币形裂纹散射声场计算及特征分析
文献类型：学位论文
| 作者 | 邓晖 |
| 学位类别 | 博士 |
| 答辩日期 | 2001 |
| 授予单位 | 中国科学院声学研究所 |
| 授予地点 | 中国科学院声学研究所 |
| 关键词 | 币形裂纹 散射 边界元 扁椭球旋转坐标系 奇点特性非唯一性问题 |
| 其他题名 | Characteristics of Scattering Field by Penny-Shaped Crack |
| 中文摘要 | 该文分别采用扁旋转椭球坐标系下的分离变量法以及边界元方法对币形裂纹散射声场进行了计算,并在此基础上研究了散射声场的一些特征.研究工作主要完成了:1.根据微分方程的奇点特性,分析构成了币形裂纹散射声场的解析解,采用连续分式法确定特征值与解级数系数.2.边界元计算中采用常规弹性波积分方程对边界面外法向求导得到的积分方程描述裂纹的散射远场,克服了裂纹厚度趋于零造成的积分方程的退化.在对含奇点的单元积分时,首先采用幂级数展开积分核中的指数项,降低积分核的奇异性阶数,处理后的积分核中的超奇异积分项采用级数展开方法,取非奇异与低阶奇异项作积分.低阶奇异积分的奇异性通过全域与局域坐标变换消除.数值实现中不连续元的采用既保证了节点满足裂纹散射的边界积分方程,而且使超奇异积分项的处理可行.由于采用了求导后的积分方程形式,避免了非唯一性问题(虚特征频率)的出现. |
| 英文摘要 | Scattering field by penny-shaped crack is calculated by the separation of variable method in oblate spheroidal coordinate system and BEM separately. On the basis of the computation results, the directivity and characteristics of the scattering far field on different conditions are discussed and compared with each other. Following Main Problems are solved: Analytical solution of scattering field by penny-shaped crack is determined by the properties of singularity. The eigenvalues and the coefficients of these solution series are calculated by power series expansion method and continued fraction method. Derived along the normalized direction of the crack surface, the standard boundary integral equation for elastodynamics become available to describe the three-dimensional scattering field by crack. To avoid the singularity induced by the acute edge of the crack, the discontinuous elements are chosen. For the integration on the singular element, the singularity of integrated kernels is reduced to the lower order of (l/r~3 ) by expanding the exponential term in series form. Then the result hypersingular item in the integrated kernel is treated further. Each item in hypersingular kernel is expanded as the series, the regular item and the weak singular item are integrated. The singularity of the weak singular item is reduced by the coordinate transformation. Every collocation points are selected as the origin of the local polar coordinate system. Besides, The nonuniqueness difficulty at certain characteristic frequencies is also circumvented by the application of normal-derivative integral equation. 3. Based on the computation results, following conclusions are drawn: On condition of normal incidence, for different values of ka, the directivity of scattering far field by penny-shaped crack carries small changes in shape. But there are obvious differences in amplitude. Strong scattering concentrates around the z-axis. When the value of ka increases, the directivity becomes keener and the scattering amplitude larger. On condition of normal incidence, the variation of the amplitude of scattering field against ka expresses frequency property of scattering field. The numerical computation results show that, when ka increases, the amplitude of scattering field increases as a whole. Thus it can be concluded that the scattering field of higher frequency components is stronger than that of lower frequency components. But at some certain frequency values, the amplitude fluctuates irregularly and violently. The frequency dependence of amplitude is various on different directions in a complicated manner. For oblique incidence, when the incident angle begins to increase from zero degree, within a certain variance range, there is no obvious change in directivity of scattering field, i.e., strong field peak keeps around the z-axis. Until the incident angle reaches a certain value (this angle value is referred to as critical in angle), the strong scattering peak moves to the reflection direction of the incidence (the same azimuth angle to z-axis). When incident angle approaches to grazing incidence angle, there exists another critical angle (the second). Once the incident angle exceeds this angle, the scattering peak begins to point to x-axis and keep to it. The value of ka has influence on the two critical incident angles. But no intensive influence is found. Further, when ka is small, the variance of scattering field against the direction of cp is little. This variance is also affected by incident angle. But it is not so much more affected by incident angle than by ka. (4)For quite a few incident angles, strong scattering peak not only occurs at the reflection direction of the incidence, but also around the corresponding axis. The peak around the axis is called subordinate peak. Under several conditions, the strength of scattering around the axis even exceeds that at the reflection direction. The subordinate peak depends on both the incident angles and ka. When ka is small, it occurs more frequently and its amplitude is larger. (5)For arbitrary incidence, when the incident angle begins to increase, the maximal intensity of scattering field decreases rapidly and then approaches to a constant. The larger the ka is, the steeper the descent is. |
| 语种 | 中文 |
| 公开日期 | 2011-05-07 |
| 页码 | 62 |
| 源URL | [http://159.226.59.140/handle/311008/808]  |
| 专题 | 声学研究所_声学所博硕士学位论文_1981-2009博硕士学位论文 |
| 推荐引用方式 GB/T 7714 | 邓晖. 币形裂纹散射声场计算及特征分析[D]. 中国科学院声学研究所. 中国科学院声学研究所. 2001. |
入库方式： OAI收割
来源：声学研究所
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