Small superimposed radial oscillations for a class of damaged limited elastic, incompressible, isotropic and homogeneous thick-walled circular cylindrical tube are examined. Both the damage function and the considered limited elastic class depend only on the first invariant \( I_{1} \) of the left Cauchy–Green deformation tensor. The present work puts some light in the context of the surgical procedure of angioplasty, used especially to treat cardiovascular diseases. Our simplified isotropic assumption allows for a much faster and analytical computation of comparably accurate results. The examples of three limited elastic material models are presented, namely the Arruda–Boyce, Gent, and Demiray. The radial oscillations are further investigated for a damaged limited elastic thin membrane, and the examples above are explored. Universal relations are found for the three material membranes. The obtained results are matched with the clinical data of the existing literature. It appears that the pressure ratio for the virgin and damaged arterial tissue is higher before angioplasty and vice versa. A similar trend for the frequency ratio also follows.

研究了一类受损的有限弹性，不可压缩，各向同性和均质厚壁圆柱管的小叠加径向振动。损伤函数和所考虑的有限弹性类别都仅取决于第一个不变\（I_ {1} \）左柯西-格林变形张量。目前的工作在血管成形术的外科手术方面尤其是心血管疾病的治疗上取得了一些进展。我们简化的各向同性假设可以更快，更解析地计算出相对准确的结果。给出了三个有限弹性材料模型的示例，即Arruda-Boyce，Gent和Demiray。对于损坏的有限弹性薄膜，进一步研究了径向振动，并探讨了上面的示例。发现了三种材料膜的通用关系。获得的结果与现有文献的临床数据相匹配。似乎在血管成形术之前，原始和受损的动脉组织的压力比较高，反之亦然。