In order to improve the spherical thin shells’ vibrations analysis, we introduce a new analytical method. In this method, we take into consideration the terms of the inertial couples in the stress couples’ differential equations of motion. These inertial couples are omitted in the theories provided by Naghdi–Kalnins and Kunieda. The results show that the current method can solve the axisymmetric vibrations’ equations of elastic thin spherical shells. In this paper, we focus on verifying the current method, particularly for free vibrations with free edge and clamped edge boundary conditions. To check the validity and accuracy of the current analytical method, the natural frequencies determined by this method are compared with those available in the literature and those obtained by a finite element calculation.

中文翻译：

---

球形薄壳轴对称振动的一种新的解析方法

为了改善球形薄壳的振动分析，我们引入了一种新的解析方法。在这种方法中，我们考虑了应力偶运动微分方程中的惯性偶项。这些惯性耦合在Naghdi-Kalnins和Kunieda提供的理论中被省略。结果表明，目前的方法可以求解弹性薄球壳的轴对称振动方程。在本文中，我们着重于验证当前的方法，特别是对于具有自由边缘和夹紧边缘边界条件的自由振动。为了检查当前分析方法的有效性和准确性，将通过这种方法确定的固有频率与文献中提供的固有频率以及通过有限元计算获得的固有频率进行比较。