The undamped, finite amplitude horizontal motion of a load supported symmetrically between identical incompressible, isotropic hyperelastic springs, each subjected to an initial finite uniaxial static stretch, is formulated in general terms. The small amplitude motion of the load about the deformed static state is discussed; and the periodicity of the arbitrary finite amplitude motion is established for all such elastic materials for which certain conditions on the engineering stress and the strain energy function hold. The exact solution for the finite vibration of the load is then derived for the classical neo-Hookean model. The vibrational period is obtained in terms of the complete Heuman lambda-function whose properties are well-known. Dependence of the period and hence the frequency on the physical parameters of the system is investigated and the results are displayed graphically.

中文翻译：

---

在各向同性超弹性弹簧之间对称支撑的载荷的有限振幅水平运动。

在相同的不可压缩、各向同性的超弹性弹簧之间对称支撑的载荷的无阻尼、有限振幅水平运动，每个弹簧都受到初始有限单轴静态拉伸，用一般术语表示。讨论了载荷在变形静止状态下的小幅运动；并且对于工程应力和应变能函数的某些条件成立的所有此类弹性材料，都建立了任意有限振幅运动的周期性。然后为经典的新胡克模型推导出载荷有限振动的精确解。振动周期是根据完整的 Heuman λ 函数获得的，其特性是众所周知的。