Free vibration analysis of FG-GOPRPC double cylindrical shells coupled structure surrounded by the non-uniform elastic foundation under arbitrary boundary conditions

In engineering, coupled structures often encounter complex supporting conditions, in which the foundation shows heterogeneous elastic characteristics. Considering the spatial variation of soil, this will change the conventional vibration behavior of the shell. Therefore, a unified modeling method is proposed for the first time to study the vibration characteristics of the bolted functionally graded graphene oxide platelet-reinforced porous composite (FG-GOPRPC) double cylindrical shell coupled structure surrounded by a non-uniform Winkler elastic foundation under arbitrary boundary conditions. To support this, the actual soil environment is simulated by constructing the non-uniform Winkler elastic foundation. In addition, the discontinuous arc connection mode is created by improving the whole circumference continuous artificial spring distribution method to simulate the connection situation in actual bolts, and the whole circumference constrained spring distribution method is used to simulate the arbitrary boundary conditions. Addedly, the first-order shear deformation theory (FSDT) and Gegenbauer-Ritz method are combined to discover the dynamic equations of the structure. Ultimately, the natural frequency of the coupled structure is obtained, and the rationality of the analysis method in this paper is verified by the literature and finite element method (FEM). The effects of spring stiffness values, boundary conditions, size parameters, mass fraction, porosity types, GOP distribution patterns, and foundation parameters on the vibration characteristics of the structure are analyzed. For instance, the non-uniform Winkler elastic foundation can amplify the contribution of the translational spring and rotating spring in the axial direction to the natural frequency.