薄壁结构声固耦合问题的高精度边界元法研究

发布时间：2018-03-20 05:08

本文选题：边界元法　切入点：Burton-Miller边界积分方程　出处：《清华大学》2015年博士论文　论文类型：学位论文

【摘要】：航天器在发射阶段除经受运载火箭向上传递的机械振动之外,还有排气噪声和气动噪声经整流罩传递到航天器表面。因此,薄壁结构的声固耦合问题是航天器力学环境预示的重要组成部分,对于指导航天器设计有重要作用。噪声激励的频率范围可达10~10000Hz,中高频段呈现明显的随机特性,只能采用统计能量分析等方法,而低频段主要呈现确定性的耦合振动,边界元法是一种可供选择的分析方法,相关研究也有重要的理论意义。本文建立了一套求解薄壁结构声固耦合问题的高精度边界元法的框架,在以下四个方面取得了创新成果。第一,提出了声场问题的一种新的高精度边界元法。这种新方法基于声场的Burton-Miller边界积分方程,采用保持边界原始几何形状的声压连续单元,在初始设定比较合理网格的基础上,充分保证核函数与形函数乘积在单元上积分的精度,求解得到初始解,同时用相邻单元间声压梯度的相对间断值作为离散误差指示来显示解的精度,并指导网格细分重新计算,再通过比较两次计算结果来判断收敛情况,决定是否还要进一步细分网格,直至得到满意的收敛解。文中以球形边界为例,构造了四类球面参数单元,用刚球散射声场问题对误差指示进行了验证,并用它求解了较复杂的多球散射问题。第二,发展了球面单元上弱奇异积分和超奇异积分的计算方法。推导了球面单元上各种奇异积分的最终格式。用Guiggiani方法求解了球面单元的超奇异积分,高精度的计算结果表明了超奇异积分计算的准确性。并将高效伟提出的径向积分方法用于求解声学问题中的超奇异积分计算,与Guiggiani方法进行了对比。第三,为建立三维薄壁结构弹性动力学频域分析的高精度边界元法,发展了保证核函数与形函数乘积在单元上积分精度的高效方法,其中包括:推导了自由项的最终格式,实现了自由项的直接计算;实现了球面单元、8节点等参单元上Cauchy主值积分的直接计算。第四,提出了将声场频域分析与三维薄壁结构弹性动力学频域分析直接耦合的声固耦合问题的高精度边界元法计算方案,为求解声固耦合问题提供了新思路。耦合后的方程是全边界元方程,因此边界元方法中的快速算法将可方便地引入,为高性能边界元法(即引入快速算法的高精度边界元法)的建立提供了基础。
[Abstract]:In addition to the mechanical vibration transmitted upward by the launch vehicle during the launch phase, the spacecraft also has exhaust noise and aerodynamic noise transmitted to the surface of the spacecraft through the fairing. The acousto-solid coupling problem of thin-walled structures is an important part of spacecraft mechanical environment prediction, and plays an important role in guiding spacecraft design. The frequency range of noise excitation can reach 10 ~ 10000Hz. The method of statistical energy analysis can only be used, while the low frequency band mainly presents deterministic coupled vibration. The boundary element method is an alternative analysis method. In this paper, a set of high-precision boundary element method for solving acousto-solid coupling problem of thin-walled structures is established, and some innovative results are obtained in the following four aspects. A new high-precision boundary element method for acoustic field problems is proposed, which is based on the Burton-Miller boundary integral equation of sound field and adopts the sound pressure continuous element with preserving the original geometry shape of the sound field. The accuracy of the product of kernel function and shape function is fully guaranteed on the element, and the initial solution is obtained. The relative discontinuous value of sound pressure gradient between adjacent elements is used as the indication of discrete error to show the accuracy of the solution, and the mesh subdivision recalculation is guided. The convergence is judged by comparing the results of two calculations, and it is decided whether to subdivide the mesh further until a satisfactory convergence solution is obtained. In this paper, four kinds of spherical parameter elements are constructed, taking the spherical boundary as an example. The error indication is verified by the sound field problem of rigid sphere scattering, and the more complex multi-sphere scattering problem is solved. In this paper, the calculation methods of weak singular integrals and hypersingular integrals on spherical elements are developed. The final forms of various singular integrals on spherical elements are derived. The hypersingular integrals of spherical elements are solved by Guiggiani method. The high precision calculation results show the accuracy of the hypersingular integral calculation. The radial integral method proposed by Hexiwei is compared with the Guiggiani method in solving the acoustic problem. In order to establish a high-precision boundary element method for the frequency-domain analysis of three-dimensional thin-walled structures in elastic dynamics, an efficient method to ensure the integration accuracy of the product of kernel function and shape function on the element is developed, which includes: the final format of the free term is derived. Direct calculation of free term and direct calculation of Cauchy principal integral on 8 node isoparametric element of spherical element are realized. 4th, A high-precision boundary element method is proposed to calculate the acousto-solid coupling problem in which the acoustic field frequency domain analysis is directly coupled with the three-dimensional thin-walled structure elastic dynamics frequency domain analysis. The coupled equation is the whole boundary element equation, so the fast algorithm in the boundary element method can be introduced conveniently. It provides the foundation for the establishment of high performance boundary element method (i.e. the high precision boundary element method with fast algorithm).
【学位授予单位】：清华大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：V414.4

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