为了分析脱层界面的接触对含脱层复合材料层合板的影响，采用考虑了脱层界面接触效应的四分区精确模型，对含单一贯穿脱层层合板的自由振动进行研究，通过对精确模型的结果进行分析，采用基于刚度等效的等代化模型，将脱层区等效成一个尺寸相同、铺设方式相同，但刚度折减的无脱层完善子板。然后进行算例分析，对等代化模型、精确模型和有限元模型给出的固有频率进行比较，证明了等代化模型的正确性。在此基础上，运用等代化理论和有限元模型对含多个贯穿宽度方向脱层的复合材料层合板的自由振动问题进行研究，通过参数分析发现：对于含有多个水平脱层的层合板，脱层总长度越大，层合板的固有频率越小；对于含有多个竖直向脱层复合材料层合板，脱层沿厚度均匀分布层合板的固有频率最小；一般来说，脱层数目越多，层合板的固有频率越小，但层合板的固有频率同时受脱层间相对深度的影响。研究结果表明,基于等代化理论给出的多脱层层合板的固有频率与ABAQUS有限元解非常吻合，证明了等代化理论的合理性，可为工程领域正确评估含损伤层合结构的剩余承载能力提供技术参考。

In order to investigate the influence of the contact mechanism on the composite laminates with multiple delaminations, free vibration of composite laminates containing a through-the-width delamination was analyzed with a four-region exact model in which the contact mechanism at the interfaces of the delamination is considered. By examining the solutions from the exact model and adopting equivalent model based on equivalent stiffness, the delaminated region was translated into a perfect, delamination free laminate which has the same geometric size and the stacking sequence but a reduced stiffness. Numerical calculations were carried out to justify the accuracy and effectiveness of the equivalent model by comparing the natural frequencies given by the equivalent model with those given by the exact model and the finite element model. On this basis, the free vibration of composite laminates with multiple through-the-widths delamination was analyzed using the established equivalent model and the finite element model. It is found from the analysis that for laminates with multiple horizontal delamination, the larger the total length of delamination is, the smaller the natural frequency is; for composite laminates with multiple vertical dela-mination, the natural frequency of laminates with uniform distribution of delamination along the thickness is the smallest. Generally, the natural frequency decrease with the increasing number of delamination, but the natural frequency is affected by the relative depth between layers simultaneously. The results show that the natural frequencies of the delaminated laminates from the equivalent model are in good agreement with the ABAQUS finite element solutions, and the correctness of the equivalent theory is verified. It provides strong technical support for the correct evaluation of the residual bearing capacity of the delaminated composite structures in engineering fields.