A comprehensive shell approach for vibration of porous nano-enriched polymer composite coupled spheroidal-cylindrical shells

•Employing an efficient semi-analytical strategy, denominated GDQ, for detaching governing differential equations.•Utilizing a FSDH along with general shell formulation to achieve the fundamental structure relationships.•Obtaining the vibrational behavior of shell structure with complex geometry, namely coupled spheroidal-cylindrical.•Strengthening the composite polymer matrix by GNP nano-enrichment.•Considering the porosity effect on the vibrational performance using different distribution patterns. The following article is assigned to evaluate frequency responses associated with porous nanocomposite Coupled Spheroidal-Cylindrical Shell (CSCS) supplemented by Graphene Nano Platelet (GNP) nano-enrichment. In contemplation of achieving effective mechanical features affiliated with porous nanocomposite which is strengthened by GNP, Halpin-Tsai and rule of mixture homogenization techniques are employed. Moreover, three forms associated with porosity models are applied to illustrate the impact related to the porosity on the GNP nanocomposite material. In addition, general formulation and First Shear Deformation Hypothesis (FSDH) are implemented to discover fundamental relationships and affiliated with the CSCS. Moreover, to find governing motion equations related to the CSCS structure, Hamilton’s technique is involved. Next, a well-organized strategy named Generalized Differential Quadrature (GDQ) procedure is joined to the list to separate the motion equations. After that, the eigenvalue solution is hired to extract the frequency responses correlated with the GNP porous nanocomposite CSCS. Furthermore, conducive to validate the suggested method, the outputs related to the submitted formulation are compared with the responses affiliated with FEM commercial software. At the termination, several new examples are solved to evaluate the trace of the diverse geometry and material measures associated with the GNP porous nanocomposite CSCS on the frequency answers.