平面P波入射具有不完美界面圆形夹塞的动态响应特性  

Dynamic Response Characteristics of Circular Inclusion with Imperfect Interface under Plane P-wave Incident

作　　者：陶明[1] 姚靖 李夕兵[1] TAO Ming;YAO Jing;LI Xi-bing(School of Resources and Safety Engineering,Central South University,Changsha 410083,China)

机构地区：[1]中南大学资源与安全工程学院,长沙410083

出　　处：《爆破》2022年第3期25-32,63,共9页Blasting

基　　金：国家自然科学基金资助项目(12072376)。

摘　　要：夹塞与介质的交界面并非总是完美界面,即位移应力在边界上并非是连续且相等的,入射P波在不完美界面发生的动态响应与在完美界面的动态响应有所差别。为了研究平面P波在具有不完美界面夹塞上的动应力响应情况,引入弹簧模型作为不完美界面模型,该界面模型假定为厚度无穷小且无惯性的弹性粘结层。利用波函数展开法计算平面P波入射时不完美界面周边的动应力集中因子。分析了弹簧模型的重要参数弹簧刚度对动应力集中因子的影响。计算结果表明:弹簧刚度对低波数时的动态响应有明显影响,而随着波数的增大这种影响会逐渐减弱,同时在高波数时能观察到共振散射现象。采用常见的地震波子波—雷克子波作为瞬态扰动波形,基于稳态结果利用Fourier变换得到瞬态波入射时不同弹簧刚度条件下的瞬态响应。瞬态DSCF变化情况与稳态条件下相似,但是幅值有所增加。另外,雷克子波的主频与瞬态DSCF成负相关。The interface between the inclusion and the medium is not always perfect.That is,the displacement and stress are not continuous and equal on the boundary.The dynamic response of an incident P wave at an imperfect interface is different from the that of a perfect interface.A spring model is introduced as the imperfect interface model to calculate the dynamic response of the inclusion with an imperfect interface under the plane P wave incident.This interface model is assumed to be an elastic adhesive layer with an infinitesimal thickness and no inertia.Moreover,the wave function expansion method is used to calculate the dynamic stress concentration factor around the imperfect interface under the plane P wave incident and analyze the influence of spring stiffness,an important parameter of spring model,on the dynamic stress concentration factor.The results show that the spring stiffness has an obvious effect on the dynamic response with a low wave number,and this effect will gradually weaken with the increase of the wave number.At the same time,the resonance scattering phenomenon can be observed at a high wave number.The Ricker wavelet,a common seismic wavelet,is used as the transient disturbance waveform.Based on the steady-state results,the transient responses under different values of spring stiffness are obtained by Fourier transform.The distribution of the transient DSCF is similar to that under the steady-state conditions,but the amplitude has increased.In addition,the dominant frequency of the Ricker wavelet is negatively correlated with the transient DSCF.

关 键 词：平面P波 圆柱形夹塞 不完美界面 瞬态P波散射 动应力集中因子 

分 类 号：TD235.3[矿业工程—矿井建设]