The fetal heart rate and uterine contractions monitoring, using the non-invasive technologies, are widely used. These techniques are the most appropriate because an invasive test can not be used daily to evaluate the well-being of the fetus during pregnancy and labor. This paper presents a description and a comparative study of the most non-invasive diagnostic technologies recording the vital signals of the fetal heart and those of the maternal heart and uterine contractions.

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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.

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