Free vibrations of all assemblies related to coupled hyperboloidal–cylindrical shells

Abstract

For the first time, Natural Frequencies (NFs) associated with three groups of the coupling of a hyperboloidal (H) shell with a cylindrical (CY) shell, entitled Coupled Hyperboloidal–Cylindrical Shells (CHCSs), are discovered in this article. Correspondingly, General Three-Dimension Shell Theory (GTDST) is combined with the First-order Shear Deformation Theory (FSDT) to obtain the core relationships associated with the CHCSs. Followingly, the Governing Differential Motion Equations (GDMEs) referenced to the CHCSs are determined by employing Hamilton’s principle. Next, a well-arranged procedure branded the Generalized Differential Quadrature Method (GDQM) is considered to discretize the GDMEs, Boundary Equations (BEs), and Coupling Equations (CEs) associated with the CHCSs. Later, the NFs corresponding to the CHCSs are found by implementing the eigenvalue determination related to the discretized GDMEs. Because there is no examination regarding the NFs associated with these types of CHCSs in the literature, the outputs regarded in the present procedure are compared with the results related to the FEM-based process. It should be mentioned that the maximum error obtained is less than 0.4%. Based on this, the numerical outputs related to this examination can be employed as a benchmark for future investigations. Terminally, to consider the effect of all geometrical measures on the NFs corresponding to the CHCSs, several examples are developed.