The finite amplitude radial motion of thick walled hyperelastic tubes has been extensively studied since the work of Knowles in the context of material incompressibility. This allows for explicit integration of the balance equation for linear momentum in the radial direction. We use this procedure to examine the effect of layering upon the oscillatory response of such tubes. For a suite of materials characterized by different hyperelastic constitutive laws and different material densities, we consider the parametric effect of property mismatch, relative layer thickness, and layer ordering on the qualitative shape of closed orbits in a phase space of radial displacement vs. radial velocity. Even the simple case of a two-layer system shows how changing a single parameter can give significant qualitative variation in orbital shape (e.g., eccentricity, crowding of maximum velocity locations toward minimum displacement locations, etc.) which in turn alters the orbital period (oscillation frequency). Changes in more than one parameter can either exacerbate or reduce such effects, in the latter case by for example a balancing of shear wave speeds. Equivalent results are obtained by a somewhat more direct energy treatment, either using Lagrangian dynamics or Hamilton’s principle, both of which bypass the notion of stress.

自诺尔斯在材料不可压缩性的背景下开展工作以来，厚壁超弹性管的有限振幅径向运动得到了广泛研究。这允许在径向方向上显式积分平衡方程的线性动量。我们使用此程序来检查分层对此类管的振荡响应的影响。对于一组具有不同超弹性本构定律和不同材料密度的材料，我们考虑了性质不匹配、相对层厚度和层排序对径向位移与径向速度相空间中闭合轨道定性形状的参数影响. 即使是双层系统的简单情况也显示了如何改变单个参数可以使轨道形状发生显着的定性变化（例如，偏心率，最大速度位置向最小位移位置的拥挤等），这反过来又改变了轨道周期（振荡频率）。多个参数的变化可以加剧或减少这种影响，在后一种情况下，例如通过剪切波速度的平衡。通过使用拉格朗日动力学或哈密顿原理的更直接的能量处理获得了相同的结果，两者都绕过了应力的概念。