Free oscillations of porous multi-graded graphene oxide nanocomposites coupled hemispherical-cylindrical shell-configuration structures under various edge constraints

Abstract

Quantitative investigations of the vibrational characteristics coupled hemispherical-cylindrical shells (CHSCSs) formed of three types, including of porous, nanocomposite, and porous nanocomposite, under various edge conditions are carried out here: (1) a matrix strengthened by graded graphene oxide powder (GOP), (2) a matrix with the effects of the porosity, and (3) a matrix strengthened by multi-graded GOP with the porosity characteristic. To modify the vibrational characteristics of the nanocomposite, nine different functionally graded models are evaluated for GOP distribution within the matrix and CHSCS thickness. The Halpin-Tsai homogenization formula is used to compute the GOP nanocomposite (GOPN) material's mechanical characteristics. Addedly, a functionally graded type of the effect of the porosity is used. The CHSCS equations may be derived from Donnell's theory as well as from the first shear deformation theory (FSDT). The governing equations of the CHSCSs are determined using variation calculation, named Hamilton's principle. After that, this equation system is built using the generalized differential quadrature method (GDQM). The frequencies used as benchmarks are compared to those produced here to test the system. Remarkably, the lowest frequencies of the CHSCS made of pure matrix and multi functionally graded GOPN were decreased for all BCs by extending the value of the porosity factor. In addition, by increasing the value of the porosity factor for all BCs, the porous FGO-GOPN CHSCS had the greatest variation related to decreasing the minimum frequencies.