P波对界面部分脱胶的刚性圆柱夹杂物的散射

本文求解了弹性Ｐ波对界面部分脱胶的可动刚性圆柱夹杂物的散射问题。将脱胶区看作表面不相接触的弧形界面裂纹，借助波函数展开法并利用边界条件将问题转化为一组对偶级数方程。然后通过引入裂纹面的位错密度函数，将其化为一组具有Ｈｉｌｂｅｒｔ核的第二类奇异积分方程，并进一步化为Ｃａｕｃｈｙ型奇异积分方程组，数值求解方程组可获得动应力强度因子，夹杂物刚体振动位移和散射截面等重要参量。结果显示该类结构在较低的频率上发生共振，此低频共振特性与脱胶区大小，入射波方向、材料组合等多种参数有关。与已有方法相比，本文的方法更具一般性，适用于任意材料组合。

P-wave Scattering from a Rigid Gylindrical Inclusion Partially Debonded Along the Interface

The problem of P-wave scattering from a movable rigid cylindrical inclusion partially debonded along the interface is solved in this paper. The debonding region is modeled as an interface crack withnon-contacting faces. Using the wave function expansion method and considering the mixed boundaryconditions, we obtain a set of simultaneous dual series equations. Then, by introducing the dislocationdensity functions as unknowns, these dual series equations are transformed to a set of singular integralequations of the second type with Hilbert kernels, which can be further converted to a set of Cauchysingular integral equations of the second type. The numerical results for dynamic stress intensity factors, rigid body translations of the inclusion and scattering cross sections are obtained. The resultsshow that a resonance occurs at a low frequency. This low frequency resonance is closely related tomany factors such as the debonding size, the incident wave direction, material combinations, etc.Compared with other method, the approach presented in this paper is valid for any material combinations including the case where the stresses have oscillatory singular behavior.