Multifunctional trace of various reinforcements on vibrations of three-phase nanocomposite combined hemispherical-cylindrical shells

Abstract The present study is devoted to investigating the vibrations of combined hemispherical-cylindrical shells (CHCSs) made of three-phase nanocomposite materials. The material includes a polymer matrix , namely polystyrene , reinforced with macro-scale carbon fibers and randomly orientated nano-reinforcements, namely carbon nanotube (CNT) and graphene nanoplatelet (GNP). To evaluate the effective material parameters of CNT and GNP, and obtain the equivalent mechanical properties of the crossbreed matrix (CM), the Mori-Tanaka-Eshelby approach is employed as well. The agglomeration effect of nano-reinforcements, which are dispersed in the matrix, is considered by obtaining the ratio of clusters to CM volume fraction and clusters to nano-reinforcements volume fraction. On the other hand, a renowned elasticity-based approach entitled Bridging method is utilized to homogenize the CM and macro-scale carbon fibers. Furthermore, the governing relations of the nanocomposite CHCS are based on Donnell’s shell scheme and first-order shear deformation theory (FSDT). In addition, the CHCS eigenvalue equations are developed using Hamilton’s principles and then numerically treated using generalized differential quadrature (GDQ). It should be added that combining conditions are considered for coupling the differential equations of two parts of CHCSs at the intersection of cylinder and hemisphere. Finally, the proposed formulations are validated by comparing the achieved results with reference solutions and the outputs of a commercial FEM software.