This article is formed to extract the frequencies with free-damped vibration characteristics of the tangential waves related to the Functionally Graded (FG) sandwich Merged Hemispherical-Cylindrical Shells (MHCS) under elastic springs. The wall of the MHCS contains three layers of embodied Functionally Graded Material (FGM). The material characteristics of the structure change functionally along the thickness of each layer. Equivalent Single Layer (ESL) and Rule of Mixture (RM) are applied to determine the mechanical features of the materials. In addition, eight sandwich types are examined here. Moreover, both merging and support conditions are assumed to be flexible. Artificial transitional and rotational springs are modeled to apply the effect of a semi-rigid merging between hemispherical and cylindrical parts and the support’s flexibility. Further, Donnell\\\'s hypothesis and Hamilton\\\'s scheme are utilized to acquire the kinetic differential equations related to the MCHS. A recognized semi-analytical method, labeled the Generalized Differential Quadrature Method (GDQM), is being implemented to discretize the kinetic equations. In addition, the tangential wave frequencies are determined by solving the eigenvalue problem. The available results in the submitted framework are compared with the outputs of the FE-based software to validate the proposed procedure. Several innovative parametric studies will be implemented to illustrate the impacts of different general boundary conditions, semi-rigid connections, and material features on the vibrational behavior of MHCS.

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