),进一步提高了有限元和光滑有限元计算的精度,同时对ES-FEM质量系统与刚度系统的匹配进行了研究。理论和数值研究表明：在计算时间方面,质量重构有限元(MR-FEM)不增加前处理工作量和计算时间,具有非常高的计算效率；在计算精度上,质量重构有限元技术的误差是传统有限元技术的二分之一,而基于四边形的质量重构光滑有限元(MR-SFEM)的误差是传统光滑有限元的三分之一；基于边的光滑有限元采用一致质量矩阵时比采用集中质量矩阵得到更高一阶的计算精度
4)系统地开展了汽车声固体耦合的数值方法研究,通过采用对于任意复杂的问题域都能自适应剖分的三角形单元和四面体单元,构建了一系列适应于任意复杂汽车结构的声固耦合数值方法。由于本文提出的基于三角形和四面体网格数值方法能够很好的提高声学的计算精度,因此本文构建了适合任意复杂声固耦合模型计算的耦合ES-FEM/FEM,耦合ES-/FS-FEM,耦合ES-FEM,以及耦合ES-FEM/BEM.数值分析表明：基于梯度光滑的有限元系统能够降低声固耦合有限元系统的刚度,提高声固耦合计算的精度,拓展了计算的频率范围,为三角形和四面体在工程的进一步应用打下基础。
5)为了验证上述方法的有效性,本论文在对汽车中频振动噪声分析的梯度光滑有限元及质量重构有限元进行理论研究与数值分析的同时,也开展了汽车关键零部件振动,声学模态以及及噪声传递函数试验,通过试验验证了新型数值方法在处理工程中复杂问题时可以得到较好的精度,为该方法在汽车中频NVH分析及进一步应用打下基础。
本文研究工作受到国家建设高水平大学公派研究生项目,国家博士学术新人奖,国家自然基金(11202074)以及教育部“长江学者和创新团队发展计划”项目(5311050050037)的资助。
With the increasing demand for comfort of automobiles, more and more attentions are paid on the noise and vibration (NV). In the development of the vehile,30%of TIR(Test In Road) problems are associated with NV problems at the late development stage of a vehicle, which will not only extended the development cycle, but also requires a lot of costs. In such a sophisticated design, there is also an increasing trend towards virtual design and prototyping to reduce costs and development time. In the vehicle NV simulation, the ideal tool should be applicable to all the frequency range, which is the audio-frequency range, such as20Hz-20000Hz. In practice, specific methods are applicable in a limited frequency region. Finite Element Analysis (FEA) is a "low frequency" method which is both well developed and well established. At "high frequencies", Statistical Energy Analysis (SEA) is most established. There is however a "mid-frequency" gap in the modeling capabilities:too high for FEA, too low for SEA. This is important, since mid-frequency behavior strongly affects product performance and competitiveness, and there are no effective numerical methods to calculate them, so the numerical methods for the mid-frequency of NV should be studied.
In order to simulate the vehicle NV problems in the mid-frequency range, this paper will systematically study the theory of computational acoustics, and try to seek effective numerical methods from the main reason of the dispersion error of discretized numerical model. Our studies have also revealed that the dispersion error is rooted in the discretized model, which cannot simulate the continuous media well. It is well known that the FEM suffers from the "overly-stiff problem, making the calculated waves propagate with artificially higher speeds than the actual ones in the media, and is leading to the dispersion error. One way to soften the "overly-stiff FEM model is the generalized gradient smoothing operation, which will decrease the dispersion error in the mid-frequency problem. Alternatively, the mass matrix is constructed by re-distribute the entries in the mass matrix to achieve a preferred balance between stiffness and mass of the discretized system, which minimize the dispersion error. This paper has formulated a general improvement of the discretized model to control the error of noise and vibration simulations, and the main research work and innovative achievements in this dissertation are:
1) This work studied the theory and essence of dispersion error for computational acoustics, and proposes two improved numerical models for NVH problems in mid-frequency range. The "over-stiffness" feature of FEM is illustrated from the Galerkin finite element discrete form, combined with eigenvalues caused by the balance between the stiffness and mass matrix of discrete systems, which leading to large dispersion error in mid-frequency NVH problems. A general formulation based on the stiffness and mass system of discrete model are proposed to improve the acoustic simulation, which unifies the acoustic dispersion error and theory of discrete model, establishes the error control method of discrete model, and laid the theoretical foundation for high-precision and high-efficiency computational methods for acoustic problems.
2) Made a systematic study of computational theory and methods of generalized gradient smoothing operation for vehicle NVH in mid-frequency range. By introducing the generalized gradient smoothing operation, the influence of smoothing domain, discrete system stiffness and acoustic dispersion error is founded on the basis of smoothing domain and discrete system stiffness relationship, and a series of high-precision and high-efficiency computational methods are proposed, which forming a system of the gradient smoothing finite element methods for vehicle mid-frequency NVH analysis. This work formulates the smoothed Garlerkin weak form for acoustic problems, studies the dispersion error of generalized gradient smoothed finite element methods (GS-FEM) with various smoothing domains. A "close-to-exact" discrete system can be obtained by constructing a suitable gradient smoothing domain, which will greatly reduce or even eliminate the acoustic dispersion error, and expand the frequency range of vehicle NVH computation; Derived the numerical wave number for the GS-FEM, and found that numerical wave number of NS-FEM is always larger than the actual wave number, which is complementary to the standard FEM, but the dispersion error of NS-FEM is larger than the FEM and unsuitable for acoustic analysis. An alpha finite element method (a-FEM) is then formulated for the acoustic problems, which will lead to accuracy simulation of acoustic problems; The ES-FEM using triangular mesh, and FS-FEM, ES-T-FEM using tetrahedral mesh are also formulated for dynamic and acoustic problems. Numerical studies show that:the ES-FEM gives very accurate results on the acoustic pressure and the gradient of acoustic pressure, not sensitive to the irregular mesh, provides higher convergence rate and efficiency than the traditional FEM using triangular mesh and even better than the FEM using quadrilateral mesh in the mid-frequency. In3D problems, the FS-FEM can provide more accuracy and efficiency results than the FEM, while the FS-FEM also suffer from slight overly-stiff, and can also be improved; The ES-T-FEM can provide very accurate results in dynamic problems and even can provide much better results than the traditional tetrahedral FEM, even better than the MIR method, thus very suitable for solving vehicle NVH problems in the mid-frequency range.
3) Proposed a novel approach for vehicle mid-frequency NVH analysis based on the mass system of discrete model, which is also in accordance with the mass conservation theorem. This work studies the influence of Gaussian locations on mass matrix, and establishes a perfect balance model of stiffness matrix and mass matrix under the influence of Gauss points to reduce the dispersion error, and proposes a series of simple, high-precision and high-efficiency computational methods for vehicle mid-frequency NVH analysis. In these methods, the stiffness of FEM or smoothed finite element methods are directly adopted, and the mass matrix of the discrete systems will be modified by shifting the integration points away from the usual Gaussian locations to re-distribute the entries in the mass matrix, with aim to achieve a preferred balance between stiffness and mass of the discretized system, which minimize the dispersion error. The MR-FEM and MR-SFEM have been proposed for acoustic problems. Theoretical and numerical studies verified that the present MR-FEM method works ideally for acoustic problems:they do not increase the pre-processing and computation time, and thus provide a very high computational efficiency compared with traditional FEM or SFEM; the MR-FEM can provide much more stable and accurate results(as much as four times of accuracy)compared to the standard FEM using triangular mesh and quadrilateral mesh; The ES-FEM using consistence can achieve a higher order of accuracy than the ES-FEM using lump mass matrix; The MR-SFEM can provide much more stable and accurate results(as much as three times of accuracy)compared to the SFEM,
4) Studied the numerical methods systematically for vehicle structural-acoustic problem, and propose a series of numerical methods for complex vehicle model by adopting the triangular mesh and tetrahedral mesh which have good applicability for any complex problem domain. Since the adopted triangular mesh and tetrahedral mesh used in this paper and can provide very accurate results in the mid-frequency acoustic simulation, and the coupled ES-FEM/FEM, coupled ES-/FS-FEM, coupled ES-FEM, as well as the coupling ES-FEM/BEM have been constructed for any complex structural-acoustic problems. Numerical studies have been verified that the gradient smoothing operation can reduce the stiffness of the coupled system, and provide more accurate results than the traditional coupled FEM, which laid the foundation for the further engineering application.
5) In this thesis, we studied the gradient smoothing finite element method and mass re-distribute of FEM for vibration and noise from the theoretical and numerical aspect, we also have extended it to the practical engineering application, such as the compartment of vehicle, the engine chamber, which strongly support the robustness and efficiency of proposed numerical methods. These numerical models are also verified by the test and found that the novel numerical methods can provide much better results than the FEM using same low-order elements, and even close to the accuracy of the finite element using high-order elements, which greatly improved the efficiency of computing and has abroad application in vehicle mid-frequency NVH analysis.
The work of this paper is supported by the State to the construction of the high level of Graduate Students, National Dr. Young Scholar Award, the National Natural Science Foundation (11202074) and program for Changjiang Scholar and Innovative Research Team in University (5311050050037).
引文
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