Although solving the dynamic response of layered media has always been a major concern in the engineering field, the problem of interlayer contact of layered media has seldom been addressed in the related studies. Thus, this paper proposes an algorithm to analyze the dynamic displacement and stress responses of two-dimensional layered media with imperfect interfaces between layers at an arbitrary point under time-harmonic loads. The Fourier transform was used to convert the dynamic equation of the generalized plane strain problem from the frequency-spatial domain to the frequency-wavenumber domain. In addition, combined with the introduction of dual variables, an integration algorithm with high precision was employed to solve the state equation. Based on the displacement response in the frequency-wavenumber domain, the dynamic displacement and stress responses at an arbitrary point were obtained using the inverse Fourier transform. This algorithm not only considers the transverse isotropic properties of layered media but also considers the contact problem at the interface between the adjacent layers of the layered media with different properties. In addition, the harmonic load can be applied to both the surface and inside of the medium. The accuracy of the proposed algorithm was verified by comparing the calculated data with the numerical results, and the influence of the imperfect interface parameters on the dynamic response of layered media was analyzed in detail. Finally, the mechanism of the impact of the imperfect interface between the layers on the dynamic displacement and stress responses of layered media was examined.

尽管解决层状介质的动态响应一直是工程领域的主要关注点，但相关研究中很少涉及层状介质的层间接触问题。因此，本文提出了一种算法来分析时谐载荷下任意点的层间界面不完善的二维层状介质的动态位移和应力响应。傅里叶变换用于将广义平面应变问题的动力学方程从频空域转换到频波数域。此外，结合对偶变量的引入，采用高精度积分算法求解状态方程。基于频波数域中的位移响应，使用逆傅立叶变换获得任意点的动态位移和应力响应。该算法不仅考虑了层状介质的横向各向同性特性，而且还考虑了不同性质的层状介质相邻层间界面处的接触问题。此外，谐波载荷可以施加到介质的表面和内部。通过计算数据与数值结果的对比验证了所提算法的准确性，并详细分析了不完善的界面参数对层状介质动力响应的影响。最后，研究了层间不完善的界面对层状介质的动态位移和应力响应的影响机制。