Computing Theory And Methods For Vehicle Mid-frequency Vibration And Noise With High Efficiency And Precision

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).