We study the influence of residual stress on the static and dynamic characteristics of a spherical structure. We consider a shrink-fitted compound sphere, where residual stress is developed due to the interference between outer and inner spherical layers. We calculate this residual stress and model the residually stressed material with suitable hyperelastic strain energy satisfying Initial Stress Reference Independence (ISRI). Under the action of inhomogeneous residual stress, the compound sphere behaves as an anisotropic, functionally graded composite sphere, which is reflected by the model. We apply this model to obtain stress distributions and inflation characteristics of the compound sphere. Our results demonstrate the hypothesis that residual stress moderates the stress concentration and reduces the stress gradient in biological/engineering structures. We obtain critical stretch and pressure for spherically symmetric deformations. An increase in interference/residual stress increases the critical stretch/pressure and improves the structural stability. We then apply an analytical approach to calculate the natural frequency of the compound sphere for small amplitude radial vibration. We observe that an increase in residual stress increases the natural frequency and widens the range of stable free vibration. We numerically investigate the free and forced vibration of the compound sphere. Forced vibration amplitude reduces as interference/residual stress increases, which is reflected in the frequency-amplitude plots. The frequency response shows a small hardening non-linearity. We investigate the subharmonic and superharmonic responses for small and large amplitude vibration.

我们研究残余应力对球形结构的静态和动态特性的影响。我们考虑收缩配合的复合球体，其中由于外球层和内球层之间的干涉而产生残余应力。我们计算该残余应力并使用满足初始应力参考独立性 (ISRI) 的合适超弹性应变能对残余应力材料进行建模。在非均匀残余应力的作用下，复合球体表现为各向异性、功能梯度的复合球体，模型反映了这一点。我们应用这个模型来获得复合球体的应力分布和膨胀特性。我们的结果证明了残余应力缓和应力集中并降低生物/工程结构中的应力梯度的假设。我们获得了球对称变形的临界拉伸和压力。干涉/残余应力的增加会增加临界拉伸/压力并提高结构稳定性。然后，我们应用一种分析方法来计算小振幅径向振动的复合球体的固有频率。我们观察到残余应力的增加会增加固有频率并扩大稳定自由振动的范围。我们数值研究了复合球体的自由振动和受迫振动。受迫振动幅度随着干扰/残余应力的增加而减小，这反映在频率-幅度图中。频率响应显示出小的硬化非线性。我们研究了小振幅和大振幅振动的次谐波和超谐波响应。